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Instructor: |
Dr. Peter Howard, Blocker 620D & 625B |
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Email: phoward@math.tamu.edu |
Office hours: MW 1:00-2:00; R 1:00-2:00.
Class time and place: MWF 10:20-11:10, Blocker 148.
Section web page: /~phoward/M642.html
Textbook: Principles of Applied Mathematics: Transformation and Approximation, 2nd Edition, by James P. Keener, Westview Press, 2000.
Prerequisites: Math 641 or permission of instructor.
Catalog Description: Distributions and differential operators; transform theory; spectral
theory for unbounded self-adjoint operators; applications to partial
differential equations; asymptotics and perturbation theory.
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. M642 comprises the material on distributions and
differential operators, as well as complex analysis and applications of
complex analysis to fluid flow, Fourier transforms, and asymptotic
methods.
Homework Assignments: A homework assignment will generally be posted on the course web site each Friday, due the following Friday. 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, March 7. The final exam for this class will be on Tuesday May 7, 8:00--10:00 a.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.
Learning Objectives:
Students will be able to: analyze distributions and interpret
distributional solutions of ODE; solve Sturm-Liouville and related
boundary value problems; differentiate and integrate functions of a
complex variable; analyze two-dimensional fluid flows using complex
function theory; describe and classify the spectrum of a differential
operator; compute the Fourier and related transforms of a function; use
Fourier theory to solve differential and integral equations; employ
Laplace's method of asymptotic approximation and state Watson's Lemma.
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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January 14 |
Theory of distributions. (Fri. Jan. 18 is last day for drop/add.) |
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January 21 |
Boundary and initial value ODE; Green's functions. (No class Mon. Jan. 21; Martin Luther King, Jr. Day.) |
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January 28 |
Domain of a differential operator; Adjoint of a differential operator. |
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February 4 |
Inhomogeneous ODE; Fredholm alternative for differential operators. |
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February 11 |
The Wronskian; Least squares solutions; Modified Green's functions. |
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February 18 |
Eigenfunction expansion; Dirichlet-Jordon convergence theorem. |
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February 25 |
Review of complex analysis: branches; analytic functions; complex integration. |
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March 4 |
Cauchy Integral Theorem; Mean value theorems; (Midterm exam, Thurs. Mar. 7-9.) |
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March 11 |
SPRING BREAK |
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March 18 |
Singularities; Analytic continuation; Application to fluid flow. |
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March 25 |
Blasius Theorem; Navier-Stokes equations. (No class Fri. Mar. 29.) |
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April 1 |
Bernoulli's Principle; Lift and drag. Application to curve balls. (Tues. Apr. 2 is last day for Q-drop.) |
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April 8 |
Categorization of spectrum for unbounded operators; Transforms. |
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April 15 |
Fourier transforms; Heisenberg Uncertainty Principle. |
| April 22 |
Convolution theorem; Asymptotic expansions. |
| April 29 |
Laplace's method; Watson's Lemma. (Tues. Apr. 30 is last class; Fri. classes meet.) |