Math 417-500, Numerical Analysis, Spring 2013

In this class, you will learn the basic concepts and some elementary methods in numerical analysis. We will discuss iterative methods to compute roots of nonlinear equations and linear systems of equations and study their convergence. Then, we will learn how to approximate functions by polynomials and to estimate the approximation error. Finally, you will have basic knowledge of numerical methods for the solution of ordinary differential equations.

06/5/03 Repeat the quizzes as well as the suggested exercises.

05/5/03 TYPO IN THE SYLLABUS! ----> the exam room is the lecture room Blocker 149.

05/4/03 There will be 6-7 questions in the final, approximately one from each chapter (except Chapter 1). Suggested problems are given below for both the first and second parts of the course. You MUST prepare all suggested samples: both for the first part and the second part.

02/18/03 Correction to Programming Assignment 3: 1.2 Convergence rate: "...Plot $h$ versus $h^{\alpha}$ and $h$ versus the error $|I_{exact}-I_{approx}|$ in one $loglog$-plot in Matlab. ...".
02/11/03 The date of Midterm exam is Wednesday, March 6.
01/23/03 Some misprints are fixed on the homework numbers for edition 9.

Instructor:

Assistant:

Lectures: Mondays/Wednesdays/Fridays, 11:30 am-12:20 pm, Blocker 149
Labs: Tuesdays, 08:00 am-08:50 am, Blocker 124

Numerical Analysis, 9th edition, by R. Burden and J. Faires (7th and 8th editions should also work)

Two years Calculus sequence, some knowledge of computer programming

Solving the homework problems in time helps you to understand the subject, get more learning experience and get prepared to the quizzes, midterm and final exams. Therefore, it is highly recommended to solve them in time.
There will be 5 set of programming exercises. You may have to demonstrate your program to the teaching assistant and you will have to write a short report individually. The credit will be given only for correct solutions.

There will be one midterm and one final examinations.
Midterm Wednesday, March 6, 11:30-12:20
Final May 8, 10:30 a.m.-12:30 p.m, Blocker 149

There will be one midterm and one final examinations.
Homework/Programming assignments+Quizzes: 20+20 = 40%
Midterm: 30% Final: 30%

Week 1: (Jan 14) sec. 1.2, 2.1, 2.2.
Homework:
7th edition:
  page 26: 1a,1h, 2a,2c,4a,4c,12,  page 53: 2,3,11,14,15,  page 64: 3,5,6,7,9,11,16,19,20,21,2
 
8th edition:
  page 26: 1a,1h, 2a,2c,4a,4c,12,
  page 51: 2,3,11,14,15,
  page 61: 3,5,6,7,9,11,16,19,20,21,22
 
9th edition:
  page 28: 1a,1h, 2a,2c,4a,4c,12,
  page 54: 2,3,13,16,17,
  page 65: 3,5,6,7,9,11,16,19,20,21,22  

Programming problem 1, deadline January 29.

Week 2: (Jan 21) sec. 2.3, 2.4
Homework:
7th edition:
  page 75: 1,3,5a,11,
  page 85: 1abc,4,5,7,9
 
8th edition:
  page 71: 1,3,5a,11,
  page 82: 1abc,4,5,7,
 
9th edition:
  page 75: 1,3,5a,1,
  page 85: 1abc,6,7,9,
 
Quiz 1, Friday, January 25.

Week 3: (Jan 28) sec. 3.1, 3.2, 3.3
Homework:
7th edition:
  page 119: 1a,c;2a,c,6,7,8,19,26,
  page 131: 1a,4a,7,8,9,10,12

8th edition:
  page 115: 1a,c;2a,c,
  page 115: 9a,c,13,19,23
  page 131: 1a,5,6a,9,10,11,12

9th edition:
  page 114: 1a,c;3a,c;7,10,20,
  page 123: 3b,8,7,
  page 133: 1a,8a,11,12,13,14,16

Programming problem 2, deadline Februrary 12.

Week 4: (Feb 4) sec. 3.2, 3.3

Quiz 2, Firday, February 8.

Week 5: (Feb 11) sec. 3.3, 4.1, 4.2, 4.3
Homework:
7th edition:
  page 136: 1a,b;7,
  page 177: 1,2,16,22,
  page 184: 1,8,
  page 195: 1a,b,g; 2a,b,g;7,9,11,13,14,18

8th edition:
  page 139: 1a;6,
  page 176: 1,6a,8a,19,22,
  page 184: 1a,6,
  page 195: 1a,b,g; 3a,b,g; 13,14,16,17,19

9th edition:
  page 142: 1a,b;10,
  page 182: 1,3a,22,28,
  page 191: 1,8,
  page 202: 1a,b,g;3a,b,g;13,15,17,19,20,24

Programming problem 3, deadline February 26.

Week 6: (Feb 18) sec. 4.4, 4.5
Homework:
7th edition:
  page 203: 1,2,3(a,c,g); 9,12,
 
8th edition:
  page 203: 1,2,3(a,c,g); 9,12,
 
9th edition:
  page 210: 1,3,4(a,c,g); 13,16,  

Quiz 3, Firday, February 22.

Week 7: (Feb 25) sec. 4.6, 4.7, 5.1
Homework:
7th edition:
  page 211: 1a,c,g; 3a,c,g; 5,
  page 218: 1a,c,d; 2a,c,d;
 
8th edition:
  page 211: 1a,c,g; 3a,c,g; 5,
  page 218: 1a,c,d; 2a,c,d;
 
9th edition:
  page 219: 1a,c,g; 5a,c,g; 5,
  page 227: 1a,c,d; 2a,c,d;  

Week 8: (Mar 4) sec. 5.1, 5.2
Review for the midterm exam:
(a) Iterative methods: bisection, fixed point, and Newton's method: all sections covered;
(b) Lagrange/Hermite polynomials: 3.1-3.3;
(c) Numerical differentiation: 4.1;
(d) Numerical integration: 4.3 and 4.7.

A sample of test type problems:
7th edition:
  page 53: 1,2,3,
  page 64: 5,6,7,19,
  page 75: 1,2,15,
  page 119: 1,3,22,
  page 131: 10,11,12,13,14,
  page 140: 1,2,
  page 178: 22 or similar - derive the rule type problems,
  page 195: 13,14,15,16,17,18,19,20,
  page 226: 5,6,8,  

8th edition:
  page 51: 1,2,3,
  page 61: 5,6,7,19,
  page 71: 1,2,15,
  page 116: 1,3,22,
  page 128: 10,11,12,13,14,
  page 135: 1,2,
  page 178: 22 or similar - derive the rule type problems,
  page 195: 13,14,15,16,17,18,19,20,
  page 226: 5,6,8,  

9th edition:
  page 54: 1,2,3,
  page 65: 5,6,7,19,
  page 75: 1,2,19,
  page 114: 1,5;
  page 124: 12;
  page 133: 14,15,16,17,18,
  page 142: 1,3,
  page 185: 22 or similar - derive the rule type of problems,
  page 202: 19, 20, 21, 22, 23, 24, 25, 26,
  page 234: 5, 6, 8.  

Midterm exam, Wednesday, March 6.

Week 9: (Mar 18) sec. 5.3, 5.4
Homework:
7th edition:
  page 255: 1,2,4,5,6a,b,c; 7,
  page 264: 1,2,3,4,5,7,9,10,
  page 271: 1,2,
  page 280: 1,3,5, 10,11a

8th edition:
  page 255: 1,2,4,7,8a,b,
  page 263: 1,2,3,4,5,7,9,10,
  Sec 5.3: 1,2,
  page 280: 1,3,5, 11a  

9th edition:
  page 264: 1,3,6,7,8a,b,c; 9,
  page 273: 1,2,3,5,9,11,15,12,
  page 281: 1,2,
  page 291: 1,5,17,13,16a  

Week 10: (Mar 25) sec. 5.4

Quiz 4, Wednesday, March 27.

Week 11: (Apr 1) sec. 6.1, 6.2
Homework:
7th edition:
  page 356: 1,2,5,8,9;
  page 368: 1,5;
 
8th edition:
  page 356: 1,2,5,9,10;
  page 368: 1,5;
 
9th edition:
  page 368: 1,2,3,9,12,13;
  page 379: 1, 9;
 
Programming problem 4, deadline April 2.

Week 12: (Apr 8) sec. 6.3, 6.4, 6.5
Homework:
7th edition:
  page 379: 1,2,4,5,7;
  page 386: 1,3,5,6,7,8,10,11;
  page 396: 1a,b;2a,b;4a,b;
 
8th edition:
  page 384:1,2,4,6,7;
  page 386: 1,3,5,6,7,8,10,11;
  page 396: 1,2,3a,b;
 
9th edition:
  page 391: 5,8,10,9,11;
  page 399: 1,5,6,7,8,10,11;
  page 409: 1a,b;2a,b;8a,b;
 
Quiz 5, Friday, April 12.

Week 13: (Apr 15) sec. 7.1, 7.2
Homework:
7th edition:
  page 428: 1-4,6-9;
  page 436: 1-5;
 
8th edition:
  page 427: 1-4,6-9;
  page 435: 1-5;
 
9th edition:
  page 441: 1-4,6-9;
  page 449: 1-4;6,8,9;
 
Programming problem 5, deadline April 16.

Week 14: (Apr 22) Review for Final

A sample of test type problems for the second part:
7th edition:
  Sec: 5.1:  page 255: 1a,2b;
  Sec: 5.2:  page 263: 1b,2a;
  Sec: 5.4:(only second order RK schemes)  page 280: 1b,2b;5,6;
  Sec: 6.1:  page 357: 9,10;
  Sec: 6.3:  page 379: 1b,5,7a,b;
  Sec: 6.4:  page 387: 5,6,7,8;
  Sec: 6.5:  page 396: 6a,c;
  Sec: 6.6:  page 410: 2,16,17,18,19;
  Sec: 7.1:  page 427: 1,2,4;
  Sec: 7.2:  page 435: 1a,c,e;7;
 
8th edition:
  Sec: 5.1:  page 255: 1a,2b;
  Sec: 5.2:  page 263: 1b,2a;
  Sec: 5.4:(only second order RK schemes)  page 280: 1b,2b;5,6;
  Sec: 6.1:  page 357: 9,10;
  Sec: 6.3:  page 379: 1b,5,7a,b;
  Sec: 6.4:  page 387: 5,6,7,8;
  Sec: 6.5:  page 397: 6a,c;
  Sec: 6.6:  page 410: 2,16,17,18,19;
  Sec: 7.1:  page 427: 1,2,4;
  Sec: 7.2:  page 435: 1a,c,e;7;
 
9th edition:
  Sec: 5.1:  page 264: 1a,2b;
  Sec: 5.2:  page 274: 1b,3a;
  Sec: 5.4:(only second order RK schemes)  page 291: 1b,9b;17,12;
  Sec: 6.1:  page 368: 12,13;
  Sec: 6.3:  page 390: 5b,9,11a,b;
  Sec: 6.4:  page 399: 5,6,7,8;
  Sec: 6.5:  page 411: 10a,c;
  Sec: 6.6:  page 425: 22,23,24,25; NOTE: some of the exercises were not covered during the class, so skip them.
  Sec: 7.1:  page 441: 1,2,4;
  Sec: 7.2:  page 435: 1a,c,e;13;
  Repeat a matrix and a vector norms.
 
There will be 6-7 questions, approximately one from each chapter (except Chapter 1). You should also prepare a sample of test type problems that was suggested (NOT only given) for the midterm.

Make-ups for exams will only be given with documented University-approved excuses (see University Regulations). Consistent with University Student Rules, students are required to notify an instructor by the end of the next working day after missing an exam. Otherwise, they forfeit their rights to a make-up.

Students may work together and discuss the homework problems with each other. Copying work done by others is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. For more information on university policies regarding scholastic dishonesty, see University Student Rules.

All printed hand-outs and web materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor.

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