STEM / applied
Engineering mathematics · Undergraduate · Math
Learning objectives from the Engineering mathematics 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 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)
Learning objectives
Click an objective for study materials.
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)
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.
- 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
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$1,162 · Engineering mathematics · 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.