UT Dallas Syllabus for math2420.501.11f taught by Zalman Balanov (zxb105020)

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Math 2420.501.11f: Differential Equations and Applications

Fall 2011, MW: 5:30pm–6:45pm, GR 2.302

Instructor: Dr. Zalman BalanovOffice: Founders Building 2.408EOffice hours: MW 2:00pm – 3:00pm

E-mail: [email protected]: (972) 883 6591

Textbook

William E. Boyce and Richard C. DiPrima, Elementary differential equations and boundary

value problems, John Wiley & Sons, Inc. Ninth edition.

Course description

This is an introductory course to the theory of ordinary differential equations (ODEs). Topics to

be covered include: first order differential equations, second and higher order linear equations,series solutions of second order linear equations, special functions, the method of Frobenius,Laplace transform techniques, and systems of first order linear equations.

Assignments, quizzes and exams

Assignments: The assignments will be posted weekly at MuchLearning. The students canaccess MuchLearning through a link at eLearning. The following are the instructions for settingup MuchLearning through eLearning. A graphical instruction is attached in the end of thisdocument.

1. Log into eLearning

https://elearning.utdallas.edu/webct/entryPageIns.dowebct

2. Click on the link for your eLearning course.

3. In your courses homepage you will see a link titled “Link2MuchLearning”. Click on it.

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4. Read the terms of service then click on the “I Accept. Create my Account” button tocreate an anonymous account on MuchLearning.

5. Click on “login” to finish the process.

6. In the left menu you will find a link to your course - please click it.

7. Your assignments can be found in the link labelled Assignments in the left menu. Tologin to your account in the future simply click the “Login to MuchLearning” link in youreLearning course.

Assignments posted online are expected to be completed online by the students and will begraded automatically. All the assignments should be completed independently by the students.Each assignment is due within one week unless otherwise indicated in the assignment. Late

assignments will NOT be accepted.Quizzes: Beginning the second week of this course, there will be a weekly quiz during the

problem session organized and marked by the teaching assistant.Exams: There will be three common examinations (two midterms and final) for both sec-

tions. Textbooks, notes, calculators or other electronic devises won’t be allowed during exam-ination. However, half-page (one side only) hand written formula sheet (letter size) will beallowed on final exam. No exams and assignment may be dropped except in extraordinary cir-cumstances. Missed exams and assignments are a zero. The midterms and final examinationshave been scheduled as following:

Midterm Exam I: date: 9/28/2011, location: SLC 1.102, time: 7:15 PM - 9:00 PM

Midterm Exam II: date: 11/9/2011, location: SLC 1.102, time: 7:15 PM - 9:00 PMFinal Exam: December 14, 5:00 pm.

Grading policy

Graded assignments: 15%Weekly Quizzes in Problem Sessions: 15%Midterm exam I: 20%Midterm exam II: 20%Final exam: 30%.

Important Dates

August 24, Fall 2011: Classes beginSeptember 5, Fall 2011: University Closing: Labour DaySeptember 9, Fall 2011: Census DaySeptember 9, Fall 2011: Last Day to drop a class without a ”W”September 28, Wednesday, Fall 2011: Midterm Exam I

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November 9, Wednesday, Fall 2011: Midterm Exam II

November 24-25, Fall 2011: University Closing: Thanksgiving HolidaysDecember 6, Fall 2011: Last Day of Full-Term SessionDecember 14, Wednesday, Fall 2011, Final Exam.

Detailed course description

No. Topics Remarks

1. Introduction: Some basic examples of models, classification of differential equation, standard forms, initial value conditions.Few remarks on applications. First Order Differential Equa-tions (ODE): Existence and Uniqueness Results. Higher OrderODEs.

2. Separable equations, homogeneous equations: techniques of solving.

Review of techniquesof integration recom-mended

3. First order linear ODEs and Bernoulli’s equation: integratingfactor method. Exact equation and integrating factor method.

Review of gradient vec-tor fields recommended

4. Second order linear ODEs: general theory, homogeneous andnon-homogeneous equations, Wronskian and linear indepen-dence of solutions.

Review of linear alge-bra: linear indepen-dence and basis recom-mended

5. Reduction of order for second order linear ODEs (homogeneousand nonhomogeneous).

6. Second order linear homogeneous ODEs with constant co-efficients: characteristic equation, real characteristic roots,complex characteristic roots, repeated roots. Remarks abouthigher order linear ODEs with constant coefficients.

Review of complexnumbers and complexexponential functionrecommended

7. Second order linear nonhomogeneous ODEs: method of unde-termined coefficient, variation of parameters method.

8. Review of power series (analytic functions, domains of conver-gence, tests for convergence, basic analytic functions and theirpower series)

Review of calculus re-lated to infinite seriesrecommended

9. Second order linear ODEs with non-constant coefficients: se-ries solutions near an ordinary point, recurrence formula andexamples

The difficult part of thecourse

10. Euler equation: indicial equation, distinct real, complex andrepeated roots of indicial equation.

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11. Second order linear ODEs with non-constant coeffi-cients:regular singular points,Frobenius series solutionnear a regular singular point, a recurrence formula.Bessel’s equation and Bessel’s functions.

The difficult part of thecourse

12. Laplace transform: definition and its properties, deriva-tion of table of Laplace transforms. Gamma function andits properties, convolution integral. Laplace transforms of discontinue functions and impulse functions. Solving lin-ear nonhomogeneous ODEs (with constant coefficients)using Laplace transforms. Examples.

Review of improper integralsand criteria for their conver-gence recommended

13. Systems of linear ODEs: General existence and unique-ness result. Solving systems of ODEs (with constant co-efficients) using Laplace transforms.

Review of linear algebra re-lated to matrices and deter-minants recommended

14. Systems of linear homogeneous and non-homogeneousODEs: Fundamental solution matrix and the variationof parameter formula. Systems with constant coefficients:finding fundamental solution matrix. Exponential matrix.

Review of eigenvalues andeigenvectors recommended

15. Review and practice exam.

UT Dallas Syllabus Policies and Procedures

The information contained in the following link constitutes the Universitys policies and proce-dures segment of the course syllabus. Please go to http://go.utdallas.edu/syllabus-policies for

these policies.These descriptions and timelines are subject to change at the discretion of the Professor.

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http://go.utdallas.edu/syllabus-policies

http://go.utdallas.edu/syllabus-policies



MuchLearning Setup for Students

1. Log into eLearning (https://elearning.utdallas.edu/webct/logonDisplay.dowebct)2. Click on your eLearning course link. For example, Math 2312 001 Precalculus -S11

3. In your course’s homepage you will see a link titled “Login to MuchLearning”. Click on it.

4. At “User Association”, click “For Students” button.



5. Read the terms of service then click on the “I Accept. Create my Account” button to

create an anonymous account on MuchLearning.



6. Click on “login” to finish the process.

7. In the left menu you will find a link to your course - please click it.



8. Click link “Assignments” in the left menu to review your assignments.



To login to your account in the future, simply click the “Login to MuchLearning” link in your

eLearning course.

Documents

UT Dallas Syllabus for math2420.501.11f taught by Zalman Balanov (zxb105020)