This textbook bridges the gap between introductory and advanced numerical methods for engineering students. The book initially introduces readers to numerical methods before progressing to linear and nonlinear equations. Next, the book covers the topics of interpolation, curve fitting and approximation, integration, differentiation and differential equations. The book concludes with a chapter on advanced mathematical analysis which explains methods for finite difference, method of moments and finite elements. The book introduces readers to key concepts in engineering such as error analysis, algorithms, applied mathematics with the goal of giving an understanding of how to solve engineering problems using computational methods. Each of the featured topics is explained with sufficient detail while retaining the usual introductory nuance. This blend of beginner-friendly and applied information, along with reference listings makes the textbook useful to students of undergraduate and introductory graduate courses in mathematics and engineering.