### Calculus-III

UNIVERSITY OF SARGODHA

DEPARTMENT OF MATHEMATICS

COURSE OUTLINE                                                                                                  FALL 2020

Course Tittle: CALCULUS-III

Course Code: MATH-5106

Credit Hours: 03

Instructor: MUHAMMAD QAIS ALI KHAN

Email: [email protected]

DESCRIPTION & OBJECTIVES

This is the third course of the basic sequence Calculus-1, II and III, serving as the foundation of advanced subjects in all areas of mathematics

READINGS

Recommended Books

1. Thomas, Calculus, latest Edition. Addison Wesley Publishing Company.

2.  Anton H., Bevens I., Davis H., Calculus, latest Edition, John Wiley & Sons, Inc.

3. Larson E. Calculus, latest edition,  Brooks/Cole Cengage Learning.

4. Hallett H.  Gleason, McCallum, et al, Calculus Single and Multivariable, latest Edition. John  Wiley & Sons, Inc.

5. Swokowski E. W., Calculus with Analytic Geometry latest edition PWS Publishers, Boston, Massachusetts.

6. Liebeck M. A Concise introduction to pure Mathematics, CRC Press, 2011.

7. A. Kaseberg. Intermediate Algebra, Thomson Brooks/cole, 2004.

8. Stewart J., Calculus, latest edition Brooks/COLE.

CONTENTS

Vectors and analytic geometry in space: Coordinate systems, rectangular, cylindrical and spherical coordinates, the dot product, the cross product, equations of lines and planes, quadric surfaces, vector-valued functions, and space curves , arc length, curvature, normal and binormal vectors, Multivariable functions and partial derivatives: Functions of several variables, limits and Continuity, partial derivatives, composition and chain rule, directional derivatives and the gradient vector, maximum and minimum values, optimization problems, Lagrange Multipliers. Multiple integrals: Double integrals over rectangular domains and iterated integrals, Non-rectangular domains, double integrals in polar coordinates, triple integrals in rectangular, cylindrical and spherical coordinates, applications of double and triple integrals, change of variables in multiple integrals. Vector calculus: Vector fields, line integrals, Green's theorem, curl and divergence, surface integrals over scalar and vector fields, divergence theorem, Stokes' theorem.

COURSE SCHEDULE

Week

# Topics and Readings

## Dates

1.

Vectors and analytic geometry in space: Coordinate systems,

Oct 12-16, 2020

2.

rectangular, cylindrical and spherical coordinates, the dot product

Oct 19-23, 2020

3.

the cross product, equations of lines and planes

Oct 26-30, 2020

4.

quadric surfaces

Nov 2-6, 2020

5.

vector-valued functions, and space curves

Nov 9-13, 2020

6.

arc length, curvature, normal and binormal vectors

Nov 16-20, 2020

7.

, Multivariable functions and partial derivatives: Functions of several variables, limits and Continuity

Nov 23-27, 2020

8.

partial derivatives, composition and chain rule

Nov 30-Dec 4, 2020

9.

directional derivatives and the gradient vector, maximum and minimum values

Dec 7-11, 2020

10.

Mid Term Exam

Dec 14-18, 2020

11.

optimization problems, Lagrange Multipliers.

Dec 21-25, 2020

12.

Winter Break

Dec 28-, 2020– Jan 1,2021

13.

Winter Break

Jan 4-8 , 2021

14.

Multiple integrals: Double integrals over rectangular domains and iterated integrals, Non-rectangular domains, double integrals in polar coordinates, triple integrals in rectangular, cylindrical and spherical coordinates

Jan 11-15, 2021

15.

applications of double and triple integrals , change of variables in multiple integrals. Vector calculus: Vector fields

Jan 18-22. 2021

16.

, line integrals, Green's theorem, curl and divergence

Jan 25-29, 2021

17.

, surface integrals over scalar and vector fields, divergence theorem, Stokes' theorem.

Feb 1-5, 2021

18.

Final term Exam

Feb 8-12, 2021

RESEARCH PROJECT

N/A

ASSESSMENT CRITERIA

Mid exam:       30

Sessional:        20

Project:            --

Assignments:   10

Presentation:   10

Final exam:     50

Total:               100

RULES AND REGULATIONS

75% attendance is compulsory to appear in Final Term exam.