We cover Integrals, Applications of Integration, Techniques of Integration, and further applications of Integration to the Sciences and Engineering

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FACULTY OF SCIENCES - DEPARTMENT OF MATHEMATICS COURSE SYLLABUS

MATH 202: Calculus II

COURSE TITLE ENGLISH

CODE/NO

ARABIC CODE/NO.

CREDITS Th. Pr. Tr. Total

Calculus II MATH 202 202 ر 3 3

Pre-requisites: MATH 110

Course Role in Curriculum

(Required/Elective): Required Course

Catalogue Description:

This course deals mainly with Integral Calculus. We cover Integrals, Applications of Integration, Techniques of Integration, and further applications of Integration to the Sciences and Engineering.

Textbooks:

1. J. Stewart, Calculus, Early Transcendentals, Seventh Edition. International Metric Version, 2012.

Supplemental Materials:

Course Learning Outcomes:

By the completion of the course the student should be able to:

1. Comprehend the connection between differential and integral calculus, and use of integrals to find the area bounded by curves.

2. Calculate the volume of solids, lengths of plane curves, work done by a varying force, etc. by means a definite integral;

3. Use exponential and logarithmic functions to describe exponential growth and decay in problems of applied nature;

4. Evaluate the integrals using different techniques and integral formulae;

5. Distinguish between proper and improper integrals;

6. Perform numerical integration.

Topics to be Covered:

1. Integration

a. Sigma Notation b. Areas and Distances c. The Definite Integral

d. The Fundamental Theorem of Calculus

e. Indefinite Integrals and the Net Change Theorem f. The Substitution Rule

2. Applications of Integration a. Areas between Curves b. Volumes

c. Volumes by Cylindrical Shells

2 d. Work

e. Average Value of a Function 3. Techniques of Integration

a. Integration by Parts b. Trigonometric Integrals c. Trigonometric Substitution

d. Integration of Rational Functions by Partial Fractions e. Strategy for Integration

f. Approximate Integration g. Improper Integrals

4 Further Applications of Integration a. Arc Length

b. Area of a Surface of Revolution

c. Applications to Physics and Engineering d. Applications to Economics and Biology e. Probability