Chapter 1: Overview of 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.