Engineering Mathematics

This course aims to provide a broad introduction to the fundamental mathematical theories and applications of differential calculus, complex variables, integral calculus, Fourier analysis, and partial differential equations needed by electrical, electronic, communications and computer systems engineers. The course builds on the foundations laid in first and second year mathematics at university level and in turn aims to lay the foundation for more advanced mathematics courses that follow. Topic areas include

• Introductory Fourier Analysis:
  Fourier series, Fourier integrals, Fourier transforms, Inverse Fourier transforms.
• Sturm-Liouville problems:
  Sturm-Liouville differential equations, Green equation, Basic properties of Sturm-Liouville eigenvalue problem.
• Partial Differential Equations(PDE):
  Definition of a PDE, first and second linear PDE, Heat, Wave, and Laplas equations, application of Fourier analysis in solving homogeneous and non-homogeneous boundary value problems involving a PDE.
• Complex Variables:
  operations with complex numbers, solution to equations, representation of complex numbers in Cartesian form, polar form, exponential form and in phasor notation, powers and roots of complex numbers, complex functions (exponential, hyperbolic, trigonometric and logarithm) and complex differentiation (derivative of a complex-valued function and Cauchy-Riemann equations), analytic functions, mapping properties of elementry complex functions, line integrals, complex integration, series of complex functions, Laurant series, residue and poles, Residue Theorem, applications of residue theorem, conformal mappings.

Textbooks:

1. Advanced Engineering Mathematics, by Erwin Kreyszig, 12th Edition.
2. Elementary Differential Equations, by William E. Boyce  and, Richard C. DiPrima, 9th. Edition, Part Two.
3. Complex Variables and Applications, James Ward Brown and  Ruel V. Churchill, 7th. Edition.