Written for high school students who have some experience with computation and an interest in math modeling, this handbook is designed to take you from basic graphic calculator or spreadsheet experience to the next level, which includes programming basics, working with large data sets, and visualization techniques. The handbook is also written for ......
A great deal can be learned through modeling and mathematical analysis about real-life phenomena, even before numerical simulations are used to accurately portray the specific configuration of a situation. Scientific computing also becomes more effective and efficient if it is preceded by some preliminary analysis. These important advantages of ......
This introductory textbook grew out of several courses in linear algebra given over more than a decade and includes such helpful material as: constructive discussions about the motivation of fundamental concepts many worked-out problems in each chapter, and topics rarely covered in typical linear algebra textbooks. The authors use abstract ......
Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more ......
The mathematical challenges coming from the social and behavioral sciences differ significantly from typical applied mathematical concerns. ""Change,"" for instance, is ubiquitous, but without knowing the fundamental driving force, standard differential and iterative methods are not appropriate. Although differing forms of aggregation are widely ......
This book provides a thorough and careful introduction to the theory and practice of scientific computing at an elementary, yet rigorous, level, from theory via examples and algorithms to computer programs. The original FORTRAN programs have been rewritten in MATLAB and now appear in a new appendix and online, offering a modernized version of this ......
Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains ......
"If mathematical modeling is the process of turning real phenomena into mathematical abstractions, then numerical computation is largely about the transformation from abstract mathematics to concrete reality. Many science and engineering disciplines have long benefited from the tremendous value of the correspondence between quantitative ......
Highly oscillatory phenomena range across numerous areas in science and engineering and their computation represents a difficult challenge. A case in point is integrals of rapidly oscillating functions in one or more variables. The quadrature of such integrals has been historically considered very demanding. Research in the past 15 years (in which ......
