Week

Section

Section Title

Chapter Title

1-2

1.1

Programming Suggestions

2-Number Representation and Errors

1.2

Review of Taylor Series

2.2

Floating Point Representation

3-4

3.1

Bisection Method

3-Locating Roots of Equations

3.2

Newton’s Method

3.3

Secant Method

5-6

4.1

Polynomial Interpolation

4-Interpolation and Numerical Differentiation

4.2

Errors in Polynomial Interpolation

4.3

Estimating Derivatives and Richardson Extrapolation

Exam I

7-8

5.1

Definite Integral

5-Numerical Integration

5.2

Trapezoid Rule

5.4

An Adaptive Simpson’s Scheme

5.5

Gaussian Quadrature Formulas

9-10

6.1

Naïve Gaussian Elimination

6-Systems of Linear Equations

6.2

Gaussian Elimination with Scaled Partial Pivoting

6.3

Tridiagonal and Banded Systems

6.4

LU Factorization

11

7.1

First-degree and Second-Degree Splines

7-Approximation by Spline Functions

7.2

Natural Cubic Splines

Exam II

12-13

8.1

Taylor Series Methods

10-Smoothing of Data and the Method of Least Squares

8.2

Runge-Kutta Methods

8.3

Stability and Adaptive Runge-Kutta Methods

10.1

The Methods of Least Squares

14-15

12.1

Shooting Method

12-Boundary Value Problems for Ordinary Differential Equations

12.2

A Discretization Method

Exam I

15%

Exam II

15%

Final Exam

30%

Computer Assignment & Homework

40%