UNIVERSITY OF SARGODHA
DEPARTMENT OF MATHEMATICS
COURSE OUTLINE FALL 2020
Course Tittle: CALCULUSIII
Course Code: MATH5106
Credit Hours: 03
Instructor: MUHAMMAD QAIS ALI KHAN
Email: [email protected]
DESCRIPTION & OBJECTIVES
This is the third course of the basic sequence Calculus1, 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, vectorvalued 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, Nonrectangular 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 1216, 2020 
2. 
rectangular, cylindrical and spherical coordinates, the dot product 
Oct 1923, 2020 
3. 
the cross product, equations of lines and planes 
Oct 2630, 2020 
4. 
quadric surfaces 
Nov 26, 2020 
5. 
vectorvalued functions, and space curves 
Nov 913, 2020 
6. 
arc length, curvature, normal and binormal vectors 
Nov 1620, 2020 
7. 
, Multivariable functions and partial derivatives: Functions of several variables, limits and Continuity 
Nov 2327, 2020 
8. 
partial derivatives, composition and chain rule 
Nov 30Dec 4, 2020 
9. 
directional derivatives and the gradient vector, maximum and minimum values 
Dec 711, 2020 
10. 
Mid Term Exam 
Dec 1418, 2020 
11. 
optimization problems, Lagrange Multipliers. 
Dec 2125, 2020 
12. 
Winter Break 
Dec 28, 2020– Jan 1,2021 
13. 
Winter Break 
Jan 48 , 2021 
14. 
Multiple integrals: Double integrals over rectangular domains and iterated integrals, Nonrectangular domains, double integrals in polar coordinates, triple integrals in rectangular, cylindrical and spherical coordinates 
Jan 1115, 2021 
15. 
applications of double and triple integrals , change of variables in multiple integrals. Vector calculus: Vector fields 
Jan 1822. 2021 
16. 
, line integrals, Green's theorem, curl and divergence 
Jan 2529, 2021 
17. 
, surface integrals over scalar and vector fields, divergence theorem, Stokes' theorem.

Feb 15, 2021 
18. 
Final term Exam 
Feb 812, 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.