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Instructor: |
Dr. Peter Howard, Blocker 620D & 625B |
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Email: phoward@math.tamu.edu |
Office hours: MW 11:00-12:00; T 2:00-3:00.
Class time and place: MW 4:10-5:25, Zachry 105B.
Section web page: http://www.math.tamu.edu/~phoward/M641.html
Textbook: Principles of Applied Mathematics: Transformation and Approximation, 2nd Edition, by James P. Keener, Westview Press, 2000.
Prerequisites: Undergraduate courses in linear algebra and analysis.
Catalog Description: Review of preliminary concepts; sequence and function spaces; normed linear spaces, inner product spaces; spectral theory for compact operators; fixed point theorems; applications to integral equations and the calculus of variations.
Course Goal: The broad goal of the sequence M641-M642 is to cover fundamental concepts and applications of linear algebra, real analysis, and complex analysis. M641 comprises the material on linear algebra and most of the material on real analysis. This will include all topics in the catalog description.
Homework Assignments: A homework assignment will generally be posted on the course web site each Wednesday, due the following Wednesday. Work will be accepted up to a week late, though five points will be deducted for each class period by which the assignment is late. A typical assignment will be worth 50 points.
Exams: There will be two exams during the semester, a midterm and a final. The midterm will be given in the evening from 7:00--9:00 p.m., Thursday, October 25. The final exam for this class will be on Monday Dec. 10, 3:30--5:30 p.m.
Grades: Final grades will be determined in the following manner: Homework assignments: 50%; Midterm: 25%; Final exam: 25%. Grade ranges will be standard: 89.50-100, A; 79.50-89.49, B; 69.50-79.49, C, 59.50-69.49, D; below 59.50, F.
Make-up policy: Make-ups for exams will only be given if the student can provide a documented University-approved excuse (see University Regulations). According to University Student Rules students are required to notify an instructor by the end of the next working day after missing an exam. Otherwise the student forfeits his or her right to a make-up.
Scholastic Dishonesty: Copying work done by others, either in-class or out of class, is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. "An Aggie does not lie, cheat, or steal or tolerate those who do." Please refer to the Honor Council Rules and Procedures, available at the Office of the Aggie Honor System.
Copyright policy: All printed materials disseminated in class or on the web are protected by copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.
Students with Disabilities: The following statement was provided by the Department of Disability Services: The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, in Cain Hall, Room B118, or call 845-1637. For additional information visit http://disability.tamu.edu.
Class Schedule: Roughly speaking, we should cover the following material on the following schedule:
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Week of Monday |
Material Covered |
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August 27 |
Overview and prerequisites. (Fri. Aug. 31 is last day for drop-add.) |
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September 3 |
Algebraic equations. |
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September 10 |
Inner product spaces; normed linear spaces; geometry of inner product spaces. |
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September 17 |
Spectral theory for matrices. |
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September 24 |
The Fredholm Alternative and linear regression. |
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October 1 |
Lebesgue measure and Lp spaces. |
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October 8 |
Hölder spaces; Sobolev spaces; embedding theorems. |
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October 15 |
Generalized Fourier series; Weierstrass Approximation Theorem. |
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October 22 |
Discrete Fourier transforms; finite elements. (Midterm exam, Thurs. Oct. 25, 7-9.) |
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October 29 |
Integral equations; bounded linear operators. (Friday, Nov. 2 is last day for Q-drop.) |
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November 5 |
Compact operators. |
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November 12 |
Spectral theory for compact operators; contraction mapping principle. |
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November 19 |
Calculus of variations: Frèchet and Gâteaux derivatives. (No class Wed. Nov. 21; Thurs. Nov. 22 is Thanksgiving.) |
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November 26 |
Euler-Lagrange equations; Hamilton’s principle. (Wed. Nov. 28 is last class meeting.) |