1st Edition
Mathematical Objects in C++ Computational Tools in A Unified Object-Oriented Approach
NUMBERS
Natural Numbers
Integer Numbers
Rational Numbers
Real Numbers
Complex Numbers
GEOMETRICAL OBJECTS
Euclidean Geometry
Analytic Geometry
COMPOSITE MATHEMATICAL OBJECTS
Sets
Vectors and Matrices
Multilevel Objects
Graphs
Polynomials
INTRODUCTION TO C
Basics of Programming
Recursion
INTRODUCTION TO C++
Objects
Vectors and Matrices
Dynamic Vectors and Lists
IMPLEMENTATION OF COMPUTATIONAL OBJECTS
Trees
Graphs
Sparse Matrices
Meshes
Triangulation
THREE-DIMENSIONAL APPLICATIONS
Mesh of Tetrahedra
Polynomials
Sparse Polynomials
Stiffness and Mass Matrices
Splines
Appendix: Solutions of Exercises
References
Index
Exercises appear at the end of each chapter.
Biography
Yair Shapira is in the computer science department at Technion. His research interests include multigrid, preconditioning, and numerical methods.
"This is an exciting book on mathematics on one hand and computer programming on the other, and the reader can concentrate on one of the topics or both. The mathematics part focuses on teaching mathematics through constructive algorithms, ready for computer implementation. I believe this is the future view of these classical mathematical subjects. Many will find this book a major refresher of the mathematics literature. The programming part of the book serves as a very good introduction to C and C++, using meaningful and motivating examples from mathematics. The book is full of useful exercises of various difficulty. This fact makes the book very suitable as a textbook for a mathematics or computer science course."
—Hans Petter Langtangen, Simula Research Laboratory and University of Oslo, Norway
