1Preliminary algebra -- 1 -- 2 Preliminary calculus -- 42 -- 3 Complex numbers and hyperbolic functions -- 86 -- 4 Series and limits -- 118 -- 5 Partial differentiation -- 154 -- 6 Multiple integrals -- 190 -- 7 Vector algebra -- 216 -- 8 Matrices and vector spaces -- 246 -- 9 Normal modes -- 322 -- 10 Vector calculus -- 340 -- 11 Line, surface and volume integrals -- 383 -- 12 Fourier series -- 421 -- 13 Integral transforms -- 439 -- 14 First-order ordinary differential equations -- 474 -- 15 Higher-order ordinary differential equations -- 496 -- 16 Series solutions of ordinary differential equations -- 537 -- 17 Eigenfunction methods for differential equations -- 581 -- 18 Partial differential equations: general and particular solutions -- 608 -- 19 Partial differential equations: separation of variables and other methods -- 646 -- 20 Complex variables -- 710 -- 21 Tensors -- 776 -- 22 Calculus of variations -- 834 -- 23 Integral equations -- 862 -- 24 Group theory -- 883 -- 25 Representation theory -- 918 -- 26 Probability -- 961 -- 27 Statistics -- 1064 -- 28 Numerical methods -- 1148 -- Appendix Gamma, beta and error functions -- 1201.