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