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# 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

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

#### 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 1

Derivatives of functions on Rn

## Session 2

Differentiation of composite functions

Taylor’s Theorem

## Session 4

Differential forms

## Session 5 & 6

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

## Session 7

Theorems of Green

## Session 8

Theorems of Gauss

## Session 9

Theorems of Stokes

## Session 10

Exact forms and closed forms

## Session 11 & 12

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

## Session 13

Differentiation of Transformations

## Session 14

Linear functions and Transformations

## Session 15

Differential and Transformations

## Session 16

Differential and Transformations

## Session 17

Inverse of Transformations

## Session 18

Implicit function Theorems

## Session 19

Functional Dependence

## Session 20

Functional Dependence

## Session 21 & 22

Project- 3 A project report on Implicit function Theorem.

Set functions

## Session 24

Transformations and Multiple integrals

## Session 25

Transformations and Multiple integrals

## Session 26

curves and Arc Length

## Session 27

curves and Arc Length

## Session 28 & 29

Project-4 - A discussion on curves and Arc length

## Session 30

Surfaces and surface area

## Session 31

Surfaces and surface area

## Session 32

integrals over curves and surfaces

## Session 33

integrals over curves and surfaces

## Session 34 & 35

Project-5 - A note on integrals over curves

Power Series

## Session 37

Improper integrals with parameters

## Session 38

Improper integrals with parameters

## Session 39

The Gamma Function

Beta Function