Computing for Numerical Methods Using 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 High-Performance Computing.

Dynamic memory allocation.

Allocation for one-dimensional arrays.

Allocation for higher-dimensional 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.

Gauss-Jordan Method.

LU Factorization Techniques.

Crout Method.

Doolittle Method.

Cholesky Method.

Thomas Algorithm.

Iterative Techniques.

Jacobi Method.

Gauss-Seidel 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.

False-point position method.

Newton method.

Secant method.

Fixed-point 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.

Least-square 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.

Runge-Kutta of order 2 method.

Runge-Kutta of order 4 method.

Higher dimensional orders.

Multistep methods: Adams-Bashforth method.

Boundary Value Problems: finite-difference 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.

One-dimensional heat problem.

Linear approximation.

Quadratic approximation.

Two-dimensional problem: triangulation method.

Visual C++ Solution Interface.

Summary.

Programming Exercises.