Advanced Engineering Mathematics / Erwin Kreyszig.

Part A. Ordinary differential equations (ODEs) -- First-order ODEs -- Linear ODEs of second and higher order -- Systems of ODEs. Phase plane, qualitative methods -- Series solutions of ODEs -- Laplace transform method for solving ODEs -- Part B. Linear algebra, vector calculus -- Matrices, vectors, determinants, linear systems of equations -- Matrix Eigenvalue problems -- Vector differential calculus grad, div, curl -- Vector integral calculus. Integral theorems -- Part C. Fourier analysis and partial differential equations (PDEs) -- Fourier series, integrals, and transforms -- Partial differential equations (PDEs) -- Part D. Complex analysis -- Complex numbers and functions. Conformal mapping -- Complex integration -- Power series, Taylor series -- Laurent series. Residue integration -- Complex analysis in potential theory -- Part E. Numeric analysis -- Numerics in general -- Numeric linear algebra -- Numerics for ODEs and PDEs -- Part F. Optimization, graphs -- Unconstrained optimization. Linear programming -- Part G. Probability and statistics -- Data analysis. Probability theory -- Mathematical statistics.

Aimed at the junior level courses in maths and engineering departments, this edition of the well known text covers many areas such as differential equations, linear algebra, complex analysis, numerical methods, probability, and more.