Exploring Odes

Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more examples as templates for further exploration.?

Discusses the direction in which the field of differential equations, and its teaching, is going.

This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the field’s most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.

To learn to program is to be initiated into an entirely new way of thinking about engineering, mathematics, and the world in general. Computation is integral to all modern engineering disciplines, so the better you are at programming, the better you will be in your chosen field. The author departs radically from the typical presentation by teaching concepts and techniques in a rigorous manner rather than listing how to use libraries and functions. He presents pointers in the very first chapter as part of the development of a computational model that facilitates an ab initio presentation of subjects such as function calls, call-by-reference, arrays, the stack, and the heap. The model also allows students to practice the essential skill of memory manipulation throughout the entire course rather than just at the end. As a result, this textbook goes further than is typical for a one-semester course -- abstract data types and linked lists, for example, are covered in depth. The computational model will also serve students in their adventures with programming beyond the course: instead of falling back on rules, they can think through the model to decide how a new programming concept fits with what they already know. The book is appropriate for undergraduate students of engineering and computer science, and graduate students of other disciplines. It contains many exercises integrated into the main text, and the author has made the source code available online.

A Modern Introduction to Differential Equations, Third Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical and numerical aspects of first-order equations, including slope fields and phase lines. The comprehensive resource then covers methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients, systems of linear differential equations, the Laplace transform and its applications to the solution of differential equations and systems of differential equations, and systems of nonlinear equations. Throughout the text, valuable pedagogical features support learning and teaching. Each chapter concludes with a summary of important concepts, and figures and tables are provided to help students visualize or summarize concepts. The book also includes examples and updated exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering. Offers an accessible and highly readable resource to engage students Introduces qualitative and numerical methods early to build understanding Includes a large number of exercises from biology, chemistry, economics, physics and engineering Provides exercises that are labeled based on difficulty/sophistication and end-of-chapter summaries

Problem-solving journal at the senior secondary and university undergraduate levels for those who practice or teach mathematics. Primarily educational in purpose, it also serves those who read it for professional, cultural and recreational reasons.