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Course List

Complex Variable and Special Functions (Math 5)

  • Course Code :
    MTH 311
  • Level :
  • Course Hours :
    3.00 Hours
  • Department :
    Department of Mechanical Engineering

Instructor information :

Area of Study :

To familiarize students with the basic concepts of Complex Variable and Special Functions and to make them able to develop an understanding of mathematical concepts that provide a foundation for the mathematics encountered in Engineering. The course allows students to work at their own level there by developing confidence in mathematics and general problem solving. On successful completion of this course the student will be able to: 1. demonstrate a sound understanding of a number of mathematical topics that are essential for studies in Engineering; 2. interpret and solve a range of problems involving mathematical concepts relevant to MTH 311; 3. Effectively communicate the mathematical concepts and arguments contained in this course.

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Complex Variable and Special Functions (Math 5)

Course outcomes:

a. Knowledge and Understanding:

1- Provide a through understanding and working knowledge of mathematics relevant to this course
2- Develop techniques for solving problems that may arise in every day life

b. Intellectual Skills:

1- Demonstrate knowledge of the theory, concepts, methods,and techniques of Complex variables and Special Functions, and ordinarily equations
2- Think logically
3- Rules and solve problems
4- Organize tasks into a structured form
5- Evaluate the evolving state of knowledge in a rapidly developing area
6- Transfer appropriate knowledge and methods from one topic within the subject to another

c. Professional and Practical Skills:

1- Understand Function of a complex variable and elementary functions
2- Understand the analytically, Cauchy Riemann equations and Complex integrals
3- Know the Taylor and Laurent series and be able to evaluation real integrals by residues
4- The relationship between Gamma and Beta functions and be able to calculate integrals
5- Understand conformal Mapping and be able to calculate integrals
6- Know Bessel’s functions and be able to calculate the solution of differential equation
7- Understand the definitions and types of partial differential equations
8- Understand D’fflambert solution of Wave Equation and Separation of variables for Heat Equation and be able to determine a unique solution. But first we will relate the canonical forms to equations describing physical phenomena.
9- know Finite difference method for partial solutions of differential equations

d. General and Transferable Skills:

1- Gain the principle of quality control
2- Develop skills related to creative thinking, problem solving

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Complex Variable and Special Functions (Math 5)

Course topics and contents:

Topic No. of hours Lecture Tutorial/Practical
Functions of a complex variable: Elementary functions, analytically, Cauchy-Riemann equations. 10 6 4
Complex Integrals: Cauchy Integral formula, Taylor and Laurent series 10 6 4
Cauchy Residues Theorem (Evaluation of real integrals by residues), Conformal Mapping 2 2 0
First Exam 5 3 2
Special functions: Gamma and Beta functions, Bessel functions and Legendre polynomials, power series solution of ordinary differential equations 16 12 4
Partial differential equation: Definitions and types, solution of Wave Problem 16 12 4
Second Exam 3 1 2
Heat Equation, Laplace’s equations in different systems of coordinates, and Finite difference method for partial solutions of differential equations 16 12 4
Final Exam 2 2 0

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