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MATH 204

Course ID:
Course Code & Number
MATH 204
Course Title
Vector and Complex Calculus
Level
BS
Credit Hours/ ECTS Credits
(3+0+0) 3 TEDU Credits, 5 ECTS Credits
Year of Study:
Sophomore
Semester:
Spring
Type of Course:
Compulsory
Mode of Delivery:
Face-to-face
Language of Instruction:
English
Pre-requisite / Co-requisite::
Pre-requisites: MATH 101 OR MATH 111
Co-requisites: NONE
Catalog Description
Vector Calculus: Vectors basics, vector fields. Vector differential calculus, gradient, curl, divergence. Vector integral calculus, line, surface and volume integrals, Stokes and Divergence theorems. Complex Calculus: Complex algebra. Complex analytic functions. Contour integration. Cauchy's theorem. Taylor and Laurent series. Singularities. Residue calculus. Fourier analysis. Laplace transforms.
Course Objectives

The main goal of this course is to provide the basic concepts of vector calculus and complex variable theory. The students will acquire the techniques to handle scalar and vector fields, operators such as gradient, divergence and curl; and line and surface integrals. The course will also enable the students to understand complex-valued functions of a complex variable. In terms of a thorough knowledge of complex integration, Laurent series, residues and the argument principle, the students will be ready to study and understand various applications of these concepts, such as the phasor domain analysis in circuit theory; Fourier, Laplace and Z-transforms in signal analysis; and the Nyquist criterion in control theory.

Software Usage
MATLAB
Course Learning Outcomes

Upon succesful completion of this course, a student will be able to
1. Utilize vector and scalar functions in the description of physical quantities. 
2. Formulate and interpret Cartesian, cylindrical and spherical coordinate systems.
3. Identify the concepts of gradient, divergence, curl.
4. Calculate line, surface and volume integrals.
5. Apply divergence and Stokes’ theorems.
6. Solve boundary value problems governed by Laplace’s equation in Cartesian coordinates.
7. Identify the properties of functions of a complex variable and solve equations involving complex variables.
8. Interpret analyticity, differentiability; and identify Cauchy-Riemann equations.
9. Solve equations involving elemantary complex functions (e.g., exponential, logarithmic, etc)
10. Perform integration in the complex plane.
11. Identify and formulate complex series.
12. Display a professional commitment to group work through cooperative quizzes.

Learning Activities and Teaching Methods:
Telling/Explaining Questioning Reading Demonstrating Problem Solving Video Presentations Brainstorming Web Searching
Assessment Methods and Criteria:
Test / Exam Quiz
Assessment Methods and Criteria Others:
Design Content
Recommended Reading
1. R. V. Churchill, J. W. Brown, "Complex Variables and Applications", 7th ed, McGraw Hill, 2003. 2. Wilfred Kaplan, "Advanced Calculus", 5th ed., Addison Wesley, 2002
Required Reading
1. Erwin Kreyszig, "Advanced Engineering Mathematics," 10th ed., Wiley, 2011.
Grading

Quiz - 15% 
Homework/Project - 10% 
Exam 1 - 23% 
Exam 2 - 23% 
Final - 30%

Learning Activities and Teaching Methods Others:
Course Coordinator:
Student Workload:
WorkloadHrs
Course & Program Learning Outcome Matching: