Mathematical physics
Undergraduate · Physics
Syllabus focus
Standard syllabus · Theoretical / proof-based
Pricing calculator
Choose materials, tutoring, or both — or book a single session as needed. Customize your plan on the subscribe page.
Billed in 15-minute increments (15-minute minimum, up to 4 hours). No subscription required.
$60.00 · 60 min · Undergraduate · Online ($60/hr)
Book through intake or schedule a session.
Topics typically covered
Standard syllabus
Complex analysis for physics
- Analytic functions and Cauchy–Riemann equations
- Contour integrals and residue theorem
- Branch cuts and multivalued functions
- Fourier and Laplace transforms
- Dispersion relations (Kramers–Kronig intro)
Linear algebra and tensors
- Eigenvalue problems in coupled systems
- Function spaces and orthonormal bases
- Tensor notation and index gymnastics
- Metric tensors and raising/lowering indices
- Rotation groups and representations
Differential equations
- Sturm–Liouville theory and eigenfunction expansions
- Bessel, Legendre, and Hermite equations
- Green's functions for inhomogeneous PDEs
- Separation of variables in curvilinear coordinates
- Perturbation theory for linear operators
Theoretical / proof-based
Rigorous methods
- Self-adjoint operators on Hilbert spaces
- Spectral decomposition and completeness
- Distribution theory and delta functions
- Variational principles with constraints
- Asymptotic analysis of integrals (steepest descent)
Group theory
- Lie algebras from commutators
- SU(2) and angular momentum addition
- Casimir operators and irreducible reps
- Young tableaux for identical particles (intro)
- Application to crystal point groups
Advanced PDE theory
- Well-posedness and boundary value problems
- Maximum principles for elliptic equations
- Method of characteristics for hyperbolic PDEs
- Integral equations and Fredholm theory sketch
- Conformal mapping techniques
Notes
Topics reflect common upper-division physics syllabi at US colleges and universities. Prerequisites, lab pairing, and mathematical depth vary by department.