Math 343 - Numerical Methods I - Course Outline, Fall, 2017

Tentatively, hour exams are scheduled on these dates

Lecture

Topic/Section/Reading

1.0

 

A Brief Introduction to MatLab

 

Lecture Notes  (in html)  Lecture Notes  (in pdf)

 

1.1

 

Approximation of pi

Lecture Notes  (in pdf)

 

Homework 1 - Due Wednesday, August 30

Exercises 1, 2, 3, 5

Extra points: 4, 6

ex1.m , ex2.m, approx_pi.m, approx_pi3.m

 

Power series Formulas

 

Solutions

 

1.2

 

Computer Arithmetic and Round-off

Lecture Notes  (in pdf)

 

Homework 2 - Due Wednesday, September 6

 

Exercises 1, 2, 4

Extra points: 3

Solutions

 

Reading Materials:

(1) The Explosion of the Ariane 5:  CNN News     Why

(2) The Patriot Missile Failure:  Report

 

1.3

Algorithms and their Convergence

Lecture Notes  (in pdf)

 

Homework 3 - Due Wednesday, September 20

 

Exercises 1, 2(b)(c), 3, 4

Solutions

 

MatLab sample for Exercise 1(b): hw3_sample.m

 

 

 

2.1

Bisection Method

Lecture Notes  (in pdf)

Notes in Slides (in pdf)

 

MatLab program for Bisection Method:  bisect.m

 

Homework 4 - Due Wednesday, September 28

Exercises 1-5

 

Solutions

 

2.2

Newton Method and Secant Method

Lecture Notes  (in pdf)

 

MatLab programs newton.m secant.m

 

Homework 5 - Due Wednesday, October 4

Exercises 1-4

Extra points:  5

Solutions

 

Hour Exam 1 on Wednesday, October 4

 

2.3

The Fixed-Point Algorithm

 

Lecture Notes  (in pdf)

Notes in Slides (in pdf)

 

MatLab programs fixpt.m 

 

Homework 6 - Due Wednesday, October 11

Exercises 1-2, 3(find 4 g(x) such that g(x)=x is equivalent to f(x)=0.

 

Homework 7 - Due Wednesday, October 18

Section 2.3:  3, 4(a)(b)(c), 5, 6, 7

 

2.4

 

Convergence of the Newton Method and Modified Newton Method

 

Lecture Notes  (in pdf)

Notes in Slides (in pdf)

 

MatLab programs newtonM.m

 

Homework 8 - Due Wednesday, November 1

Exercises: 2-5

 

 

2.5

Convergence of Secant Method

 

Lecture Notes  (in pdf)

 

Homework 9 - Due Wednesday, November 8

Exercises: 1-2

 

 

2.6

Accelerating Convergence: Aitken’s Delta Square Method

 

Lecture Notes  (in pdf)

 

Homework 10 - Due Wednesday, November 15

Exercises: 1(1)(2)(3), 2(1)(2)

 

aitken.m,  steffensne.m 

 

 

 

3.1

Regression


Lecture Notes
 
 (in pdf) 

  

Homework 11 - Due Wednesday, November 15

Exercises: 1-2

 

- Due Wednesday, Dec 6

Exercises: 3-4

 

On Thursday, Nov 16 -

Hour Exam 2 on Sections 2.2, 2.3, 2.4, 2.5, 2.6

 

A short paper on Numerical Methods

 

3.2

Interpolation and Lagrange Interpolating Polynomials

 

Lecture Notes  (in pdf) 

 

neville.m

 

Homework 12 Due Dec 6  

Exercises 1

 

 Exercises 2, 4, 6, 7 will be on the final. 

3.3

Interpolating Polynomials in Newton’s Forward-Divided Differences Form

 

Lecture Notes  (in pdf) 

 

newtonfd.m

 

3.4

Piecewise Linear and Quadratics Interpolation – Linear and Quadratic Splines

 

Lecture Notes  (in pdf)  Solutions

 

3.5

Cubic Splines

 

Lecture Notes  (in pdf) 

 

cbspfun.m   (free spline)     cbspcl.m   (clamped spline)

 

 

 

4.1

Numerical Differentiation

4.2

Richardson Extrapolation

4.3

Numerical Integration

 

 

 

Final Exam: December 8, 8-11am

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