## Content

```	1 TAYLOR POLYNOMIALS
1.1 The Taylor polynomial
1.2 The error in Taylor's polynomial
1.3 Polynomial evaluation

2 COMPUTER REPRESENTATION OF NUMBERS
2.1 The binary number system
2.2 Floating-point numbers

3 ERROR
3.1 Errors: definitions, sources, examples
3.2 Propagation of error
3.3 Summation

4 ROOTFINDING
4.1 The bisection method
4.2 Newton's method
4.3 Secant method
4.4 Ill-behaved rootfinding problems

5 INTERPOLATION
5.1 Polynomial interpolation
5.2 Divided differences
5.3 Error in polynomial interpolation
5.4 Interpolation using spline functions

6 APPROXIMATION OF FUNCTIONS
6.1 The best approximation problem
6.2 Chebyshev polynomials
6.3 A near-minimax approximation method

7 NUMERICAL INTEGRATION AND DIFFERENTIATION
7.1 The trapezoidal and Simpson rules
7.2 Error formulas
7.3 Gaussian numerical integration
7.4 Numerical differentiation

8 SOLUTION OF SYSTEMS OF LINEAR EQUATIONS
8.1  Systems of linear equations
8.2  Gaussian elimination
8.3  Matrix arithmetic
8.4  The LU factorization
8.5  Error in solving linear systems
8.6  Least squares data fitting
8.7  The eigenvalue problem

9 THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS
9.1	Theory of differential equations: An introduction
9.2	Euler's method
9.3	Convergence analysis of Euler's method
9.4	Taylor and Runge-Kutta methods
9.5	Multistep methods
9.6	Stability of numerical methods
9.7	Systems of differential equations

Appendix A Mean Value Theorems
Appendix B Mathematical Formulas
Appendix C Numerical Analysis Software Packages
ANSWERS TO SELECTED PROBLEMS
REFERENCES
INDEX
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