Numerical analysis : mathematics of scientific computing / David Kincaid, Ward Cheney.

CONTENT

1. Mathematical preliminaries
1.0 Introduction
1.1 Basic concepts and taylor theorem
1.2 Order of convergence and additional basic concepts
1.3 Difference equations

2. Computer arithmetic
2.0 Introduction
2.1 Floating point numbers and round off errors
2.2 Absolute and relative errors : loss of significance
2.3 Stable and unstable computation : conditioning

3. Solution of nonlinear equations
3.0 Introduction
3.1 Bisection ( interval halving ) method
3.2 Newton's method
3.3 Secant method
etc

4. Solving system of linear equation
4.0 Introduction
4.1 Matrix algebra
4.2 LU and chlolesky factorization
4.3 Pivoting and constructing an algorithms
ect
5. Selected topics in numerical linear Algebra
5.0 Review of basic concepts
5.1 Matrix eigenvalue problem : power method
5.2 Shur's and gershorin theorems
etc

6. Approximation function
6.0Introduction
6.1. Polynomial interpolation
6.2 Divided differences
6.3 Hermite interpolation
etc

7. Numerical differentiation and integration
7.1 Numerical differentiation and richarson extrapolation
7.2 Numerical intergration based on interpolation
7.3 Gaussian quadrature
etc

8. Numerical solution of ordinary differential equations
8.0 Introduction
8.1 The existence and uniqueness of solutions
8.2 Taylor seirs method
8.3 Runger- kutte methods
etc

9. Numerical solution of partial differential equations
9.0 Introduction
9.1 Parabolic equations : Explicit methods
9.2 Parabolic equations : implicit methods
9.3 Problems without time dependence : finite differenc
etc

10 : Linear programming and related topics
10.1 Convexity and linear in equalities
10.2 Linear in equalities
10.3 Linear programming
10.4 The simplex algorithms

11. Optimisation
11.0 Introduction
11.1 One variable case
11.2 Descent methods
11.3 Analysis of quadratic objective functions
etc

Bibliography : p745- 769 ._ Index : p 771-788