Standard syllabus
Complex variables for engineers · Undergraduate · Math
Learning objectives from the Complex variables for engineers syllabus, grouped by unit. Click an objective for study materials.
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
Learning objectives
Click an objective for study materials.
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
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
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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$1,162 · Complex variables for engineers · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.