
25735: Engineering Mathematics
Course Name: Engineering Mathematics
Course Number: 25735
Prerequisite(s): 22034 (Differential Equations)
Co-requisite(s): -
Units: 3
Level: Undergraduate
Last Revision: Winter 2020
Description:
Syllabus:
Course Number: 25735
Prerequisite(s): 22034 (Differential Equations)
Co-requisite(s): -
Units: 3
Level: Undergraduate
Last Revision: Winter 2020
Description:
This course serves as a bridge between the first-year general mathematics courses and the engineering courses that students will take in the department in subsequent terms on the analysis of Electrical Engineering systems and processes. The course syllabus includes coverage of mathematical concepts such as the Fourier expansion of functions, analysis of the behavior of dynamical systems, complex plane analysis, analytic functions, series, and expansion of functions. Objectives of the course include offering an engineering perspective into the application of mathematical tools such as the use of partial differential equations for modeling the dynamics of physical phenomena, the use of the Fourier series for modeling the behavior of signals and systems, and the use of complex analysis for efficient mathematical modeling of periodic functions.
Syllabus:
- Fourier Series
- Periodic functions
- Introduction to the Fourier series
- Euler Formula
- Convergence
- Forced oscillations
- Even and odd functions
- Half-range expansions
- Approximation by Trigonometric Polynomials
- Bessel’s inequality and Parseval’s identity
- Sturm-Liouville problems
- Generalized Fourier series
- Legendre’s equation
- Bessel’s equation
- Fourier integral
- Sine and cosine Fourier integrals
- The complex form of Fourier integral
- Fourier Transform
- Fourier Transform Review
- Properties of Fourier Transform
- Convolution
- Filtering
- Partial Differential Equations
- Basic concepts of PDEs
- Vibrating string, wave equation
- Solution by separating variables – Use of Fourier series
- D’Alembert’s solution of the wave equation
- Types and normal forms of PDEs
- Heat equation
- Steady two-dimensional heat problems
- Two-dimensional wave equation
- 2D wave equation: rectangular membrane
- Laplacian in polar coordinates
- Circular membrane: Fourier–Bessel series
- Introduction to complex analysis
- Complex Analysis
- Complex numbers, complex plane
- Polar form, roots, and powers
- Regions in the complex plane
- Complex differentiation
- Analytic functions
- Cauchy–Riemann equations
- Harmonic functions
- Basic complex functions:
- Exponential Function
- Trigonometric / Hyperbolic Functions
- Logarithmic Function
- Complex Exponents
- Inverse Trigonometric / Hyperbolic Functions
- Line integrals in the complex plane
- Cauchy’s integral theorem
- Cauchy’s integral formula
- Derivatives of analytic functions
- Sequences and series, convergence
- Power series, functions given by power series
- Taylor and Maclaurin series
- Laurent series
- Singularities and zeros, infinity
- Applications of complex analysis / power series in Systems Theory
- Residue integration
- Mapping
- Riemann surfaces
- Conformal mapping
- Linear fractional transformations
- Special linear fractional transformations / Other functions
- Erwin Kreyszig, Advanced Engineering Mathematics, Edition 10, 2011
- Complex Variables and Applications, Brown & Churchill, Edition 8, 2009
Last Update: 2024-05-06