Syllabus

Math 450 - SYLLABUS - Fall 2006

Any student with disabilities or other special needs are encouraged to share these concerns or requests as soon as possible.

Prerequisite: CSIS 152 and Math 323.

Instructor: Timothy Peil, Ph. D.
Text: Numerical Analyis, 8th Edition by Burden and Faires
Office: Basement Science Lab Building Phone: 218-477-2454
Office Hrs: MWF 10:00-10:50; TH 9:30-10:50 MTHF 1:00-1:50.
E-mail: peil@mnstate.edu Web homepage: http://web.mnstate.edu/peil

Topics: Chapter 1 - Mathematical Preliminaries
               Chapter 2 - Solutions of Equations in One Variable
               Chapter 3 - Interpolation and Polynomial Approximation
               Chapter 4 - Numerical Differentiation and Integration
               Chapter 5 - Initial-Value Problems for Ordinary Differential Equations

General Information. Four exams and a comprehensive final will be given. Homework will collected once each week. You may use a calculator or computer for the exercises. (Caution: Do not overuse.) The computer software Mathcad will be used for projects, assignments, and writing programs. We will not do proofs as rigorous as in Math 361 - Analysis, but we will do some proofs that help explain the processes. You will be expected to write some of these proofs.

Final Exam: December 19th at 3:00 p.m. Comprehensive final.

GRADES: Grades will be based on the total points from exams, comprehensive final exam, collected assignments, and quizzes. Grades will be based on the following scale:
                A: 90% to 100%
                B: 80% to 89%
                C: 70% to 79%
                D: 60% to 69%
                F: Below 60%

Makeup exams will be given only in cases of extreme illness, family emergency, or university-approved activities; you must notify me before the exam takes place.

Chapter One Read Sections 1.1, 1.2, and 1.3

Exercise Set p. 14 #1(b,c), 3(b,c), 4(b,c), 5, 7, 17, 21, 22, 24
p. 26 #1, 4(a), 5(c,h), 10(a), 11, 13(c), 21
p. 37 #6(b), 7(b), 8, 11 write pseudocode.

Mathcad 1. Example 1 pp. 6 - 8, Example 3 pp. 11 - 14.
2. Explore how Mathcad rounds.
3. Write a Mathcad program that rounds by (a) chopping (b) rounding; then use to do Example 7 of lecture notes.
4. p. 37 #11 write Mathcad program; also modify the program for chopping and rounding; include examples.

Hand in p. 14 #1(d), 3(d), 4(d), 11, 18 (Error in book #3(d) interval should be [–1,2].)
p. 26 #6(c,h), 12, 14(c)
Evaluate f(x) = x³–4.75x² + 2.98x + 7.48 at x = 4.73 (a) exact (b) chopping (c) rounding 3-digit; compute absolute and relative errors; do as written and in nested form.
p. 37 #9 write pseudocode and Mathcad program; also modify for chopping and rounding; include examples. (Use a vector for input of coefficients.)

Chapter Two Read Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.6

Exercise Set Notes #1 - 4
p. 51 #1, 3, 5(a,c), 11, 15
p. 61 #1, 2, 6, 7
p. 71 #1, 23, 27
p. 82 #1, 3, 6, 7, 8, 9, 10, 11, 14
p. 86 #1(b,d) due both Aitken's and Steffensen's, #7
Notes #6 –13
p. 96 #1(a,d), 3(a,d), 7

Mathcad 1. Write a program that finds a root by the Bisection Method.
2. Write a program for Fixed-Point Iteration.
3. Write programs for Newton-Raphson, Secant, and False Position.
4. Write a program for the Modified Newton's Method.
5. Write a program for Aitken's Method.
6. Write a program for Steffensen's Method.
7. Write a program for Horner's Method.
8. Write a program that uses Horner's and Newton's Method.
9. Write a program for Müller's Method.

Hand in p.51 #2(a), 10, 14
p. 61 #4, 8, 12(c) Write a Mathcad program for Fixed-Point Iteration.
p. 71 #6(a), 8(a), 10(a), 18 Write a Mathcad program for Secant.
p. 82 #2(a), 4(a), 6(b)
p. 86 #8 use Aitken's, Steffensen's, and Newton's compare, 14(a), Write a Mathcad program for Steffensen's Method.
Notes #7, 10(b), 11(b), 12(d)
p. 96 #2(a), 4(a). Write a program for Müller's Method.

Chapter
Three Read Sections 3.1, 3.2, 3.3, 3.4

Exercise Set Notes #1–3
p. 115 #1(a), 3(a), 5(a), 9(a), 11(a), 17, 19(a)
p. 127 #1(a), 3(a), 5(a), 17
Section 3-2 Notes #1–8
p. 135 1(a,d), 3(a,d)
p. 153 #3(a,c), 5(a,c)

Mathcad 1. Write a program for Neville's Iterated Interpolation
2. Write a program for natural cubic spline.

Hand in Notes #2
p. 115 #6(c), 8(c), 18
p. 127 #2(a), 4(a), 6(a)
Section 3-2 Notes #1, 4, 5(2d), 7, 8(d)
Write a program for Newton's Divided Difference.
p. 135 #2(c), 4(c) (Do both ways.)
p. 153 #1, 2, 4(c), 16

Chapter
Four Read Sections 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7

Exercise Set P. 176 #1, 2(a), 18(a)
Notes Section 4.2 #1; p. 184 #5
p. 195 #1–11(a) odd, 13, 17, 19
p. 203 #1–5(a,e,g) odd, 11
p. 211 #1(a, b), 3 (a, b) Notes Section 4.5 #3
p. 219 #1–2 (a, b) Notes Section 4.6 #2(a)
p. 226 #1–2 (a, b)

Mathcad 1. Composite Simpson's Rule
2. Composite Midpoint Rule
3. Composite Trapezoidal Rule
4. Romberg Integration
5. Adaptive Quadrature

Hand in Notes Section 4.1 #1, 2, 3.
Notes Section 4.2 #2; p. 184 #6
p. 195 #2–12(b) even, 18
Notes Section 4.4 #1, 2; p. 203 #2–6(b) even, 12
Notes Section 4.5 #4
Notes Section 4.6 #1, 2(b)
Notes Section 4.7 #3(a), 4, 5

Chapter
Five Read Sections 5.1, 5.2, 5.3, 5.4

Exercise Set p. 255 #1(a,d), 3(a,d), 5(a), 8(a,b)

Mathcad Program Euler's Method.

Hand in p. 255 #2(a,d), 4(a,d)
p. 263 #1(b), 3(b), 5(b), 7(b), 15, Program Euler's Method.
p. 271 #10
p. 281 #2(c), 6(c), 10(c), 14(c)
p. 289 #2(a)
p. 301 #2(c)

13 No Class!! Study Day

19

Final exam. 3:00 p.m.

The following are required to be on the syllabus by MnSCU.

Where and when is class. MTHF 2:00 - 2:50 in Bridges 262.

Course Description from the Minnesota State University Moorhead Bulletin.
Math 450 Numerical Analysis I (4)
Numerical solutions to systems of equations and differential equations, finite differences, interpolation formulas, numerical calculus, and approximating functions. Prerequisite: CSIS 152, Math 323.

E1 – Mathematics Student Learning Outcomes
http://web.mnstate.edu/math/MathStudentLearningOutcomes.htm

Attendance Policy. http://web.mnstate.edu/acadaff/Departments/policies/studentabsence.htm

Academic Honesty. http://web.mnstate.edu/sthandbook
http://web.mnstate.edu/math/MSUMAcademicHonestyPolicy.htm

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Chapter One	*Read*	Sections 1.1, 1.2, and 1.3
	Exercise Set	p. 14 #1(b,c), 3(b,c), 4(b,c), 5, 7, 17, 21, 22, 24 p. 26 #1, 4(a), 5(c,h), 10(a), 11, 13(c), 21 p. 37 #6(b), 7(b), 8, 11 write pseudocode.
	Mathcad	1. Example 1 pp. 6 - 8, Example 3 pp. 11 - 14. 2. Explore how Mathcad rounds. 3. Write a Mathcad program that rounds by (a) chopping (b) rounding; then use to do Example 7 of lecture notes. 4. p. 37 #11 write Mathcad program; also modify the program for chopping and rounding; include examples.
	Hand in	p. 14 #1(d), 3(d), 4(d), 11, 18 (Error in book #3(d) interval should be [–1,2].) p. 26 #6(c,h), 12, 14(c) Evaluate f(x) = x³–4.75x² + 2.98x + 7.48 at x = 4.73 (a) exact (b) chopping (c) rounding 3-digit; compute absolute and relative errors; do as written and in nested form. p. 37 #9 write pseudocode and Mathcad program; also modify for chopping and rounding; include examples. (Use a vector for input of coefficients.)
Chapter Two	*Read*	Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.6
	Exercise Set	Notes #1 - 4 p. 51 #1, 3, 5(a,c), 11, 15 p. 61 #1, 2, 6, 7 p. 71 #1, 23, 27 p. 82 #1, 3, 6, 7, 8, 9, 10, 11, 14 p. 86 #1(b,d) due both Aitken's and Steffensen's, #7 Notes #6 –13 p. 96 #1(a,d), 3(a,d), 7
	Mathcad	1. Write a program that finds a root by the Bisection Method. 2. Write a program for Fixed-Point Iteration. 3. Write programs for Newton-Raphson, Secant, and False Position. 4. Write a program for the Modified Newton's Method. 5. Write a program for Aitken's Method. 6. Write a program for Steffensen's Method. 7. Write a program for Horner's Method. 8. Write a program that uses Horner's and Newton's Method. 9. Write a program for Müller's Method.
	Hand in	p.51 #2(a), 10, 14 p. 61 #4, 8, 12(c) Write a Mathcad program for Fixed-Point Iteration. p. 71 #6(a), 8(a), 10(a), 18 Write a Mathcad program for Secant. p. 82 #2(a), 4(a), 6(b) p. 86 #8 use Aitken's, Steffensen's, and Newton's compare, 14(a), Write a Mathcad program for Steffensen's Method. Notes #7, 10(b), 11(b), 12(d) p. 96 #2(a), 4(a). Write a program for Müller's Method.
Chapter Three	*Read*	Sections 3.1, 3.2, 3.3, 3.4
	*Exercise Set*	Notes #1–3 p. 115 #1(a), 3(a), 5(a), 9(a), 11(a), 17, 19(a) p. 127 #1(a), 3(a), 5(a), 17 Section 3-2 Notes #1–8 p. 135 1(a,d), 3(a,d) p. 153 #3(a,c), 5(a,c)
	*Mathcad*	1. Write a program for Neville's Iterated Interpolation 2. Write a program for natural cubic spline.
	*Hand in*	Notes #2 p. 115 #6(c), 8(c), 18 p. 127 #2(a), 4(a), 6(a) Section 3-2 Notes #1, 4, 5(2d), 7, 8(d) Write a program for Newton's Divided Difference. p. 135 #2(c), 4(c) (Do both ways.) p. 153 #1, 2, 4(c), 16
Chapter Four	*Read*	Sections 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7
	*Exercise Set*	P. 176 #1, 2(a), 18(a) Notes Section 4.2 #1; p. 184 #5 p. 195 #1–11(a) odd, 13, 17, 19 p. 203 #1–5(a,e,g) odd, 11 p. 211 #1(a, b), 3 (a, b) Notes Section 4.5 #3 p. 219 #1–2 (a, b) Notes Section 4.6 #2(a) p. 226 #1–2 (a, b)
	*Mathcad*	1. Composite Simpson's Rule 2. Composite Midpoint Rule 3. Composite Trapezoidal Rule 4. Romberg Integration 5. Adaptive Quadrature
	*Hand in*	Notes Section 4.1 #1, 2, 3. Notes Section 4.2 #2; p. 184 #6 p. 195 #2–12(b) even, 18 Notes Section 4.4 #1, 2; p. 203 #2–6(b) even, 12 Notes Section 4.5 #4 Notes Section 4.6 #1, 2(b) Notes Section 4.7 #3(a), 4, 5
Chapter Five	*Read*	Sections 5.1, 5.2, 5.3, 5.4
	*Exercise Set*	p. 255 #1(a,d), 3(a,d), 5(a), 8(a,b)
	*Mathcad*	Program Euler's Method.
	*Hand in*	p. 255 #2(a,d), 4(a,d) p. 263 #1(b), 3(b), 5(b), 7(b), 15, Program Euler's Method. p. 271 #10 p. 281 #2(c), 6(c), 10(c), 14(c) p. 289 #2(a) p. 301 #2(c)
13	No Class!!	Study Day
19		Final exam. 3:00 p.m.