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
Linear Algebraic Equations, Matrices, and Eigenvalues. Scalar ODEs I: Homogeneous Problems. Scalar ODEs II: Nonhomogeneous Problems. Linear Systems of ODEs. Matrix Theory. Geometry, Calculus, and Other Basic Tools. Integral Theorems, Multiple Integrals, and Applications. Numerical Methods I. Series Solutions of ODEs. Fourier Series. PDE Models. Seperation of Variables for PDEs. Numerical Methods II. Integral Transform Methods. Optimization. Calculus of Variations: Problems and Methods. Complex Variables I. Complex Variables II. Nonlinear ODEs. Perturbation Methods. Appendices.