Theoretical / proof-based
Mathematical physics · Undergraduate · Physics
Learning objectives from the Mathematical physics syllabus, grouped by unit. Click an objective for study materials.
Learning objectives
Click an objective for study materials.
Complex analysis for physics
- Analytic functions and Cauchy–Riemann equations — Analytic functions and Cauchy–Riemann equations
- Contour integrals and residue theorem — Contour integrals and residue theorem
- Branch cuts and multivalued functions — Branch cuts and multivalued functions
- Fourier and Laplace transforms — Fourier and Laplace transforms
- Dispersion relations (Kramers–Kronig intro) — Dispersion relations (Kramers–Kronig intro)
Linear algebra and tensors
- Eigenvalue problems in coupled systems — Eigenvalue problems in coupled systems
- Function spaces and orthonormal bases — Function spaces and orthonormal bases
- Tensor notation and index gymnastics — Tensor notation and index gymnastics
- Metric tensors and raising/lowering indices — Metric tensors and raising/lowering indices
- Rotation groups and representations — Rotation groups and representations
Differential equations
- Sturm–Liouville theory and eigenfunction expansions — Sturm–Liouville theory and eigenfunction expansions
- Bessel, Legendre, and Hermite equations — Bessel, Legendre, and Hermite equations
- Green's functions for inhomogeneous PDEs — Green's functions for inhomogeneous PDEs
- Separation of variables in curvilinear coordinates — Separation of variables in curvilinear coordinates
- Perturbation theory for linear operators — Perturbation theory for linear operators
What 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 analysis for physics
Analytic functions and Cauchy–Riemann equations
Coming soon - Linear algebra and tensors
Eigenvalue problems in coupled systems
Coming soon - Differential equations
Sturm–Liouville theory and eigenfunction expansions
Coming soon
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$1,162 · Mathematical physics · 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.