Math205

Form (6)

Course Description form

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

Objectives:  Prefer In points

On completion of the course, the students should be able to

• know about the convergence and divergence of Infinite series, power, Taylor,  Maclaurin and Fourier series;
• use Double and  Triple integrals in two and three dimensions to describe the area of surface and the volume of region  in space;
• understand sketching of vector fields;
• comprehend gradient, divergence and curl of the vector fields and their use to describe  the work, circulations, flux and potential functions;
• grasp the idea of line integrals and surface integrals , and understand the methods for parameterization surface;
• learn the idea of Stokes, Green, Divergence and Unified theorems;

          solve multiple integrals in different coordinates.

Contents:

       Chapter 1 Infinite sequence and series

1.    Sequences

2.    Infinite Series

3.    The  Integral Test

4.    Comparison Tests

5.    The Ratio and Root Tests

6.    Alternating Series, Absolute and Conditional Converge

7.    Power Series

8.    Taylor and  Maclaurin Series

9.    Convergence of Taylor Series

10. Application of Power Series

11. Fourier Series

       Chapter 2 Multiple Integrals

1.    Multiple Integrals

2.    Area, Moments, and Centers of Mass

3.    Double Integrals in Polar Form

4.    Triple Integrals in Rectangular Coordinates

5.    Masses and Moments in Three Dimensions

6.    Triple Integrals in Cylindrical and Spherical Coordinates

7.    Substitution in Multiple Integral

       Chapter 3 Integration in Vector Field

1.    Line Integrals

2.    Vector Fields, Work, Circulations, and Flux

3.    Path Independence, Potential Functions, and Conservative Fields

4.    Green Theorem in the Plane

5.    Surface Area and Surface Integrals

6.    Parameterized Surface

7.    Stokes Theorem

8.    The Divergence Theorem and a Unified Theory

9.    Review

Course Outcomes:

A-   Knowledge:

     Students will learn a particular set of mathematical facts and how to apply them; more importantly, from this course students will learn how to think logically and mathematically.

B-Cognitive Skills:

    Mental skills, Knowledge, Analysis, Comprehension, Applications and Evaluation

C- Interpersonal skills and responsibilities:

    - questioning during lecture

   -submitting assignments etc

   - group discussions

   - understand and response the questions

   - communicate effectively

D- Analysis and communication:

    (communication, mathematical and IT skills)

    Assessment methods for the above elements:

    Quizzes, Assignments, and Examinations.

Text book:  

         Thomas’ Calculus, Eleventh Edition, Media Upgrade

         Publisher: Pearson. Addison- Wesley         

         Authors: Weir, Hass and Giordano, 2008

Supplementary references

        Textbook: Calculus, Third Edition 

        Publisher: McGraw-Hill

        Authors: R. T. Smith and R. B. Minton

        Year: 2008.

        Book Title: Textbook: Calculus, Eighth Edition, Early Transcendental  

        Publisher: John Wiley& Sons, Inc.

        Authors: H. Anton, I. Bivens and S. Davis.

        Year: 2005