Engineering mathematics
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Engineering Mathematics — scope drawn from open engineering mathematics sequences and typical US engineering math syllabi.
Vector calculus
- Vectors in R³ — Vectors in R³; dot and cross products
- Vector-valued functions — Vector-valued functions
- Curvature — Curvature
- Partial derivatives and the gradient — Partial derivatives and the gradient
- Directional derivatives — Directional derivatives
- Tangent planes — Tangent planes
- Chain rule for multivariable functions — Chain rule for multivariable functions
Multiple integration and vector fields
- Double and triple integrals — Double and triple integrals; change of variables
- Line integrals and work — Line integrals and work; conservative fields
- Green's theorem in the plane — Green's theorem in the plane
- Surface integrals and flux — Surface integrals and flux
- Divergence theorem and Stokes' theorem (statements and applications) — Divergence theorem and Stokes' theorem (statements and applications)
Differential equations for engineers
- First- and second-order linear ODEs (review and extension) — First- and second-order linear ODEs (review and extension)
- Systems of ODEs and matrix exponential (introduction) — Systems of ODEs and matrix exponential (introduction)
- Laplace transforms for engineering IVPs — Laplace transforms for engineering IVPs
- Fourier series for periodic forcing functions — Fourier series for periodic forcing functions
- Introduction to PDEs — Introduction to PDEs
- Wave equations (overview) — Wave equations (overview)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Vector calculus
Vectors in R³; dot and cross products
Coming soon - Multiple integration and vector fields
Double and triple integrals; change of variables
Coming soon - Differential equations for engineers
First- and second-order linear ODEs (review and extension)
Coming soon
Notes
Undergraduate Engineering Mathematics — scope drawn from open engineering mathematics sequences and typical US engineering math syllabi. Topic outline: `content/topics/undergraduate/engineering_math.json`.