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. This course is a continuation of Calculus I. At the end of this course, students will be able understand derivatives inside and out, and know basic integrals. They will be able to use integration and infinite series in different physical problems.

Pre Requisit

Calculus-I

Learning Outcomes

This course is a continuation of Calculus-I. At the end of this course, students will be able understand derivatives inside and out, and know basic integrals. They will be able to use integration and infinite series in different physical problems.

COURSE CONTENTS

1. Techniques of integration: Integrals of elementary.
2. Hyperbolic, trigonometric, logarithmic and exponential functions.
3. Integration by parts, substitution and partial fractions, improper integrals.
4. Applications of integrals: Area between curves, average value.
5. Volumes, arc length, area of a surface of revolution.
6. Infinite series: Sequences and series, convergence and absolute convergence.
7. Tests for convergence, divergence test.
8. Integral test, p series test, comparison test, limit comparison test.
9. Alternating series test, ratio test, root test.
10. Power series, convergence of power series, representation of functions as power series.
11. Differentiation and integration of power series, Taylor and McLaurin series.
12. Conic section, parameterized curves and polar coordinates.
13. Curves defined by parametric equations.
14. Calculus with parametric curves, tangents, areas, arc length, polar coordinates, polar curves.
15. Tangents to polar curves, areas and arc length in polar coordinates.
16. Polar coordinates, polar curves, tangents to polar curves, areas and arc length in polar coordinate

Recommended Book

Calculus Early Transcendentals, eighth edition by James Stewart (Chapter 6, 7 and 8)

Suggested Books

1. Thomas Calculus Latest ed. (Addison Wesley Publishing Company)
2. Anton H., Bevens I., Davis H. Calculus Latest ed. (John Wiley & Sons, Inc.)
3. Larson E. Calculus Latest ed.(Brooks/Cole Cengage Learning)

ASSESSMENT CRITERIA

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

Mid-Term Exam:   30

Final-Term Exam: 50