Numerical Methods and Modelling for Engineering

✍ Scribed by Richard Khoury, Douglas Wilhelm Harder (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 343
• Edition: 1
• Category: Library

✦ Synopsis

This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems.

✦ Table of Contents

Front Matter....Pages i-xvii
Modelling and Errors....Pages 1-12
Numerical Representation....Pages 13-30
Iteration....Pages 31-38
Linear Algebra....Pages 39-65
Taylor Series....Pages 67-75
Interpolation, Regression, and Extrapolation....Pages 77-113
Bracketing....Pages 115-118
Root-Finding....Pages 119-156
Optimization....Pages 157-189
Differentiation....Pages 191-217
Integration....Pages 219-249
Initial Value Problems....Pages 251-284
Boundary Value Problems....Pages 285-306
Back Matter....Pages 307-332

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering; Computational Mathematics and Numerical Analysis; Math Applications in Computer Science