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.
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.