Week 1 (Lecture 1)
Sept 2015
S M Tu W Th F S
30 31 1 2 3 4 5
 Course Outline
 Introduction
Reading:
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
Reading:
Overton: Chapters 23.

Week 3 (Lectures 34)
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
Reading:
Overton: Chapters 47; Cheney and Kincaid: 1.3

Week 4 (Lectures 67)
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
Reading:
 Overton: Chapters 1011. Cheney and Kincaid: 1.2, 1.4, 2.1

Week 5 (Lectures 89)
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
Reading:
Cheney and Kincaid: 2.2 & 2.3

Week 6 (Lectures 1011)
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
Reading:
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 1213)
October 2015
S M Tu W Th F S
18 19 20 21 22 23 24
 Solving a nonlinear equation:
 Newton's method, ctd.
 The secant method
 Comparsions of the three methods.
 Polynomial interpolation:
Reading:
Cheney and Kincaid: 3.3, 4.1.

Week 9 (Lectures 1415)
October, Novemebr 2015
S M Tu W Th F S
25 26 27 28 29 30 31
Polynomial interpolation:
 Lagrange form
 Newton form
Reading:
Cheney and Kincaid: 4.2

Week 10 (Lectures 1617)
November 2015
S M Tu W Th F S
1 2 3 4 5 6 7
Spline interpolation:
 Linear spline
 Cubic spline
Reading: Cheney and Kincaid: 6.1, 6.2

Week 11 (Lectures 1819)
November 2015
S M Tu W Th F S
8 9 10 11 12 13 14
 Least squares approximation
 Numerical integration:
 Rectangle rule
 Midpoint rule
Reading: Cheney and Kincaid: 9.1, 5.1

Week 12 (Lectures 2021)
November 2015
S M Tu W Th F S
15 16 17 18 19 20 21
Numerical integration:
 Trapezoid rule
 Simpson's rule
 Adaptive Simpson's rule
 Gaussian quadrature rules
Reading: Cheney and Kincaid: 5.3, 5.4.

Week 13 (Lectures 2223)
Necember 2015
S M Tu W Th F S
22 23 24 25 26 27 28
 Gaussian quadrature rules, ctd.
 Numerical solutions of ordinary differential equations:
 Introduction
 Euler's method
 Types of errors
 TrapezoidEuler method and MidpointEuler method
Reading: Cheney and Kincaid: 7.1

Week 14 (Lectures 2425)
November, December 2015
S M Tu W Th F S
29 30 1 2 3 4 5
 General Taylor series methods
 Runge Kutta Mathods
 Review
Reading: Cheney and Kincaid: 7.2
