Prerequisite(s): Calculus-I

Credit Hours: 3+0

Objectives of the course:

This is the second course of the basic sequence Calculus I, II and III, serving as the foundation of advanced subjects in all areas of mathematics. The sequence, equally, emphasizes basic concepts and skills needed for mathematical manipulation. As continuation of Calculus-I, It focuses on the study of functions of a single variable.

Course Contents:

Techniques of integration: Integrals of elementary, hyperbolic, trigonometric, logarithmic and exponential functions, integration by parts, substitution and partial fractions, improper integrals.

Applications of integrals: Area between curves, average value, volumes, arc length, area of a surface of revolution.

Infinite series: Sequences and series, convergence and absolute convergence, tests for convergence, divergence test, integral test, p series test, comparison test, limit comparison test, alternating series test, ratio test, root test, power series, convergence of power series, representation of functions as power series, differentiation and integration of power series, Taylor and McLaurin series.

 Conic section, parameterized curves and polar coordinates: Curves defined by parametric equations, Calculus with parametric curves, tangents, areas, arc length, polar coordinates, polar curves, tangents to polar curves, areas and arc length in polar coordinates.

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, 2011. A Concise introduction to pure Mathematics, CRC Press.
7. A. Kaseberg, 2004. Intermediate Algebra, Thomson Brooks/cole.
8. Stewart J., Calculus, latest edition Brooks/COLE

ASSESMENT CRITERIA

Mid Term exam: 30 marks

Sessional: 20 marks

Final Term Exam: 50 marks

Total: 100 marks