Standard syllabus
Complex variables for engineers · Undergraduate · Math
Topics
Complex arithmetic and functions
- Complex numbers, polar form, and Euler's formula
- Complex functions and mappings in the plane
- Limits, continuity, and analyticity (engineering emphasis)
- Cauchy–Riemann equations and harmonic conjugates
- Elementary functions: exp, log, sin, cos in the complex plane
Integration and series
- Contour integrals and Cauchy's integral theorem
- Cauchy's integral formula and derivatives
- Taylor and Laurent series; residues at poles
- Residue theorem for evaluating real integrals
- Inverse Laplace transforms via contour integration (introduction)
Conformal mapping and applications
- Conformal maps and angle preservation
- Möbius transformations and standard mappings
- Potential theory and 2D steady-state problems
- Joukowski transformation and airfoil profiles (introduction)
- Branch cuts in transform methods
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$1,162 · Complex variables for engineers · 18 tutoring hrs
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