Numerical Methods and Modelling for Engineering - Khoury, Richard; Harder, Douglas Wilhelm; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2016)
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. Uses a "building-block" approach, starting with simpler mathematical tools and using them to develop more and more complex models and methods; Integrates modelling, error measuring, and programming, with numerical methods, in order to give an engineering emphasis to an otherwise mathematical topic; Demonstrates not only how the math and algorithms work but also how they can be used in engineering practice.
Modelling and Errors -- Numerical Representation -- Iteration -- Linear Algebra -- Taylor Series -- Interpolation, Regression, and Extrapolation -- Bracketing -- Root Finding -- Optimization -- Differentiation -- Integration -- Initial Value Problems -- Boundary Value Problems.
Keywords: Engineering mathematics; Engineering -- Data processing; Mathematics -- Data processing; Computer science -- Mathematics; Mathematical and Computational Engineering Applications; Computational Mathematics and Numerical Analysis; Mathematical Applications in Computer Science