M3 LESSON PLAN
LESSON
PLAN
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Subject : MATHEMATICS-VC&FT |
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Year : I B-Tech |
Semester : I |
Branch :ECE |
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Faculty : T
JYOTHI |
Reg : R19 |
Academic Year : 2020-21 |
COURSE OBJECTIVES:
In
this course the students can Perform calculations and algebraic
manipulations, particularly differentiation and integration, quickly and
accurately. StudentsUse the language of mathematics to communicate mathematical
ideas, using symbols and notations correctly, and presenting solutions in a
clear and organized way. Use concepts of calculus to the model real-world
problems. : Make connections between different mathematical concepts, such as
geometric, analytic and numerical interpretations of functions, derivatives and
integrals. : Develop ability to understand and create rigorous formal
mathematical arguments. Apply basic mathematical logic.
COURSE OUTCOMES:
|
1 |
Factual |
·
Interpret
the physical meaning of different
operators such as gradient, curl and divergence (L5) ·
Estimate the work done against a field, circulation and flux using vector
calculus (L5)
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|
2 |
Conceptual |
·
Apply the
Laplace transform for solving differential equations (L3).
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3 |
Procedural |
·
Find or
compute the Fourier series of periodic signals (L3)
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4 |
Applied |
·
Know and be able to apply integral expressions for the
forwards and inverse Fourier transform to
a range of non-periodic waveforms (L3) ·
Identify
solution methods for partial differential equations that model physical
processes (L3)
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TEXT BOOKS/ REFERENCE BOOKS:
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T/R |
BOOK
TITLE/AUTHORS/PUBLICATION |
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T |
B. S.
Grewal, Higher Engineering Mathematics, 43rd Edition, Khanna Publishers. |
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T |
B.
V. Ramana, Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill
Education. |
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R |
Erwin Kreyszig, Advanced Engineering Mathematics, 10th
Edition, Wiley-India. |
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R |
Dean. G. Duffy, Advanced
Engineering Mathematics with MATLAB, 3rd Edition, CRC Press. |
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R |
Peter O’ Neil, Advanced Engineering Mathematics, Cengage.
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R |
Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press. |
UNIT – 1: Vector calculus [Total Classes : 11] Activity:
|
1 |
Factual |
Compute
dot product, cross product, length of vectors. Estimate a derivative,
integral or quantity defined by a vector field, given the graph of a function
or vector field. |
|
2 |
Conceptual |
Can Compute partial
derivatives, derivatives of vector-valued functions, gradient functions. |
|
3 |
Procedural |
Optimize a function of two or more variables,
organizing work into main steps, carefully justifying determination of
critical points |
|
4 |
Applied |
Use concepts of calculus to
the model real-world problems. : Make connections between different
mathematical concepts, such as geometric, analytic and numerical
interpretations of functions, derivatives and integrals. |
Pre-Class : Videos, E-books, Web links etc…
In-Class : Explanation on concept, discussion, Poll, doubts clarification, Demo etc.. Post-Class : Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
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CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction to vector calculus |
To introduce Basic concepts of dot product and cross
product |
VEDIO LINK: https://www.slideshare.net/AshrafulTauhid/dot-cross-product-of-vectors
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
2. |
Vector Differentiation: Gradient |
To Understand the
concept of differentiation of vectors in scalar field. |
VEDIO LINK: https://www.youtube.com/watch?v=NomUbVmmyro
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Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
3. |
Directional
derivatives |
To Understand the
concept of derivatives in vector field |
Video Link : https://www.slideserve.com/rhian/directional-derivatives-and-the-gradient-vector
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
4. |
Divergence |
To Understand the concept
of |
Video Link : https://en.wikipedia.org/wiki/Divergence
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Discussion on pre-requisites (5 Min) PPT presentation |
. Discussion Forum on the topic in the group |
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Divergence
of fluid in vector field |
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(30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Review on the topic
Share material on the topic |
|
5. |
Curl:scalar
potential; |
To Understand the
concept of curl ,curl and irrotational |
Video Link : https://mathinsight.org/curl_idea
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group
Review on the topic |
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Share material on the topic |
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6. |
Line integral |
To Understand the concept of work done by force by curve
integral |
Video Link : https://mathinsight.org/line_integral_vector_field_introduction
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
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Exercises to solve |
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7. |
Surface integral |
To Understand the
concept of finding surface areas. |
Video Link : https://mathinsight.org/surface_integral_vector_field_introduction
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Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group
Review on the topic |
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Web Link :
https://nptel.ac.in/cours
es/122/104/122104017/ |
Share material on the topic |
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Exercises to solve |
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8. |
Volume integrals |
Able to find volumes of surfaces |
Video Link : https://www.youtube.com/watch?v=_GRF5WaPBFU
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group
Review on the topic
Share material on the topic
Exercises to solve |
|
9. |
Gauss divergence theorem |
To Understand the
concept of converting line to volume integrals |
Video Link : https://www.slideserve.com/bjorn/divergence-theorem
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group
Review on the topic
Share material on the topic
Quiz |
|
10. |
Greens theorem |
To Understand the concept of curve integration to surface in xy plane |
Video Link : https://www.youtube.com/watch?v=a_zdFvYXX_c
ppt link: https://www.slideshare.net/samiul11/application-of-gsg
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
11. |
Stokes theorem |
To Understand the concept of changing curve to surface
integration. |
Video Link : https://www.math24.net/stokes-theorem/
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group
Review on the topic
Share material on the topic
Quiz |
UNIT – 2 : Laplace Transforms [Total Classes :9] Activity:
|
1 |
Factual |
Solve an initial value problem
for an n th order ordinary differential equation using the Laplace transform. |
|
2 |
Conceptual |
. Analyze and
solve engineering problems using Laplace Series.Video
Lectures related to laplace transforms |
|
3 |
Procedural |
To understand the concept of transforms,and apply
its properties to solve the problems. |
|
4 |
Applied |
Problems Solving and Applications solving by practice
sessions and Assignments Quiz etc… |
Activity
/ Schedule of UNIT-2 :
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, Poll, doubts clarification, Demo etc.. Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction
on laplace transforms. |
To introduce The concept of transformation |
Video Link : https://tutorial.math.lamar.edu/classes/de/LaplaceIntro.aspx
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
2. |
Laplace
transforms of certain functions |
To apply
definition of LT on functions |
Video Link : https://www.youtube.com/watch?v=cHe_ya566bA
ppt: https://www.academia.edu/10952057/Laplace_Transformation
|
Revise previous class – (5 Mins)
Asking Questions on previous class randomly (5 Mins)
PPT presentation/
class (30 min)
Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
3. |
Shifting theorems |
To understand the concept of shifting theorems |
Video Link : https://www.youtube.com/watch?v=_CvlSs0T8ok
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation/class (30 min) Doubts clarification |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
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(10 min) |
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4. |
Transforms
of derivatives and integrals |
To understand the concept of finding LT of derivatives
and integrals |
Video Link : https://www.youtube.com/watch?v=lEwfeY_yxEA
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation/
class (30 min)
Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
5. |
Unit step
function |
To understand the concept of Unit step function |
Video Link : https://www.youtube.com/watch?v=JewW5ukzwlc
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Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation/class (30 min)
Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
6. |
Dirac
Delta function |
To understand the concept of Dirac Delta function |
Video Link :
https://www.youtube.com/watch?v=J-oyM1GyyDk
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Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
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7. |
Inverse
laplace transforms |
To understand how to apply inverse laplace transforms |
Video
Link : https://www.youtube.com/watch?v=Y8GXpS31CGI
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min)
Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
8. |
Convolution
theorem |
To understand the concept of Convolution
theorem |
Video Link : https://mathworld.wolfram.com/ConvolutionTheorem.html
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
9. |
Solving
ordinary differential equations using Laplace transforms |
To understand the concept of applying LTs to solvd ODE |
Video Link : https://www.youtube.com/watch?v=0jHn2I2y6Mw
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
UNIT – 3: Fourier series and Fourier Transforms [Total Classes: 12] Activity:
|
1 |
Factual |
Introduce the Fourier series and its
application to the solution of partial differential equations. |
|
2 |
Conceptual |
Find the solution of the wave, diffusion and Laplace equations using the Fourier series. |
|
3 |
Procedural |
Refer to
text book content of Fourier series and Fourier
Transforms in Understanding the concept with examples(simple to complex) |
|
4 |
Applied |
Problems Solving and Applications solving by practice
sessions and Assignments Quiz etc… |
Activity / Schedule of UNIT-3:
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Fourier Series: Introduction |
To introduce The concept of Fourier series |
Video Link : https://slideplayer.com/slide/4213412/
https://www.youtube.c om/watch?v=L7Yy0I MshbE
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
2. |
Periodic functions |
To
introduce The concept |
Video Link : |
Revise previous class – (5 mins) |
Discussion Forum on the topic in the |
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of Periodic functions |
https://en.wikipedia.org/wiki/Mean-periodic_function
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Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
group
Review on the topic
Share material on the topic |
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3. |
Fourier series of periodic function |
To introduce The concept of fourier series periodic
function
|
VIDEO
LINK: https://en.wikipedia.org/wiki/Mean-periodic_function
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins) |
Discussion Forum on the topic in the group
Review on the topic |
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PPT presentation & demo (30 min) Doubts clarification (10 min) |
Share material on the topic |
|
4. |
Dirichlet’s
conditions s |
To introduce the concept of Dirichlet’s conditions
|
Video
Link : https://www.youtube.com/watch?v=blS_OImUJ-c
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
5. |
Even
and odd functions |
To introduce the concept |
Video
Link :
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Revise previous class – (5 mins) |
Discussion Forum on the topic in the |
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of Even
and odd functions |
https://www.purplemath.com/modules/fcnnot3.htm
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Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
group
Review on the topic
Share material on the topic |
|
6. |
Change of interval |
To demonstrate Change
of interval |
Video Link : https://www.youtube.com/watch?v=2_i1fz38QSw
PDF: https://math.mit.edu/~gs/cse/websections/cse41.pdf
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
7. |
Half-range sine and cosine series |
To introduce the concept of Half-range sine and cosine series
|
Video Link : https://www.youtube.com/watch?v=Sq2FhCxcyI8
Ppt: https://www.slideshare.net/hardik6034off/half-range-sine-cosine-fourier-series
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
8. |
Fourier Transforms: Fourier integral theorem |
To introduce Fourier
Transforms |
Video Link : https://www.youtube.com/watch?v=4VlyGap4Tpg
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 |
Discussion Forum on the topic in the group Review
on the topic |
|
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Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Share material on the topic |
|
9. |
Fourier sine and cosine integrals |
To demonstrate Method
of Fourier sine and cosine integrals |
Video Link : https://www.youtube.com/watch?v=OWFm2sZ2Rxg
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
10. |
Sine
and cosine transforms |
To Introduce the concept of Sine and cosine transforms |
Video Link : https://www.youtube.com/watch?v=zkkqTpXMeVo
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
11. |
Properties |
To
explain the properties of Fourier Transforms |
Video
Link : https://www.youtube.com/watch?v=0USI-48ovJI
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
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12. |
Finite Fourier transforms.
|
To
explain the concept of Finite Fourier
transforms |
https://www.math.usm.edu/lambers/mat417/lecture18.pdf
|
Revising the concepts discussed so far
Any topic to Repeat
asked by students. |
Assignment-3
Quiz-3 |
UNIT 4PDE of first order [Total Classes: 10] Activity:
|
1 |
Factual |
To Analyse, synthesise, organise and
plan projects in the field of study. Reading Prerequisite concepts- partial
differentiation Videos Referring the content on the
Internet |
|
2 |
Conceptual |
Video Lectures On partial differentiation NPTEL Videos Links from the Internet Solved Examples from Internet |
|
3 |
Procedural |
Refer to text book content and Examples, Understanding
the partial differentiation with examples(simple to
complex) |
|
4 |
Applied |
Problems Solving and Applications
solving by practice sessions and Assignments Quiz etc… |
Activity
/ Schedule of UNIT-4 :
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, Poll, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Formation of partial differential equation by
eliminating arbitrary constants |
To introduce The concept of forming the partial differential
equation |
Vedio link: https://www.youtube.com/watch?v=3c71y8N9qj0
PPT: https://www.slideshare.net/sidpatel143/pde-41689592 NPTEL: https://www.slideshare.net/sidpatel143/pde-41689592
|
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
2. |
Formation of partial differential equation by
eliminating arbitrary functions |
To Introduce the concept of Taylors theorem for
functions of several variables |
Video Link : https://www.youtube.com/watch?v=33vJ1wz3rfU Ppt: https://nitkkr.ac.in/docs/11-%20Partial%20Differential%20Equations.pdf
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
3. |
Solutions of first order
linear (Lagrange) equation
|
To
Introduce the concept of Mc Lauren’s theorem |
Video Link : https://www.youtube.com/watch?v=Qpudxz275eo
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
4. |
Solutions of first order nonlinear (standard types) equations.
|
To Introduce the concept of Jacobian, functional
dependent and independent |
Video Link : https://en.wikipedia.org/wiki/Nonlinear_partial_differential_equation
|
Revise previous class – (5 mins)
Asking Questions on previous class randomely (5 Mins)
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
UNIT – 5: Second order PDE and Applications [Total Classes : 8] Activity:
|
1 |
Factual |
Create and
analyze mathematical models using higher order differential equations to
solve application problems such as harmonic oscillator and circuits.
|
|
2 |
Conceptual |
Student will
have a working knowledge of basic application problems described by second
order linear differential equations with constant coefficients. Video Lectures l Videos and NPTEL Videos Links from the Internet Solved Problems, Examples from
Internet |
|
3 |
Procedural |
Refer to text book
content and Examples, Understanding
the multiple integrals with examples(simple to complex) |
|
4 |
Applied |
Problems Solving and Applications
solving by practice sessions and Assignments Quiz etc… |
Activity / Schedule of UNIT- 5:
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, Poll, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Solutions of linear
partial differential equations with constant coefficients |
To introduce The concept of linear partial
differential equations with constant coefficients |
Video Link : http://www.fen.bilkent.edu.tr/~gurses/constantcoefficientpdes.pdf
|
Discussion on pre-requisites (10
Min)
PPT presentation/Clas
s/demo (35 Min)
Summary (5min)
Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
2. |
Solutions of linear
partial differential equations with constant coefficients RHS term
of the type eax + by |
To find the particular integral of pde RHS term of the type eax + by
|
Video Link : https://www.youtube.com/watch?v=7sJvNWsSqus
|
Discussion on pre-requisites (10
Min)
PPT presentation/Clas
s/demo (35 Min)
Summary (5min)
Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
3. |
Solutions of linear
partial differential equations with constant coefficients RHS term
of the type ,sin(ax + by), cos(ax
+ by), |
To find the particular integral of pde RHS term of the type sin(ax + by), cos(ax + by), |
Video Link : https://www.youtube.com/watch?v=7sJvNWsSqus
|
Discussion on pre-requisites (10
Min)
PPT presentation/Clas
s/demo (35 Min)
Summary (5min)
Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
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4. |
Solutions of linear
partial differential equations with constant coefficients RHS term
of the type xm yn |
To find the particular integral of pde RHS term of the type
xm yn
|
Vedio
link: https://www.slideshare.net/prathab1983/chapter-1-maths-3
|
Discussion on pre-requisites (10
Min)
PPT presentation/Clas
s/demo (35 Min)
Summary (5min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
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Doubts clari- fication (10 min) |
|
|
5. |
Applications of PDE: Method of separation of Variables |
To explain Applications of PDE: Method of separation of Variables http://www2.gcc.edu/dept/math/faculty/BancroftED/teaching/handouts/sep_of_var_examples.pdf |
Video Link : http://www2.gcc.edu/dept/math/faculty/BancroftED/teaching/handouts/sep_of_var_examples.pdf
|
Discussion on pre-requisites (10
Min)
PPT presentation/Clas
s/demo (35 Min)
Summary (5min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
|
|
|
|
Doubts clari- fication (10 min) |
|
|
6. |
Solution of One dimensional Wave equation |
To introduce
The concept of Evaluating Wave equation |
Video Link : https://www.youtube.com/watch?v=IAut5Y-Ns7g
https://www.youtube.com/watch?v=IAut5Y-Ns7g
|
Discussion on pre-requisites (10
Min)
PPT presentation/Clas
s/demo (35 Min)
Summary (5min)
Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
7. |
Solution of One
dimensional Heat equation |
To introduce
The concept of Evaluating Solution of One
dimensional Heat equation |
Video Link : https://www.youtube.com/watch?v=PbucCMGDuao
|
Discussion on pre-requisites (10
Min)
PPT presentation/Clas
s/demo (35 Min)
Summary (5min)
Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
|
8. |
Solution of two-dimensional Laplace equation.
|
To introduce The concept of Checking Solution of two-dimensional Laplace equation.
|
Video Link : https://www.youtube.com/watch?v=DNo0FmsGZKg
|
Discussion on pre-requisites (10
Min)
PPT presentation/Clas
s/demo (35 Min)
Summary (5min)
Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group
Review on the topic
Share material on the topic |
Prepared by Approved by
Faculty Signature HOD
(T JYOTHI)LESSON
PLAN
|
Subject : MATHEMATICS-VC&FT |
||
|
Year : I B-Tech |
Semester : I |
Branch :ECE |
|
Faculty : T
JYOTHI |
Reg : R19 |
Academic Year : 2020-21 |
COURSE OBJECTIVES:
In
this course the students can Perform calculations and algebraic
manipulations, particularly differentiation and integration, quickly and
accurately. StudentsUse the language of mathematics to communicate mathematical
ideas, using symbols and notations correctly, and presenting solutions in a
clear and organized way. Use concepts of calculus to the model real-world
problems. : Make connections between different mathematical concepts, such as
geometric, analytic and numerical interpretations of functions, derivatives and
integrals. : Develop ability to understand and create rigorous formal
mathematical arguments. Apply basic mathematical logic.
COURSE OUTCOMES:
|
1 |
Factual |
·
Interpret
the physical meaning of different
operators such as gradient, curl and divergence (L5) ·
Estimate the work done against a field, circulation and flux using vector
calculus (L5) |
|
2 |
Conceptual |
·
Apply the
Laplace transform for solving differential equations (L3). |
|
3 |
Procedural |
·
Find or
compute the Fourier series of periodic signals (L3) |
|
4 |
Applied |
·
Know and be able to apply integral expressions for the
forwards and inverse Fourier transform to
a range of non-periodic waveforms (L3) ·
Identify
solution methods for partial differential equations that model physical
processes (L3) |
TEXT BOOKS/ REFERENCE BOOKS:
|
T/R |
BOOK
TITLE/AUTHORS/PUBLICATION |
|
T |
B. S.
Grewal, Higher Engineering Mathematics, 43rd Edition, Khanna Publishers. |
|
T |
B.
V. Ramana, Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill
Education. |
|
R |
Erwin Kreyszig, Advanced Engineering Mathematics, 10th
Edition, Wiley-India. |
|
R |
Dean. G. Duffy, Advanced
Engineering Mathematics with MATLAB, 3rd Edition, CRC Press. |
|
R |
Peter O’ Neil, Advanced Engineering Mathematics, Cengage. |
|
R |
Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press. |
UNIT – 1: Vector calculus [Total Classes : 11] Activity:
|
1 |
Factual |
Compute
dot product, cross product, length of vectors. Estimate a derivative,
integral or quantity defined by a vector field, given the graph of a function
or vector field. |
|
2 |
Conceptual |
Can Compute partial
derivatives, derivatives of vector-valued functions, gradient functions. |
|
3 |
Procedural |
Optimize a function of two or more variables,
organizing work into main steps, carefully justifying determination of
critical points |
|
4 |
Applied |
Use concepts of calculus to
the model real-world problems. : Make connections between different
mathematical concepts, such as geometric, analytic and numerical
interpretations of functions, derivatives and integrals. |
Pre-Class : Videos, E-books, Web links etc…
In-Class : Explanation on concept, discussion, Poll, doubts clarification, Demo etc.. Post-Class : Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction to vector calculus |
To introduce Basic concepts of dot product and cross
product |
VEDIO LINK: https://www.slideshare.net/AshrafulTauhid/dot-cross-product-of-vectors |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Vector Differentiation: Gradient |
To Understand the
concept of differentiation of vectors in scalar field. |
VEDIO LINK: https://www.youtube.com/watch?v=NomUbVmmyro |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
3. |
Directional
derivatives |
To Understand the
concept of derivatives in vector field |
Video Link : https://www.slideserve.com/rhian/directional-derivatives-and-the-gradient-vector |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
4. |
Divergence |
To Understand the concept
of |
Video Link : https://en.wikipedia.org/wiki/Divergence |
Discussion on pre-requisites (5 Min) PPT presentation |
. Discussion Forum on the topic in the group |
|
|
|
Divergence
of fluid in vector field |
|
(30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Review on the topic Share material on the topic |
|
5. |
Curl:scalar
potential; |
To Understand the
concept of curl ,curl and irrotational |
Video Link : https://mathinsight.org/curl_idea |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic |
|
|
|
|
|
Share material on the topic |
|
|
6. |
Line integral |
To Understand the concept of work done by force by curve
integral |
Video Link : https://mathinsight.org/line_integral_vector_field_introduction |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
Exercises to solve |
|
|
7. |
Surface integral |
To Understand the
concept of finding surface areas. |
Video Link : https://mathinsight.org/surface_integral_vector_field_introduction |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic |
|
|
|
|
Web Link :
https://nptel.ac.in/cours
es/122/104/122104017/ |
Share material on the topic |
|
|
|
|
|
|
Exercises to solve |
|
8. |
Volume integrals |
Able to find volumes of surfaces |
Video Link : https://www.youtube.com/watch?v=_GRF5WaPBFU |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic Exercises to solve |
|
9. |
Gauss divergence theorem |
To Understand the
concept of converting line to volume integrals |
Video Link : https://www.slideserve.com/bjorn/divergence-theorem |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic Quiz |
|
10. |
Greens theorem |
To Understand the concept of curve integration to surface in xy plane |
Video Link : https://www.youtube.com/watch?v=a_zdFvYXX_c ppt link: https://www.slideshare.net/samiul11/application-of-gsg |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
11. |
Stokes theorem |
To Understand the concept of changing curve to surface
integration. |
Video Link : https://www.math24.net/stokes-theorem/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic Quiz |
UNIT – 2 : Laplace Transforms [Total Classes :9] Activity:
|
1 |
Factual |
Solve an initial value problem
for an n th order ordinary differential equation using the Laplace transform. |
|
2 |
Conceptual |
. Analyze and
solve engineering problems using Laplace Series.Video
Lectures related to laplace transforms |
|
3 |
Procedural |
To understand the concept of transforms,and apply
its properties to solve the problems. |
|
4 |
Applied |
Problems Solving and Applications solving by practice
sessions and Assignments Quiz etc… |
Activity
/ Schedule of UNIT-2 :
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, Poll, doubts clarification, Demo etc.. Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction
on laplace transforms. |
To introduce The concept of transformation |
Video Link : https://tutorial.math.lamar.edu/classes/de/LaplaceIntro.aspx |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Laplace
transforms of certain functions |
To apply
definition of LT on functions |
Video Link : https://www.youtube.com/watch?v=cHe_ya566bA ppt: https://www.academia.edu/10952057/Laplace_Transformation |
Revise previous class – (5 Mins) Asking Questions on previous class randomly (5 Mins) PPT presentation/
class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
3. |
Shifting theorems |
To understand the concept of shifting theorems |
Video Link : https://www.youtube.com/watch?v=_CvlSs0T8ok |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
(10 min) |
|
|
4. |
Transforms
of derivatives and integrals |
To understand the concept of finding LT of derivatives
and integrals |
Video Link : https://www.youtube.com/watch?v=lEwfeY_yxEA |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/
class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
5. |
Unit step
function |
To understand the concept of Unit step function |
Video Link : https://www.youtube.com/watch?v=JewW5ukzwlc |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
6. |
Dirac
Delta function |
To understand the concept of Dirac Delta function |
Video Link :
https://www.youtube.com/watch?v=J-oyM1GyyDk |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
|
|
|
7. |
Inverse
laplace transforms |
To understand how to apply inverse laplace transforms |
Video
Link : https://www.youtube.com/watch?v=Y8GXpS31CGI |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
8. |
Convolution
theorem |
To understand the concept of Convolution
theorem |
Video Link : https://mathworld.wolfram.com/ConvolutionTheorem.html |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
9. |
Solving
ordinary differential equations using Laplace transforms |
To understand the concept of applying LTs to solvd ODE |
Video Link : https://www.youtube.com/watch?v=0jHn2I2y6Mw |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
UNIT – 3: Fourier series and Fourier Transforms [Total Classes: 12] Activity:
|
1 |
Factual |
Introduce the Fourier series and its
application to the solution of partial differential equations. |
|
2 |
Conceptual |
Find the solution of the wave, diffusion and Laplace equations using the Fourier series. |
|
3 |
Procedural |
Refer to
text book content of Fourier series and Fourier
Transforms in Understanding the concept with examples(simple to complex) |
|
4 |
Applied |
Problems Solving and Applications solving by practice
sessions and Assignments Quiz etc… |
Activity / Schedule of UNIT-3:
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Fourier Series: Introduction |
To introduce The concept of Fourier series |
Video Link : https://slideplayer.com/slide/4213412/
https://www.youtube.c om/watch?v=L7Yy0I MshbE |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Periodic functions |
To
introduce The concept |
Video Link : |
Revise previous class – (5 mins) |
Discussion Forum on the topic in the |
|
|
|
of Periodic functions |
https://en.wikipedia.org/wiki/Mean-periodic_function |
Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
group Review on the topic Share material on the topic |
|
|
|
|
|
|
|
|
3. |
Fourier series of periodic function |
To introduce The concept of fourier series periodic
function |
VIDEO
LINK: https://en.wikipedia.org/wiki/Mean-periodic_function |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) |
Discussion Forum on the topic in the group Review on the topic |
|
|
|
|
|
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Share material on the topic |
|
4. |
Dirichlet’s
conditions s |
To introduce the concept of Dirichlet’s conditions |
Video
Link : https://www.youtube.com/watch?v=blS_OImUJ-c |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
5. |
Even
and odd functions |
To introduce the concept |
Video
Link : |
Revise previous class – (5 mins) |
Discussion Forum on the topic in the |
|
|
|
of Even
and odd functions |
https://www.purplemath.com/modules/fcnnot3.htm |
Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
group Review on the topic Share material on the topic |
|
6. |
Change of interval |
To demonstrate Change
of interval |
Video Link : https://www.youtube.com/watch?v=2_i1fz38QSw PDF: https://math.mit.edu/~gs/cse/websections/cse41.pdf |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
7. |
Half-range sine and cosine series |
To introduce the concept of Half-range sine and cosine series |
Video Link : https://www.youtube.com/watch?v=Sq2FhCxcyI8 Ppt: https://www.slideshare.net/hardik6034off/half-range-sine-cosine-fourier-series |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
8. |
Fourier Transforms: Fourier integral theorem |
To introduce Fourier
Transforms |
Video Link : https://www.youtube.com/watch?v=4VlyGap4Tpg |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 |
Discussion Forum on the topic in the group Review
on the topic |
|
|
|
|
|
Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Share material on the topic |
|
9. |
Fourier sine and cosine integrals |
To demonstrate Method
of Fourier sine and cosine integrals |
Video Link : https://www.youtube.com/watch?v=OWFm2sZ2Rxg |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
10. |
Sine
and cosine transforms |
To Introduce the concept of Sine and cosine transforms |
Video Link : https://www.youtube.com/watch?v=zkkqTpXMeVo |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
11. |
Properties |
To
explain the properties of Fourier Transforms |
Video
Link : https://www.youtube.com/watch?v=0USI-48ovJI |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
|
|
|
12. |
Finite Fourier transforms. |
To
explain the concept of Finite Fourier
transforms |
https://www.math.usm.edu/lambers/mat417/lecture18.pdf |
Revising the concepts discussed so far Any topic to Repeat
asked by students. |
Assignment-3
Quiz-3 |
UNIT 4PDE of first order [Total Classes: 10] Activity:
|
1 |
Factual |
To Analyse, synthesise, organise and
plan projects in the field of study. Reading Prerequisite concepts- partial
differentiation Videos Referring the content on the
Internet |
|
2 |
Conceptual |
Video Lectures On partial differentiation NPTEL Videos Links from the Internet Solved Examples from Internet |
|
3 |
Procedural |
Refer to text book content and Examples, Understanding
the partial differentiation with examples(simple to
complex) |
|
4 |
Applied |
Problems Solving and Applications
solving by practice sessions and Assignments Quiz etc… |
Activity
/ Schedule of UNIT-4 :
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, Poll, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Formation of partial differential equation by
eliminating arbitrary constants |
To introduce The concept of forming the partial differential
equation |
Vedio link: https://www.youtube.com/watch?v=3c71y8N9qj0 PPT: https://www.slideshare.net/sidpatel143/pde-41689592 NPTEL: https://www.slideshare.net/sidpatel143/pde-41689592 |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Formation of partial differential equation by
eliminating arbitrary functions |
To Introduce the concept of Taylors theorem for
functions of several variables |
Video Link : https://www.youtube.com/watch?v=33vJ1wz3rfU Ppt: https://nitkkr.ac.in/docs/11-%20Partial%20Differential%20Equations.pdf |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
3. |
Solutions of first order
linear (Lagrange) equation |
To
Introduce the concept of Mc Lauren’s theorem |
Video Link : https://www.youtube.com/watch?v=Qpudxz275eo |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
4. |
Solutions of first order nonlinear (standard types) equations. |
To Introduce the concept of Jacobian, functional
dependent and independent |
Video Link : https://en.wikipedia.org/wiki/Nonlinear_partial_differential_equation |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
UNIT – 5: Second order PDE and Applications [Total Classes : 8] Activity:
|
1 |
Factual |
Create and
analyze mathematical models using higher order differential equations to
solve application problems such as harmonic oscillator and circuits. |
|
2 |
Conceptual |
Student will
have a working knowledge of basic application problems described by second
order linear differential equations with constant coefficients. Video Lectures l Videos and NPTEL Videos Links from the Internet Solved Problems, Examples from
Internet |
|
3 |
Procedural |
Refer to text book
content and Examples, Understanding
the multiple integrals with examples(simple to complex) |
|
4 |
Applied |
Problems Solving and Applications
solving by practice sessions and Assignments Quiz etc… |
Activity / Schedule of UNIT- 5:
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, Poll, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Solutions of linear
partial differential equations with constant coefficients |
To introduce The concept of linear partial
differential equations with constant coefficients |
Video Link : http://www.fen.bilkent.edu.tr/~gurses/constantcoefficientpdes.pdf |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Solutions of linear
partial differential equations with constant coefficients RHS term
of the type eax + by |
To find the particular integral of pde RHS term of the type eax + by |
Video Link : https://www.youtube.com/watch?v=7sJvNWsSqus |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
3. |
Solutions of linear
partial differential equations with constant coefficients RHS term
of the type ,sin(ax + by), cos(ax
+ by), |
To find the particular integral of pde RHS term of the type sin(ax + by), cos(ax + by), |
Video Link : https://www.youtube.com/watch?v=7sJvNWsSqus |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
|
|
|
4. |
Solutions of linear
partial differential equations with constant coefficients RHS term
of the type xm yn |
To find the particular integral of pde RHS term of the type
xm yn |
Vedio
link: https://www.slideshare.net/prathab1983/chapter-1-maths-3 |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
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Doubts clari- fication (10 min) |
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5. |
Applications of PDE: Method of separation of Variables |
To explain Applications of PDE: Method of separation of Variables http://www2.gcc.edu/dept/math/faculty/BancroftED/teaching/handouts/sep_of_var_examples.pdf |
Video Link : http://www2.gcc.edu/dept/math/faculty/BancroftED/teaching/handouts/sep_of_var_examples.pdf |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
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Doubts clari- fication (10 min) |
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6. |
Solution of One dimensional Wave equation |
To introduce
The concept of Evaluating Wave equation |
Video Link : https://www.youtube.com/watch?v=IAut5Y-Ns7g
https://www.youtube.com/watch?v=IAut5Y-Ns7g |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
7. |
Solution of One
dimensional Heat equation |
To introduce
The concept of Evaluating Solution of One
dimensional Heat equation |
Video Link : https://www.youtube.com/watch?v=PbucCMGDuao |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
8. |
Solution of two-dimensional Laplace equation. |
To introduce The concept of Checking Solution of two-dimensional Laplace equation. |
Video Link : https://www.youtube.com/watch?v=DNo0FmsGZKg |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
Prepared by Approved by
Faculty Signature HOD
(T JYOTHI)
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