Course Content
The text book for this course is
`Applied Numerical Analysis' by Curtis F. Gerald and Patrick O. Wheatley,
sixth edition, Addison-Wesley, 1999.
In addition, consult
the lecture notes.
Below are some supplemental materials to the lectures.
0. Numerical Computing and Computers
L-1 What is numerical analysis?
L-2 Bisection Method; Errors
L-3 Floating-Point Arithmetic
L-4 Floating-Point Arithmetic (continued); Measuring Efficiency
1. Solving Nonlinear Equations
L-5 The secant method
L-6 Newton's method and Fixed-Point Iterations
L-7 Errors and Convergence
L-8 Roots of Polynomials
L-9 Multiple Roots; Golden Section Search
2. Solving Sets of Equations
L-10 Introduction to Linear Algebra
L-11 Elimination Methods
L-12 The LU decomposition
L-13 The cost of elimination
L-14 Improve the stability by pivoting
L-15 Norms and Condition Numbers
L-16 Condition Numbers
L-17 Multidimensional Newton Method
L-18 Review for Exam I
L-19 Exam I:
(a)
+ answers
(b)
+ answers
(c)
+ answers
3. Interpolation and Curve Fitting
L-20 Lagrange and Neville Interpolation
L-21 Divided Differences
L-22 Least Squares Approximation
L-23 Errors and Complexity
4. Approximation of Functions
L-24 Chebyshev polynomials
L-25 Padé approximations
5. Numerical Differentiation and Numerical Integration
L-26 Interpolation for Derivatives and Integrals
L-27 Extrapolation and Newton-Cotes integration formulas
L-28 Composite Rules and Romberg Integration
L-29 Gaussian Quadrature
L-30 Fast Fourier Transform
L-31 Errors
L-32 Review for Exam II
with answers
L-33 Exam II:
(a)
+ answers
(b)
+ answers
(c)
+ answers
6. Numerical Solution of ODEs
L-34 Taylor Series and Euler Methods
L-35 Runge-Kutta and Multistep Methods
L-36 Predictor-Corrector Methods
L-37 Convergence and Stability
7. Boundary-Value Problems
L-38 The Shooting Method
L-39 Finite Differences
L-40 Boundary Derivative Conditions
L-41 Characteristic-Value Problems
Review
L-42 Review of Chapters 0, 1, and 2
+ partial answers
L-43 Review of Chapters 3, 4, and 5
+ answers
L-44 Review of Chapters 6 and 7
+ partial answers