Lecture Content, Notes and Reading

## Week 1 (Lecture 1)

```   Sept 2015
S  M Tu W Th  F  S
30 31  1 2  3  4  5
```
• 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 12
```
• 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 19
```
• 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 26
```
• 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  3
```
Solving a linear system of equations
• 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 10
```
Solving a nonlinear equation:
• 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 24
```
Solving a nonlinear equation:
• 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 31
```
Polynomial interpolation:
• 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  7
```
• 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 14
```
• 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 21
```
Numerical integration:
• 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 28
```
• Gaussian quadrature rules
Numerical solutions of ordinary differential equations:
• 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  5
```
• General Taylor series methods
• Runge Kutta Methods
• Review
```   December 2015
` `