This book presents an introduction to numerical methods targeted at undergraduate materials scientists and engineers. What we hope to achieve through this text is a situation where the model formulation proceeds without regard for the ease of numerical solution. Once the model is rigorously formulated, the appropriate numerical solution is then identified. Thus the science guides the numerical techniques, rather than the other way around. The philosophy espoused in this book is to equip the student with a compact but broadly applicable set of practical problem-solving tools such that the student emerges at the end of the course with the belief, "If I can formulate the problem as a mathematical model, I can solve it."