This is the third course of the basic sequence Calculus I, II and III, serving as the foundation of advanced subjects in all areas of mathematics. This course is designed to develop the topics of multivariate calculus. Emphasis is placed on multivariate functions, partial derivatives and multiple integrals.

Pre Requisits

Calculus-I, Calculus-II

Learning Outcomes

Upon completion of the course Calculus III, the students will be able to interpret the area enclosed between curves as a definite integral and compute its value. Set up the Riemann sum representing the volume enclosed by a geometric solid, convert the result to definite integral and compute its value. Interpret a volume of revolution of a functions graph around a given axis as a (Riemann) sum of disks or cylinder shells, convert to definite integral form and compute its value.

COURSE CONTENTS

1. Vectors and analytic geometry in space: Coordinate systems,
2. Rectangular, Cylindrical and spherical coordinates,
3. The dot product, the cross product, equations of lines and planes,
4. Quadric surfaces, vector-valued functions,
5. Space curves, derivatives and integrals of vector valued functions,
6. Arc length, curvature, normal and binormal vectors,
7. Multivariable functions and partial derivatives: Functions of several variables, limits and Continuity, partial derivatives,
8. Composition and chain rule, directional derivatives and the gradient vector,
9. Maximum and minimum values, optimization problems, Lagrange Multipliers,
10. Multiple integrals: Double integrals over rectangular domains and iterated integrals,
11. Non-rectangular domains, double integrals in polar coordinates,
12. Triple integrals in rectangular, cylindrical and spherical coordinates,
13. Applications of double and triple integrals change of variables in multiple integrals,
14. Vector calculus: Vector fields, line integrals, Green's theorem, curl and divergence,
15. Surface integrals over scalar and vector fields,
16. Divergence theorem, Stokes' theorem.

Recommended Book

Calculus Early Transcendentals, eighth edition by James Stewart (Chapter 13-16)

Suggested 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, Wiley & Sons, Inc).
5. Swokowski E. W., Calculus with Analytic Geometry latest edition, (PWS Publishers, Boston,Massachusetts).

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50