Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system. Ordinary Differential Equations and Linear Algebra: A Systems Approach systematically develops the linear algebra needed to solve systems of ODEs and includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters). It emphasizes mathematical modeling and contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modeling of a system, the solution of the model, and the resulting physical description.
This is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations and will be most appropriate for upper level undergraduate and graduate students in the fields of ...
The contents of the book have been made user-friendly through concise useful theoretical discussions and numerous illustrative examples practical and pathological.
Written for beginners, this well organized introduction promotes a solid understanding of differential equations that is flexible enough to meet the needs of many different disciplines. With less emphasis on...
Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more.
The summation in (43.37) is now the same as the right side of L. (c) of (43.2). B. Integral Property of Laguerre Polynomials. Theorem 43.4. Let Losa), L1(c), L2(a), . . . , be Laguerre polynomial solutions of (43.1).
Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters.
This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students.
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students.
The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations.
Problems at the end of each chapter and two Appendixes on special topics enrich the text.