13507_MTH212

Lovely Professional University, Punjab Course Code

Course Title

Course Planner

MTH212

MULTIVARIATE ANALYSIS LINEAR ALGEBRA AND SPECIAL FUNCTIONS Courses with Numerical focus

13507::Deepika

Course Category

Lectures

Tutorials Practicals Credits

3.0

0.0

TextBooks Sr No

Title

Author

Edition

Year

Publisher Name

T-1

Advanced Engineering Mathematics

Peter V.O'Niel

7th

2012

Cengage Learning

T-2


R.K.Jain, SRK Iyenger

3rd

2012

Narosa Publishing House Pvt. Ltd

Reference Books Sr No

Title

Author

Edition

Year

Publisher Name

R-1


Erwin Kreyszig

4th

2007

John Wiley & Sons

R-2

Higher Engineering Mathematics

B.S. Grewal

42th

2012

Khanna Publishers

R-3

Calculus Early Transcendentals

soo T. Tan

1st

2012

Cengage Learning

Relevant Websites Sr No

(Web address) (only if relevant to the course)

Salient Features

RW-1

http://tutorial.math.lamar.edu/Classes/DE/FourierSeries.aspx

Introduction to FourierSeries

RW-2

http://www.math.psu.edu/papikian/Kreh.pdf

Introduction to Bessel Functions

RW-3

http://www.efunda.com/math/legendre/

Introduction to Legendre Polynomials

RW-4

http://sces.phys.utk.edu/~moreo/mm08/Riddi.pdf

Beta Function and its Applications

RW-5

http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.html

Introduction to the Gamma Function

RW-6

http://www.math.utah.edu/online/2210/notes/ch13.pdf

Basic Concept on vector algebra

RW-7

http://tutorial.math.lamar.edu/Classes/CalcIII/GreensTheorem.aspx

Basic Concept on Green's Theorem

RW-8

http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceIntegrals.aspx

Applications of surface integral

RW-9

https://www.khanacademy.org/math/calculus/partial_derivatives_topic

Partial derivatives, gradient, divergence, curl

RW-10

http://www.personal.soton.ac.uk/jav/soton/HELM/workbooks/workbook_28/28_3_ortho Orthogonal Curvilinear Coordinates g_curv_coords.pdf

RW-11

http://www.academia.edu/3003410/Gradient_Divergence_and_Curl_in_Curvilinear_Co Gradient, Divergence and Curlin Curvilinear Coordinates ordinates

RW-12

http://opencourses.emu.edu.tr/pluginfile.php/2306/mod_resource/content/0/Gradient_etc Gradient, Divergence, Curl, and Laplacian Operations .pdf

0.0

3.0

RW-13

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/3.double-integrals-and-line-integrals-in-the-plane/part-c-greens-theorem/session-72simply-connected-regions-and-conservative-fields/MIT18_02SC_MNotes_v5.pdf

Simply-Connected Regions

RW-14

http://astrowww.phys.uvic.ca/~tatum/stellatm/atm3.pdf

THE EXPONENTIAL INTEGRAL FUNCTION

RW-15

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/3.double-integrals-and-line-integrals-in-the-plane/part-a-double-integrals/session-47definition-of-double-integration/

Definition of Double Integration

RW-16

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/3.double-integrals-and-line-integrals-in-the-plane/part-c-greens-theorem/session-65greens-theorem/

Greens theorem

Audio Visual Aids Sr No

(AV aids) (only if relevant to the course)

Salient Features

AV-1

http://nptel.iitm.ac.in/courses/111104024/51

some problems on multivariate function

LTP week distribution: (LTP Weeks) Weeks before MTE

7

Weeks After MTE

7

Spill Over

3

Detailed Plan For Lectures Week Number

Lecture Number

Broad Topic(Sub Topic)

Chapters/Sections of Text/reference books

Week 1

Lecture 1

Multivariate functions(Limits)

T-2:ch 2 2.1

Lecture 2

Multivariate functions(Continuity and Differentials)

T-2:ch 2 2.2

Other Readings, Lecture Description Relevant Websites, Audio Visual Aids, software and Virtual Labs DK-1

Learning Outcomes

Pedagogical Tool Demonstration/ Case Study / Images / animation / ppt etc. Planned

Definition and examples After this lecture Discussion of limit student will be able to Define, compare and recognize relations and function in Multivariate functions Definition and examples Student will learn Discussion of Continuity and calculus of Multivariate Differentials functAfter this lecture student will be able to Define, compare and recognize relations and function in Multivariate functionsion

Week 1

Lecture 3

Multivariate functions(Partial derivatives)

T-2:ch 2 2.3

Week 2

Lecture 4

Multivariate functions(MaximumMinimum problems)

T-2:ch 2 2.5

Lecture 5

Multivariate functions (Langragians)

T-2:ch 2 2.5.1

DK-2

method to solve Maximum Minimum

Lecture 6

Multivariate functions(Chain rule)

T-2:ch 2 2.3.3

DK-2

Definition and examples In this lecture student Discussion of Chain rule will know how to find the instantaneous rate of change of one variable with respect to multivariable

Lecture 7

Multivariate functions(Double integrals)

T-2:ch 2 2.6.1

Definition and method to solve Double integrals

Student will learn to find the Area using Double integrals

Multivariate functions(Iterated integrals)

R-3:ch13 13.2


student will learn Discussion method to solve Double intStudent will learn to find the Area using Double integralsegrals

Lecture 8

Multivariate functions(Double integrals)

T-2:ch 2 2.6.1


Student will learn to find the Area using Double integrals

Discussion

Lecture 9

Multivariate functions(Triple integrals)

T-2:ch 2 2.6.2

Definition and example of method to solve triple integral

Student will learn to find the volume using triple integrals

Discussion

Lecture 10

Multivariate functions(Jacobians)

T-2:ch2 2.26

Definition and example of Jacobians

Student will learn solution with determinants

Discussion

Lecture 11

Fourier Series and Integral(Fourier series and integral)

T-2:ch 9 9.2 9.2.1

Definition and example of Fourier series and integral

Student will learn The capable of analyzing the fre quency components of certain, discreet frequencies in tegers of a given function

Discussion

Week 3

Week 4

DK-2

Definition and examples In this lecture student Discussion of Partial derivatives will know how to find the instantaneous rate of change of one variable with respect to multivariable Definition and examples after this lecture student Discussion of Maxima Minima will able to find the condition under which the given function will give maximum or minimum value

RW-1

Student will learn method to find the Maximum Minimum using Langragians

Discussion

Discussion

Week 4

Lecture 12

Fourier Series and Integral (Dirichlet conditions)

T-2:ch 9 9.2.2


Student will learn methods to solve Fourier series and integraStudent will learn The capable of analyzing the fre quency components of certain, discreet frequencies in tegers of a given functionl

Discussion

Week 5

Lecture 13

Fourier Series and Integral (Parseval's identity)

R-2:ch22 22.7



Discussion

Lecture 14

Fourier Series and Integral (Convolution theorem)

T-1:ch15 15.4.4 T-2:ch9 9.14



Discussion

Definition and example Asymptotic formula for Tnl

Student will learn Discussion Asymptotic formula for Tnl

Fourier Series and Integral (Asymptotic formula for T(n)l) Lecture 15 Week 6

Lecture 16

Test 1 Fourier Series and Integral (Dirichlet integral)

T-2:ch2 2.6.4

Definition and example of Dirichlet integral

Student will learn methods to solve Fourier series and integral

Discussion

Fourier Series and Integral(Sine and Cosine integrals)

T-1:ch15 15.2 T-2:ch 9 9.4

Definition and example of Sine and Cosine integrals


Discussion

RW-14

Definition and example Exponential integral


Discussion

RW-2

Definition and example of Bessels differential equation and function first and second kind

Student will learn Application of Bessel Equation Heat Transfer in a Circular Fin

Discussion

Lecture 17

Fourier Series and Integral (Exponential integral)

Lecture 18

Special Function(Bessel's differential equation and function (first and second kind))

T-1:ch 16 16.2.2 16.2.3 T-2:ch7 7.4

Week 7

Lecture 19

Special Function(Legendre differential equation)

T-2:ch 7 7.50

RW-3

Definition and example of Legendre differential equation

Special Function(Legendre polynomials)

T-1:ch16 16.1

RW-3

Definition and example Student will learn of Legendre polynomials methods to solve Legendre polynomials

Special Function(Some applications) Lecture 20

Lecture 21

T-1:ch16 16.1 16.1.1 16.1.2

Special Function(Beta function)

T-2:ch1 1.5.4

Special Function(Other special functions – Error function)

T-2:ch1 1.5.6

Special Function(Gamma Function)

T-1:ch16 16.2 T-2:ch1 1.5.4

students will learn Discussion about the solutions of some physical problems using numerical methods Discussion

Definition and example Student will learn Some Discussion of Legendre polynomials applications of and its application differential equation RW-4

RW-5

Definition and example of Beta function

Student will learn about Discussion how to replace definite integral to indefinite integral

Definition and example of Other special functions – Error function

Student will learn about Discussion Error function

Definition and example of Gamma Function

Student will learn about Discussion relation between gamma function and factorial notation

MID-TERM Week 8

Week 9

Week 10

Lecture 22

Vector Algebra(Laws of vector algebra)

R-3:ch10 10.1 10.2

RW-6

Lecture 23

Vector Algebra(Operations- (dot, cross, triple products))

R-3: ch 10 10.3 10.4

Lecture 24

Vector Algebra(Vector function – Limits, Continuity and Derivatives)

T-2:ch15 15.2

Lecture 25

Vector Algebra(Geometric interpretation)

T-2:ch15 15.2

Lecture 26

Vector Algebra(Gradient)

T-2:ch15 15.3

RW-9

Definition and example of Gradient

Application of Del on scalar functions

Discussion

Lecture 27

Vector Algebra(Divergence and Curl – formulae)

T-2:ch 15 15.4

RW-11

Definition and example Application of Del on of Divergence and Curl – vector functions formulae

Discussion

Lecture 28

Vector Calculus I(Orthogonal Curvilinear Coordinates)

R-1:A 3.4 R-2:ch8 8.19

RW-10

Definition and example of Orthogonal Curvilinear Coordinates

RW-9 DK-2

Definition and example of Laws of vector algebra

Student will learn basics of vectors algebra

Discussion

Definition and example Student will learn of Operations dot, cross, basics of vectors triple products algebra

Discussion

Definition and example of Vector function – Limits, Continuity and Derivatives

Discussion

Student will learn Vector function – Limits, Continuity and Derivatives

Geometric interpretation Student will learn Discussion Limits, Continuity and Geometricinterpretation Derivatives of Limits, Continuity and Derivatives

students will learn Discussion about Orthogonal Curvilinear Coordinates

Week 10

Lecture 29

Vector Calculus I(Orthogonal Curvilinear Coordinates) Vector Calculus I(Gradient)

R-1:A 3.4 R-2:ch8 8.19

RW-10

Definition and example of Orthogonal Curvilinear Coordinates

students will learn Discussion about Orthogonal Curvilinear Coordinates

R-1:A 3.4

RW-9 RW-11

Definition and example of Gradient

students will learn about Gradient

Discussion

students will learn about Divergence

Discussion

Lecture 30 Week 11

Week 12

Week 13

Test 2

Lecture 31

Vector Calculus I(Divergence)

Lecture 32

Vector Calculus I(Curl and Laplacian in Curvilinear Coordinates)

Lecture 33

Vector Calculus I(Special Curvilinear Coordinates)

Lecture 34

Vector Calculus II(Line integrals)

Lecture 35

Vector Calculus II(Line integrals)

Lecture 36

Vector Calculus II(Simple Connected regions)

R-1:A 3.4

RW-9

Definition and example of Divergence

RW-12

Definition and example students will learn Discussion of Curl and Laplacian in about Curl and Curvilinear Coordinates Laplacian in Curvilinear Coordinates Definition and example of Special Curvilinear Coordinates

students will learn Discussion about Special Curvilinear Coordinates

T-1:ch13 13.1 T-2:ch15 15.5

Definition and example of Line integrals

Method to solve Line integrals involving vector functions

Discussion

T-1:ch13 13.1 T-2:ch15 15.5

Definition and example of Line integrals

Method to solve Line integrals involving vector functions

Discussion

RW-13

Definition and example of Simple Connected regions

students will learn about Simple Connected regions

Discussion

Vector Calculus II(Green's theorem)

T-1:ch13 13.2 T-2:ch15 1.5.2

RW-7 RW-16

Statement and example of Greens theorem

students will learn abou Discussion Application of line Integral

Lecture 37

Vector Calculus II(Green's theorem)

T-1:ch13 13.2 T-2:ch15 1.5.2

RW-7 RW-16

Statement and example of Greens theorem

students will learn abou Discussion Application of line Integral

Lecture 38

Vector Calculus II(Path independence)

T-1:ch13 13.3 T-2:ch15 15.5.1

Definition and example of Path independence

students will learn about Application of line Integral

Discussion

Definition and example of Surface integrals

students will learn about Application of Multiple Integral

Discussion

Statement and example of Stokes theorem


Discussion

Lecture 39 Week 14

Test 3

Lecture 40

Vector Calculus II(Surface integrals)

T-1:ch13 13.4 T-2:ch15 15.6.2

Lecture 41

Vector Calculus II(Stokes theorem)

T-1:ch13 13.8 T-2:ch15 15.7.2

DK-3

Week 14

Lecture 42

Vector Calculus II(Stokes theorem)

T-1:ch13 13.8 T-2:ch15 15.7.2

Statement and example of Stokes theorem


Discussion

SPILL OVER Week 15

Lecture 43

Spill Over

Lecture 44

Spill Over

Lecture 45

Spill Over

Scheme for CA: Component

Frequency

Test

Out Of 2

Each Marks Total Marks 3

Total :-

10

20

10

20

Details of Academic Task(s) AT No.

Objective

Topic of the Academic Task

Nature of Academic Task (group/individuals/field work

Evaluation Mode

Allottment / submission Week

Test 1

To check the knowledge of students about concept taught

Limits, Continuity and Differentials, Partial derivatives, Individual Maximum-Minimum problems, Langragians, Chain rule, Double integrals, Iterated integrals, Triple integrals, Fourier series and integral, Dirichlet conditions, Parseval's identity

Marks will be awarded on the basis of written test which contains 2 questions of 10 marks and 2 questions of 5 marks

4/5

Test 2


Laws of vector algebra, Operations- (dot, cross, triple products), Vector function – Limits, Continuity and Derivatives, Geometric interpretation, Gradient, Divergence and Curl – formulae, Orthogonal Curvilinear Coordinates

Individual


9 / 10

Test 3


Gradient, Divergence, Curl and Laplacian in Curvilinear Coordinates, Special Curvilinear Coordinates, Line integrals, Simple Connected regions, Green's theorem, Path independence,

Individual


12 / 13

13507_MTH212

Recommend Documents