Advanced Calculus

Teacher

Dr. Swarnalata Jena

Category

Domain Courses

Course Attendees

Still no participant

Course Reviews

Still no reviews

Course Name : Advanced Calculus

Code(Credit) : CUNT2482(3-0-1)

Course Objectives

  • To study about Taylor’stheorem. It provides a framework for application of Taylor’stheorem in problems
  • To construct an over view on Green, Gauss & Stokes Theorem

Course Outcomes

COs Course outcomes Mapping COs with POs (High-3, Medium-2, Low-1)
CO1 knowledge in transforming double integral to line integrals, triple integrals to surface integrals, surface integrals to line integrals and vice versa. PO2(3)
CO2 Determine the important analytical quantities associated with scalar and vector fields. PO1(3)
CO3 Solving line integral, double integral and applying these knowledge to find out work done by a force, volume of regions in space, center of gravity of a mass etc. PO1(2)

Course Syllabus

ADVANCED CALCULUS

 

 

MODULE– I

 

DerivativesoffunctionsonRn,Differentiationofcompositefunctions,Taylor’stheorem,Differentialforms.

PROJECT

A brief report on Taylor’s Theorem.

MODULE– II

Theoremsof Green,Gauss&Stokes, Exactforms andclosed forms.

PROJECT

An over view on Green, Gauss & Stokes Theorem.

MODULE– III

Differentiation of Transformations, Linear functions and Transformations, Differential and Transformations.

MODULE– IV

Inverse of Transformations, Implicit function Theorems, Functional Dependence.

PROJECT

A project report on Implicit function Theorem.

MODULE– V

Set functions, TransformationsandMultipleintegrals,curvesandArcLength.

PROJECT

A discussion on curves and Arc length

MODULE– VI

Surfaces and surface area, integrals over curves and surfaces.

PROJECT

A note on integrals over curves.

MODULE– VII

               Power Series, Improper integrals with parameters, The Gamma Function. Beta Function.

PROJECT

A brief report on Gamma function.

 

 

 

BOOKPRESCRIBED

 

1.Advanced calculus – R. C. Buck (Mc. Graw hill– Kogakusha Ltd.)Chapters:3 (3.3, 3.4, 3.5), 6 (6.3,6.4),7,8, 9 (9.2, 9.4, 9.5)

Session Plan

Session 1

Derivatives of functions on Rn

https://www.youtube.com/watch?v=1x7gwpEkwDk

Session 2

Differentiation of composite functions

https://www.youtube.com/watch?v=-k_Eily_M8g

Session 3

Taylor’s Theorem

https://www.youtube.com/watch?v=LEspaisjDFE

Session 4

Differential forms

https://www.youtube.com/watch?v=Nh5XFX0iKgE&list=PLgDV2y4Xrx7N4RnMj_gek2JfiT2SlsVm8

Session 5 & 6

Project-1 - A brief report on Taylor’s Theorem

Session 7

Theorems of Green

https://www.youtube.com/watch?v=6fJE3vvjB8o

Session 8

Theorems of Gauss

https://www.youtube.com/watch?v=cQARyhhj67I

Session 9

Theorems of Stokes

https://www.youtube.com/watch?v=CCNtL-xhF6I

Session 10

Exact forms and closed forms

https://www.youtube.com/watch?v=sl1sZRM7Tvg

Session 11 & 12

Project-2 - An over view on Green, Gauss & Stokes Theorem

Session 13

Differentiation of Transformations

https://www.youtube.com/watch?v=7sJD1pumedU

Session 14

Linear functions and Transformations

https://www.youtube.com/watch?v=eM5lPQBUJ5k

Session 15

Differential and Transformations

https://www.youtube.com/watch?v=-YxsJ_snjNc

Session 16

Differential and Transformations

https://www.youtube.com/watch?v=7sJD1pumedU&t=47s

Session 17

Inverse of Transformations

https://www.youtube.com/watch?v=tnjavCIVyFM

Session 18

Implicit function Theorems

https://www.youtube.com/watch?v=bk9IKHS5KbY

Session 19

Functional Dependence

https://www.youtube.com/watch?v=qn5neFBpU40

Session 20

Functional Dependence

https://www.youtube.com/watch?v=dR-jJimWWHA

Session 21 & 22

Project- 3 A project report on Implicit function Theorem.

Session 23

Set functions

https://www.youtube.com/watch?v=yNrMCqntlSA

Session 24

Transformations and Multiple integrals

https://www.youtube.com/watch?v=wUF-lyyWpUc

Session 25

Transformations and Multiple integrals

https://www.youtube.com/watch?v=HvEIPaOP8lE

Session 26

curves and Arc Length

https://www.youtube.com/watch?v=n4JJ3fNKHUc

Session 27

curves and Arc Length

https://www.youtube.com/watch?v=rLsmajsyaEg

Session 28 & 29

Project-4 - A discussion on curves and Arc length

Session 30

Surfaces and surface area

https://www.youtube.com/watch?v=k13kwLzoTpo

Session 31

Surfaces and surface area

https://www.youtube.com/watch?v=x4U4n4DaxZ8

Session 32

integrals over curves and surfaces

https://www.youtube.com/watch?v=0VNhvwnqoTo

Session 33

integrals over curves and surfaces

https://www.youtube.com/watch?v=Gml1HT4y3_c

Session 34 & 35

Project-5 - A note on integrals over curves

Session 36

Power Series

https://www.youtube.com/watch?v=XHoRBh4hQNU

Session 37

Improper integrals with parameters

https://www.youtube.com/watch?v=0AmKR1UKEAs&list=PLdM-WZokR4tZZxC1L0KJ4irl-1qxbpQlm

Session 38

Improper integrals with parameters

https://www.youtube.com/watch?v=4SQ3DAvfBJI

Session 39

The Gamma Function

https://www.youtube.com/watch?v=c7_F4P71E2E

Session 40

Beta Function

https://www.youtube.com/watch?v=IaG-24IhULY

Session 41 & 42

Project-6 - A brief report on Gamma function.

Our Main Teachers

Dr. Swarnalata Jena

Assistant Professor
VIEW PROFILE