Computing for Numerical Methods Using Visual C++
Computing for Numerical Methods Using Visual C++
ISBN: 9780470192627
Dec 2007
472 pages
$125.99
Description
A visual, interdisciplinary approach to solving problems in numerical methodsComputing for Numerical Methods Using Visual C++ fills the need for a complete, authoritative book on the visual solutions to problems in numerical methods using C++. In an age of boundless research, there is a need for a programming language that can successfully bridge the communication gap between a problem and its computing elements through the use of visualization for engineers and members of varying disciplines, such as biologists, medical doctors, mathematicians, economists, and politicians. This book takes an interdisciplinary approach to the subject and demonstrates how solving problems in numerical methods using C++ is dominant and practical for implementation due to its flexible language format, objectoriented methodology, and support for high numerical precisions.
In an accessible, easytofollow style, the authors cover:

Numerical modeling using C++

Fundamental mathematical tools

MFC interfaces

Curve visualization

Systems of linear equations

Nonlinear equations

Interpolation and approximation

Differentiation and integration

Eigenvalues and Eigenvectors

Ordinary differential equations

Partial differential equations
This readerfriendly book includes a companion Web site, giving readers free access to all of the codes discussed in the book as well as an equation parser called ""MyParser"" that can be used to develop various numerical applications on Windows. Computing for Numerical Methods Using Visual C++ serves as an excellent reference for students in upper undergraduate and graduatelevel courses in engineering, science, and mathematics. It is also an ideal resource for practitioners using Microsoft Visual C++.
Language style and organization.
Data types, variables.
Loops and branches.
Array, pointer, function, structure.
Classes and objects.
Inheritance, polymorphism, encapsulation.
Complexity analysis.
Chapter 2: Visual C++ Methods.
MFC library .
Fundamental interface tools.
Text displays.
Graphics and images.
Writing the first program.
Chapter 3: Fundamental Mathematical Tools.
C++ for HighPerformance Computing.
Dynamic memory allocation.
Allocation for onedimensional arrays.
Allocation for higherdimensional arrays.
Case Study: Matrix multiplication problem.
Matrix elimination problems.
Vector and matrix norms.
Row operations.
Matrix reduction to triangular form.
Computing the determinant of a matrix.
Computing the inverse of a matrix.
Matrix algebra.
Data passing between functions.
Matrix addition and subtraction.
Matrix multiplication.
Matrix inverse.
Putting the pieces together.
Algebra of complex numbers.
Addition and subtraction.
Multiplication.
Conjugate.
Division.
Inverse of a complex number.
Putting the pieces together.
Number Sorting.
Programming Exercises.
Chapter 4: System of Linear Equations.
Systems of Linear Systems.
Existence of Solutions.
Elimination Techniques.
Gauss Elimination Method.
Gauss Elimination with Partial Pivoting.
GaussJordan Method.
LU Factorization Techniques.
Crout Method.
Doolittle Method.
Cholesky Method.
Thomas Algorithm.
Iterative Techniques.
Jacobi Method.
GaussSeidel Method.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 5: Nonlinear Equations.
Iterative methods: convergence, stability.
Background: existence of solution, MVT, errors, etc..
Bisection method.
Falsepoint position method.
Newton method.
Secant method.
Fixedpoint iterative method.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 6: Interpolation and Approximation.
Concepts, existence, stability.
Lagrange.
Newton methods: forward, backward.
Stirling method.
Cubic spline interpolation.
Leastsquare approximation.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 7: Differentiation and Integration.
Taylor series.
Newton methods (forward, backward, central).
Trapezium method.
Simpson method.
Simpson 3/8 method.
Gauss quadrature.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 8: Eigenvalues and Eigenvectors.
Characteristic polynomials.
Power method.
Power method with shifting.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 9: Ordinary Differential Equations.
Existence, uniqueness, stability, convergence.
IVP: Taylor method.
Euler method.
RungeKutta of order 2 method.
RungeKutta of order 4 method.
Higher dimensional orders.
Multistep methods: AdamsBashforth method.
Boundary Value Problems: finitedifference method.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 10: Partial Differential Equations.
Existence, uniqueness, stability, convergence.
Elliptic problem: Laplace equation.
Elliptic problem: Poisson equation.
Parabolic problem: heat equation.
Hyperbolic problem: wave equation.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 11: Finite Element Methods.
Onedimensional heat problem.
Linear approximation.
Quadratic approximation.
Twodimensional problem: triangulation method.
Visual C++ Solution Interface.
Summary.
Programming Exercises.