Includes index.

Linear Algebraic Equations, Matrices, and Eigenvalues -- Matrix Theory -- Scalar ODEs I: Homogeneous Problems -- Scalar ODEs II: Nonhomogeneous Problems -- Linear Systems of ODEs -- Geometry, Calculus, and Other Tools -- Integral Theorems, Multiple Integrals, and Applications -- Numerical Methods -- Fourier Series -- Partial Differential Equations Models -- Separation of Variables for PDEs -- Numerical Methods II -- Optimization -- Calculus of Variations -- Functions of a Complex Variable -- Conformal Mappings and the Laplace Equation -- Integral Transform Methods -- Nonlinear Ordinary Differential Equations -- Key Terms

This self-contained, thorough text addresses the mathematical knowledge gaps of advanced undergraduate and beginning graduate students in engineering. It extends their knowledge of previously studied topics and introduces new topics. The text begins with coverage of linear algebra progressing to calculus of variations. It covers all the core material, including ODEs, matrix algebra, Fourier series and transforms, numerical methods, and PDEs. After studying this book, students will be mathematically prepared for engineering courses at the graduate level. Ancillary materials are available with qualifying course adoption