ABSTRACT

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes.

Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

chapter 1|18 pages

The Process of Mathematical Modeling

chapter 3|42 pages

Solutions of Systems of ODEs

chapter 4|39 pages

Stability Theory

chapter 5|36 pages

Bifurcations and Chaos

chapter 6|15 pages

Perturbations

chapter 9|38 pages

Variational Principles

chapter 10|49 pages

Modeling Fluid Flow

chapter 11|11 pages

Modeling Geophysical Phenomena

chapter 12|15 pages

Stochastic Modeling

chapter 13|27 pages

Answers to Problems