A revision of the market leader, Kreyszig is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, helpful worked examples, and self-contained subject-matter parts for maximum teaching flexibility. The new edition provides invitations - not requirements - to use technology, as well as new conceptual problems, and new projects that focus on writing and working in teams. Table of Contents ORDINARY DIFFERENTIAL EQUATIONS. First-Order Differential Equations. Linear Differential Equations of Second and Higher Order. Systems of Differential Equations, Phase Plane, Qualitative Methods. Series Solutions of Differential Equations. Special Functions. Laplace Transforms. LINEAR ALGEBRA, VECTOR CALCULUS. Linear Algebra: Matrices, Vectors, Determinants. Linear Systems of Equations. Linear Algebra: Matrix Eigenvalue Problems. Vector Differential Calculus. Grad, Div, Curl. Vector Integral Calculus. Integral Theorems. FOURIER ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS. Fourier Series, Integrals, and Transforms. Partial Differential Equations. COMPLEX ANALYSIS. Complex Numbers and Functions. Conformal Mapping. Complex Integration. Power Series, Taylor Series. Laurent Series, Residue Integration. Complex Analysis Applied to Potential Theory. NUMERICAL METHODS. Numerical Methods in General. Numerical Methods in Linear Algebra. Numerical Methods for Differential Equations. OPTIMIZATION, GRAPHS. Unconstrained Optimization, Linear Programming. Graphs and Combinatorial Optimization. PROBABILITY AND STATISTICS. Data Analysis. Probability Theory. Mathematical Statistics. Appendices. Index.