Complex variables for engineers
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Complex Variables for Engineers — scope drawn from open complex variables engineering texts and typical US engineering complex-variables syllabi.
Complex arithmetic and functions
- Complex numbers and polar form — Complex numbers and polar form
- Euler's formula — Euler's formula
- Complex functions — Complex functions
- Mappings in the plane — Mappings in the plane
- Limits and continuity — Limits and continuity
- Analyticity (engineering emphasis) — Analyticity (engineering emphasis)
- Cauchy–Riemann equations — Cauchy–Riemann equations
- Harmonic conjugates — Harmonic conjugates
- Elementary functions: exp, log, sin, cos in the complex plane — Elementary functions: exp, log, sin, cos in the complex plane
Integration and series
- Contour integrals — Contour integrals
- Cauchy's integral theorem — Cauchy's integral theorem
- Cauchy's integral formula — Cauchy's integral formula
- Derivatives — Derivatives
- Taylor and Laurent series — Taylor and Laurent series; residues at poles
- Residue theorem for evaluating real integrals — Residue theorem for evaluating real integrals
- Inverse Laplace transforms via contour integration (introduction) — Inverse Laplace transforms via contour integration (introduction)
Conformal mapping and applications
- Conformal maps and angle preservation — Conformal maps and angle preservation
- Möbius transformations — Möbius transformations
- Standard mappings — Standard mappings
- Potential theory — Potential theory
- 2D steady-state problems — 2D steady-state problems
- Joukowski transformation — Joukowski transformation
- Airfoil profiles (introduction) — Airfoil profiles (introduction)
- Branch cuts in transform methods — Branch cuts in transform methods
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Complex arithmetic and functions
Complex numbers and polar form
Coming soon - Integration and series
Contour integrals
Coming soon - Conformal mapping and applications
Conformal maps and angle preservation
Coming soon
Notes
Undergraduate Complex Variables for Engineers — scope drawn from open complex variables engineering texts and typical US engineering complex-variables syllabi. Topic outline: `content/topics/undergraduate/complex_variables.json`.