STEM / applied
Advanced engineering mathematics · Undergraduate · Math
Learning objectives from the Advanced 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 Advanced Engineering Mathematics — scope drawn from open advanced engineering math outlines (DE, linear algebra, transforms) and typical US syllabi.
Integral transforms and special functions
- Laplace transforms — Laplace transforms
- Convolution — Convolution
- Inverse Laplace transforms — Inverse Laplace transforms
- Bromwich integrals (introduction) — Bromwich integrals (introduction)
- Fourier transforms — Fourier transforms
- Discrete transforms — Discrete transforms
- Bessel functions — Bessel functions
- Orthogonal expansions (introduction) — Orthogonal expansions (introduction)
- Legendre polynomials — Legendre polynomials
- Sturm–Liouville problems (overview) — Sturm–Liouville problems (overview)
Partial differential equations
- Classification — Classification
- Canonical forms of second-order PDEs — Canonical forms of second-order PDEs
- Separation of variables for heat and wave equations — Separation of variables for heat and wave equations
- Laplace equations — Laplace equations
- Nonhomogeneous PDEs — Nonhomogeneous PDEs
- Eigenfunction expansions — Eigenfunction expansions
- Green's functions for boundary-value problems (introduction) — Green's functions for boundary-value problems (introduction)
- Method of characteristics for first-order PDEs (brief) — Method of characteristics for first-order PDEs (brief)
Complex analysis for applications
- Analytic functions — Analytic functions
- Cauchy–Riemann equations (applied view) — Cauchy–Riemann equations (applied view)
- Contour integration — Contour integration
- Residue calculus for real integrals — Residue calculus for real integrals
- Conformal mapping in potential theory (introduction) — Conformal mapping in potential theory (introduction)
- Branch cuts — Branch cuts
- Multivalued functions in engineering models — Multivalued functions in engineering models
- Inverse problems — Inverse problems
- Analytic continuation (overview) — Analytic continuation (overview)
Learning objectives
Click an objective for study materials.
Integral transforms and special functions
- Laplace transforms — Laplace transforms
- Convolution — Convolution
- Inverse Laplace transforms — Inverse Laplace transforms
- Bromwich integrals (introduction) — Bromwich integrals (introduction)
- Fourier transforms — Fourier transforms
- Discrete transforms — Discrete transforms
- Bessel functions — Bessel functions
- Orthogonal expansions (introduction) — Orthogonal expansions (introduction)
Partial differential equations
- Classification — Classification
- Canonical forms of second-order PDEs — Canonical forms of second-order PDEs
- Separation of variables for heat and wave equations — Separation of variables for heat and wave equations
- Laplace equations — Laplace equations
- Nonhomogeneous PDEs — Nonhomogeneous PDEs
- Eigenfunction expansions — Eigenfunction expansions
- Green's functions for boundary-value problems (introduction) — Green's functions for boundary-value problems (introduction)
- Method of characteristics for first-order PDEs (brief) — Method of characteristics for first-order PDEs (brief)
Complex analysis for applications
- Analytic functions — Analytic functions
- Cauchy–Riemann equations (applied view) — Cauchy–Riemann equations (applied view)
- Contour integration — Contour integration
- Residue calculus for real integrals — Residue calculus for real integrals
- Conformal mapping in potential theory (introduction) — Conformal mapping in potential theory (introduction)
- Branch cuts — Branch cuts
- Multivalued functions in engineering models — Multivalued functions in engineering models
- Inverse problems — Inverse problems
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.
- Integral transforms and special functions
Laplace transforms
Coming soon - Partial differential equations
Classification
Coming soon - Complex analysis for applications
Analytic functions
Coming soon
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$1,162 · Advanced engineering mathematics · 18 tutoring hrs
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