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Welcome to Numerical Analysis Math 448/548 Cpt S 430/530. CptS 430/Math448 Numerical Analysis Spring 2014 Instructor: John Miller, West 134E email@example.com Class web page can be found at http://www.tricity.wsu.edu/~jhmiller. Objectives:
Cpt S 430/530
Instructor: John Miller, West 134E
Class web page can be found at
To present the mathematical basis for methods of numerical analysis
To introduce students to MATLAB as a software package for
Textbook: “Numerical Mathematics and Computing” 6th Edition
by Cheney and Kincaid
Chapter 3: Locating roots of an equation
Chapters 5&6: Numerical integration
Chapter 10&11: Systems of ordinary differential equations
Chapter 2: Floating-point representation and errors
Chapters 7&8: Systems of linear equations
Chapter 12: Smoothing data and method of least squares
“Essential MATLAB for Scientist and Engineers” 2nd Edition by Hahn
Students will be assigned problems to be solved by writing MATLAB codes
Prior approval is required for late submission.
Criteria for student evaluation:
homework 25%, quizzes 25%, midterm exam 25% final exam 25%.
No partial credit on homework. Full credit for corrected homework
500-level students must define a project (subject to approval by the instructor) that involves numerical analysis and write a report that describes the numerical method, code developed, and results obtained. Project reports are due on the on the last class period.
Academic integrity will be strongly enforced in this course. Any student caught cheating on any assignment will be given an F grade for the course and will be reported to the Office Student Standards and Accountability. Cheating is defined in the Standards for Student Conduct WAC 504-26-010 (3). It is strongly suggested that you read and understand these definitions:
I encourage you to work with classmates on assignments. However, each student must turn in original work. No copying will be accepted. Students who violate WSU’s Standards of Conduct for Students will receive an F as a final grade in this course, will not have the option to withdraw from the course and will be reported to the Office Student Standards and Accountability. Cheating is defined in the Standards for Student Conduct WAC 504-26-010 (3). It is strongly suggested that you read and understand these definitions:
Academic integrity is the cornerstone of the university. Any student who attempts to gain an unfair advantage over other students by cheating, will fail the assignment and be reported to the Office Student Standards and Accountability. Cheating is defined in the Standards for Student Conduct WAC 504-26-010 (3).
WSU Tri-Cities is committed to maintaining a safe environment for its faculty, staff and students. The Campus Safety Plan can be found at http://www.tricity.wsu.edu/safetyplan/
See also the WSU Office of Emergency Management site at http://oem.wsu.edu/emergencies
Up-to-date WSU emergency alerts are available at http://alert.wsu.edu/
Disability Services Reasonable Accommodations Statement: Reasonable accommodations are available for students who have a documented disability. Classroom accommodation forms are available through the Disability Services Office. If you have a documented disability, even if it’s temporary, make an appointment as soon as possible with the Disability Services Coordinator, Cherish Tijerina Pearson, West Building, Room 269J, at 372-7352 or firstname.lastname@example.org.You will need to provide your instructor with the appropriate classroom accommodation form. The form should be completed and submitted during the first week of class. Late notification can delay your accommodations or cause them to be unavailable. All accommodations for disabilities must be approved through the Disability Services Coordinator.
Non-linear problem reduced to sequence of linear problems
written and saved
What does .^ mean?
f(x) = exp(x) - 3x2 has a root in the interval [0.5, 1.5].
Write MATLAB codes to find this root by the Bisection, Newton,
and Secant methods.
Use format long to compare your results to the value returned by
MATLAB’s fzero function.
Define convergence by Dn = |(xn – xn-1)/xn|
On a semi-log plot, compare the rates of convergence of the 3 methods.
Note: logre is a vector
Note: log(x) is natural log
Separate m-files for function and its derivative
Note @ before file name in function calls
Must be in the same folder
Inline function definitions (slide 11) could be used
When vector is single argument of plot, (k, ak) pairs are plotted
-5 corresponds to re = 10-5
What does this mean?
Example: 3.2-19 text p102
What does this imply?
Why require continuity?
Which root will bisection method converge to
in the example shown?
What is missing here? Test f(a)f(b)<0
Newton vs bisection (slide 16)?
Always use best estimate of root as xn in each cycle
If starting values are 1 and -1,
what do we expect to happen?
Use best estimate of root as xn (what value is this?)
Use bad first estimate as xn-1
Did the second attempt work?
How do we avoid this type of convergence?
Pseudo code from text p113
Newton’s method (slide 17)
en+1 = [ ] en2