This textbook for undergraduates across the range of engineering has a strong emphasis on visualization and the methods and tools needed across the whole of engineering. The book's website provides dynamic and interactive codes in Mathematica to accompany the examples for the reader to explore on their own.

Brian Vick is an associate professor at Virginia Tech in US, and a long time teacher and researcher. His style has been developed from teaching a variety of engineering and mathematical courses in the areas of heat transfer, thermodynamics, engineering design, computer programming, numerical analysis, and system dynamics at both the undergraduate and graduate levels.

1 Overview 1

2 Physical Processes 9

3 Modeling of Physical Processes 19

4 Calculus 37

5 Linear Algebra 77

6 Nonlinear Algebra: Root Finding 99

7 Introduction to Ordinary Differential Equations 119

8 Laplace Transforms 139

9 Numerical Solutions of Ordinary Differential Equations 151

10 First-Order Ordinary Differential Equations 169

11 Second-Order Ordinary Differential Equations 193