Introducation to Scientific Computing: For Scientists and Engineers

Scientific Computing for Scientists and Engineers is designed to teach undergraduate students relevant numerical methods and required fundamentals in scientific computing.

Most problems in science and engineering require the solution of mathematical problems, most of which can only be done on a computer. Accurately approximating those problems requires solving differential equations and linear systems with millions of unknowns, and smart algorithms can be used on computers to reduce calculation times from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations?

Scientific Computing for Scientists and Engineers covers:

• An introduction to a wide range of numerical methods for linear systems, eigenvalue problems, differential equations, numerical integration, and nonlinear problems;
• Scientific computing fundamentals like floating point representation of numbers and convergence;
• Analysis of accuracy and efficiency;
• Simple programming examples in MATLAB to illustrate the algorithms and to solve real life problems; Exercises to reinforce all topics.

Timo Heister is a professor in the School of Mathematical and Statistical Sciences at Clemson University in Clemson, South Carolina. Heister focuses his research on “Finite elements with a focus on adaptive mesh refinement, large-scale parallelization, and solvers; incompressible flow problems: discretizations and preconditioners; scientific software especially related to finite elements; and various applications in geophysics (mantle convection), material science (crack propagation), and others. He has published numerous books, his most recent being Numerical Analysis – An Introduction, which will be published in 2019.

Leo G. Rebholz is a professor in the School of Mathematical and Statistical Sciences at Clemson University in Clemson, South Carolina. Rebholz focuses his research on computational mathematics and applied analysis. He earned his PhD in Mathematics from Pitt in 2006 and has overseen research for nine PhD students. Rebholz has published numerous titles, his most recent being Numerical Analysis – An Introduction, which will be published in 2019