## Week 1 (Lecture 1)

Sept 2015 S M Tu W Th F S 30 31 1 2 3 4 5Reading:

- Course Outline
- Introduction

Overton: Chap 1; Cheney and Kincaid: 1.1## Week 2 (Lectures 2)

Sept 2015 S M Tu W Th F S 6 7 8 9 10 11 12Reading:

- Decimal and binary representation
- Computer representation of numbers

Overton: Chapters 2-3.## Week 3 (Lectures 3-4)

Sept 2015 S M Tu W Th F S 13 14 15 16 17 18 19Reading:

- IEEE floating point representation
- Rounding
- Floating point operations
- Exceptional situations

Overton: Chapters 4-7; Cheney and Kincaid: 1.3## Week 4 (Lectures 6-7)

Sept 2015 S M Tu W Th F S 20 21 22 23 24 25 26Reading:

- Floating point in C
- Taylor series
- Approximating a derivative
- Numerical cancellation
- MATLAB demo
- Solving a linear system of equations

- Gaussian elimination with no pivoting

- Overton: Chapters 10-11. Cheney and Kincaid: 1.2, 1.4, 2.1

## Week 5 (Lectures 8-9)

Sept, Oct 2015 S M Tu W Th F S 27 28 29 30 1 2 3Solving a linear system of equations

Reading:

- Gaussian elimination with partial pivoting
- Some theoretical results about GEPP
- Solving tridiagonal systems by GENP

Cheney and Kincaid: 2.2 & 2.3

## Week 6 (Lectures 10-11)

October 2015 S M Tu W Th F S 4 5 6 7 8 9 10Solving a nonlinear equation:Reading:

- Introduction
- The bisection method
- Newton's method

Cheney and Kincaid: 3.1, 3.2## Week 7 (Midterm)

October 2015 S M Tu W Th F S 11 12 13 14 15 16 17

- In class Midterm on Oct 14.
## Week 8 (Lectures 12-13)

October 2015 S M Tu W Th F S 18 19 20 21 22 23 24Solving a nonlinear equation:Reading:

- Newton's method
- The secant method
- Comparsions of the three methods.

Cheney and Kincaid: 3.2, 3.3

## Week 9 (Lectures 14-15)

October, Novemebr 2015 S M Tu W Th F S 25 26 27 28 29 30 31Polynomial interpolation:Reading:

- Vandermonde form
- Lagrange form
- Newton form

Cheney and Kincaid: 4.1, 4.2

## Week 10 (Lectures 16-17)

November 2015 S M Tu W Th F S 1 2 3 4 5 6 7Reading:

- Polynomial interpolation: Newton form, contd.
- Spline interpolation:

- Linear spline
- Cubic spline

Cheney and Kincaid: 6.1, 6.2## Week 11 (Lectures 18-19)

November 2015 S M Tu W Th F S 8 9 10 11 12 13 14Reading:

- Cubic spline
- Least squares approximation

Cheney and Kincaid: 6.3, 9.1## Week 12 (Lectures 20-21)

November 2015 S M Tu W Th F S 15 16 17 18 19 20 21Numerical integration:Reading:

- Rectangle rule
- Midpoint rule
- Trapezoid rule
- Simpson's rule
- Adaptive Simpson's rule

Cheney and Kincaid: 5.1, 5.3.

## Week 13 (Lectures 22-23)

November 2015 S M Tu W Th F S 22 23 24 25 26 27 28Numerical solutions of ordinary differential equations:

- Gaussian quadrature rules
Reading:

- Introduction
- Euler's method
- Types of errors
- Trapezoid-Euler method and Midpoint-Euler method

Cheney and Kincaid: 5.4, 7.1## Week 14 (Lectures 24-25)

November, December 2015 S M Tu W Th F S 29 30 1 2 3 4 5Reading:

- General Taylor series methods
- Runge Kutta Methods
- Review

Cheney and Kincaid: 7.2## Week 15 (Lectures 26)

December 2015 S M Tu W Th F S 6 7 8 9 10 11 12Class time will be office hours