Mathematical Physics
Essential Math for Physics
The mathematical machinery behind modern physics — from approximation techniques to the symmetry groups that govern the fundamental forces.
Taylor Series
Taylor Expansions for Physics
Taylor series are one of the most powerful tools in theoretical physics. Learn how to approximate functions, understand when approximations break down, and see how nearly every equation in physics is secretly a Taylor expansion.
Small-Angle ApproximationRelativistic ExpansionsPotential Energy Near EquilibriumBinomial SeriesRemainder & ConvergenceGenerating Functions
Group Theory
Group Theory for Physics
Group theory is the mathematical language of symmetry — and symmetry is the deepest organizing principle in physics. From the Standard Model gauge groups to crystal symmetries, understand why SU(3)×SU(2)×U(1) describes all known forces.
Group Axioms & ExamplesLie Groups & AlgebrasSU(2) and SpinSU(3) and Color ChargeRepresentationsStandard Model Structure
More Topics Coming Soon
Differential EquationsComplex AnalysisTensor CalculusFourier AnalysisVariational CalculusLinear AlgebraDifferential GeometryPath Integrals