sap course 1434122558

Course Code & Number:

MATH 204

Course Title:

Vector and Complex Calculus

Level of Course:

BS

Credits:

(3+0+0) 3 TEDU Credits, 5 ECTS Credits

Catalog Description:

Vector Calculus : Vectos basics, vector fileds. Vector differential calculus, gradient, curl, divergence. Vector integral calculus , line , surface and voluyme integrals, Stokes and Divergence theorems. Complex Calculus: Complex algebra. Complex analytic functions. Contour integration. Cauchy's theorem. Taylor and Laurent sries. Singularities. Residue calculus. Fourier analysis. Laplace transforms.

Pre-requisites & Co-requisites:

Pre-requisites: MATH 101 OR MATH 111
Co-requisites: NONE
Grading: 

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

Year of Study: 
Sophomore
Semester: 
Spring
Mode of Delivery: 
Face-to-face
Language of Instruction: 
English
Course Type: 
Compulsary
Required Reading: 
1. Erwin Kreyszig, "Advanced Engineering Mathematics," 10th ed., Wiley, 2011.
Course Objective: 

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.

Computer Usage: 
MATLAB
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.

Planned Learning Activities and Teaching Methods: 
Telling/Explaining
Questioning
Reading
Demonstrating
Problem Solving
Video Presentations
Brainstorming
Web Searching
Assessment Methods and Criteria: 
Test / Exam
Quiz/Homework

Student Workload:

Quizzes /Homeworks
30
hrs
Midterm Exam 1
12
hrs
Midterm Exam 2
12
hrs
Final Exam
16
hrs

Prepared By:

Revised By:

teduadmin