Math202

Course Description form

Faculties and departments requiring this course (if any): Faculties of

          Engineering and of Science.

Objectives: 

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

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

·         use exponential and logarithmic functions to describe exponential growth and decay in problems of applied nature;

·         evaluate the integrals using different techniques and integral formulae;

·         distinguish between proper and improper integrals;

     perform numerical integration.     

Contents:

     Integration

□  Estimating with finite sums,

□ Sigma notation and limits of finite sums,

□ The definite integral,

□ The Fundamental Theorem of Calculus,

□ Indefinite integrals and substitution rule.

□ Area Between curves,

     Applications of Definite Integrals

□ Volume by slicing and rotation about axes,

□ Volume by cylindrical shells,

□ Length of plane curve,

□ Moment s and center of mass,

□ Area of surface of revolution,

□ Work and fluid pressure and forces.

    Techniques of Integration

□ Basic integration formulas,

□ Integration by parts,

□ Integration of rational function by partial fraction,

□ Trigonometric integrals,

□ Trigonometric substitutions,

□ Improper integrals.

     Applications of Integration

□ Arc Length,

□ Area of a Surface of Revolution,

□ Applications to Physics and Engineering,

□ Applications to Economics and Biology,

□ Probability.

Course Outcomes:

A-           Knowledge:

         After the successful completion of this course, students will be able to know the various techniques of integrations and applicable methods which are very useful in sciences and engineering.

B-Cognitive Skills:

         Using the concepts of integration and integration techniques, students will be able to find the area, volume, surface area etc.

          Students will demonstrate a depth of knowledge of  basic Calculus and apply the methods of inquiry in other courses related to calculus.

C- Interpersonal skills and responsibilities:

         To ask questions during learning process, to submit assignments on time within the due time period, to do group discussions, to understand and response the questions.                  

D- Analysis and communication:

          To communicate effectively

          Assessment methods for the above elements

          Assignments (10%), Exam-I (25%), Exam-II (25%) and Final Exam (40%)

Text book:

               Title: Thomas' Calculus (Eleventh Edition);

               Author: M.D. Weir, J. Hass and F.R. Giordano;

               Publisher: Pearson, Addison Wesley;

               Year:2008