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Mathematics

Applied Mathematics

13 chapters, from series and complex numbers to PDEs and probability — each one worked through with real applications.

  1. 1Infinite Series and Power SeriesComing soon
  2. 2Complex NumbersBasics, infinite and power series · Trig functions · Euler formulaComing soon
  3. 3Rudiments of Linear AlgebraLinear equations · Row reduction · Matrix operations · Eigenvalues, eigenvectors, and diagonalizationComing soon
  4. 4Partial DerivativesTotal differential · Taylor and power series in several variables · Chain rule · Lagrange multipliersComing soon
  5. 5Multiple Integration and Vector AnalysisMultiple integrals · The Jacobian and change of variables · Inner, cross, and triple products · Gradient and line integrals · Green’s theorem, the divergence theorem, and Stokes’ theoremComing soon
  6. 6Fourier Series and TransformsComing soon
  7. 7Ordinary Differential Equations IConstant coefficient differential equations and the Laplace transformComing soon
  8. 8Variational CalculusEuler equation, Lagrange’s equation, and some example problemsComing soon
  9. 9Assorted Special FunctionsGamma, Beta, and error functions · Asymptotic series and Stirling’s formulaComing soon
  10. 10Ordinary Differential Equations IISeries solution of differential equations · Orthogonal functions, Legendre polynomials, Bessel functions · Other classes of orthogonal functions and their ODEsComing soon
  11. 11Partial Differential EquationsBasic types of PDEs · Model problems (heat flow, vibrating string, steady state temperature)Coming soon
  12. 12Complex Function TheoryContour integrals and Cauchy’s theorem · Laurent series and the residue calculus · Conformal mapsComing soon
  13. 13Probability and StatisticsSample spaces and random variables · Discrete and continuous distributions · The binomial, the Gaussian, and the Poisson distribution · Sampling and confidence intervals1 entry