UT Dallas Syllabus for math2420.0u1.11u taught by Zalman Balanov (zxb105020)

8/6/2019 UT Dallas Syllabus for math2420.0u1.11u taught by Zalman Balanov (zxb105020)

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Math 2420.501.11s: Differential Equations and Applications

Summer 2011, TuTh: 12:30pm2:45pm, GR 2.530

Instructor: Dr. Zalman BalanovOffice: Founders Building 2.408EOffice hours: TuTh 5:00pm 6:00pm

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

Textbook

William E. Boyce and Richard C. DiPrima, Elementary differential equations and boundaryvalue 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 first 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 two common examinations (midterm and final) for both sections.

Textbooks, notes, calculators or other electronic devises wont be allowed during examination.However, half-page (one side only) hand written formula sheet (letter size) will be allowed onfinal exam. No exams and assignment may be dropped except in extrodianry circumstances.Missed exams and assignments are a zero. The midterm and final examinations have beenscheduled as following:

Midterm Exam: June 30, 12:30 pm 2:45 pm, GR 2.530

Final Exam: August 4, 11:00 am 1:45 pm.

Grading policy

Graded assignments: 15%Weekly Quizzes in Problem Sessions: 20%One midterm exam: 30%Final exam: 35%.

Important Dates

May 23, Summer 2011: Classes beginMay 30, Summer 2011: University Closing: Memorial DayJune 2, Summer 2011: Census DayJune 2, Summer 2011: Last Day to drop a class without a W 11-week sessionJune 30, Monday, Midterm Exam , in classJuly 4, Summer 2011: University Closing: Independence DayAugust 1, Summer 2011: Last Day of Classes 11-week Session

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August 4 August 10: Summer 2011, Final Exams 11-week SessionFinal Exam: August 4, 11 am 1:45 pm

Detailed course description

No. Topics Remarks

1. Introduction: Some basic examples of models, classification ofdifferential equation, standard forms, initial value conditions.Few remarks on applications.

2. First Order Differential Equations (ODE): Existence andUniqueness Results. Higher Order ODEs.

3. Separable equations, homogeneous equations: techniques ofsolving.

Review of techniquesof integration recom-mended

4. First order linear ODEs and Bernoullis equation: integratingfactor method. Exact equation and integrating factor method.

Review of gradient vec-tor fields recommended

5. 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

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

7. 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

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

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

10. 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

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

The difficult part of thecourse

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

The difficult part of thecourse

13. Laplace transform: definition and its properties, deriva-tion of table of Laplace transforms. Gamma function andits properties, convolution integral. Laplace transforms ofdiscontinue 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

14. 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

15. 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

16. Review and practice exam.

Technical Support

If you experience any problems with your UTD account you may send an email to:

[email protected] or call the UTD Helpdesk at 972 883-2911.

Field Trip Policies Off-Campus

Instruction and Course Activities Off-campus, out-of-state, and foreign instruction and activitiesare subject to state law and University policies and procedures regarding travel and risk-relatedactivities. Information regarding these rules and regulations may be found at the website addresshttp://www.utdallas.edu/businessaffairs/risk/travel.php5. Additional information is availablefrom the office of the school dean. Below is a description of any travel and/or risk-relatedactivity associated with this course.

Student Conduct & Discipline

The University of Texas System and The University of Texas at Dallas have rules and regu-lations for the orderly and efficient conduct of their business. It is the responsibility of eachstudent and each student organization to be knowledgeable about the rules and regulationswhich govern student conduct and activities. General information on student conduct and dis-cipline is contained in the UTD printed publication, A to Z Guide, which is provided to all

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registered students each academic year. The University of Texas at Dallas administers stu-dent discipline within the procedures of recognized and established due process. Proceduresare defined and described in the Rules and Regulations, Series 50000, Board of Regents, TheUniversity of Texas System, and in Title V, Rules on Student Services and Activities of theuniversitys Handbook of Operating Procedures. Copies of these rules and regulations are avail-able to students in the Office of the Dean of Students, where staff members are available toassist students in interpreting the rules and regulations (SU 1.602, 972/883-6391) and onlineat http://www.utdallas.edu/judicialaffairs/UTDJudicialAffairs-HOPV.html. A student at theuniversity neither loses the rights nor escapes the responsibilities of citizenship. He or she isexpected to obey federal, state, and local laws as well as the Regents Rules, university regula-tions, and administrative rules. Students are subject to discipline for violating the standardsof conduct whether such conduct takes place on or off campus, or whether civil or criminalpenalties are also imposed for such conduct.

Academic integrity

The faculty expects from its students a high level of responsibility and academic honesty. Be-cause the value of an academic degree depends upon the absolute integrity of the work doneby the student for that degree, it is imperative that a student demonstrate a high standard ofindividual honor in his or her scholastic work. Scholastic Dishonesty, any student who commitsan act of scholastic dishonesty is subject to discipline. Scholastic dishonesty includes but is notlimited to cheating, plagiarism, collusion, the submission for credit of any work or materialsthat are attributable in whole or in part to another person, taking an examination for another

person, any act designed to give unfair advantage to a student or the attempt to commit suchacts. Plagiarism, especially from the web, from portions of papers for other classes, and fromany other source is unacceptable and will be dealt with under the universitys policy on plagia-rism (see general catalog for details). This course will use the resources of turnitin.com, whichsearches the web for possible plagiarism and is over 90% effective.

Copyright Notice

The copyright law of the United States (Title 17, United States Code) governs the mak-ing of photocopies or other reproductions of copyrighted materials, including music and soft-

ware. Copying, displaying, reproducing, or distributing copyrighted works may infringe thecopyright owners rights and such infringement is subject to appropriate disciplinary action aswell as criminal penalties provided by federal law. Usage of such material is only appropri-ate when that usage constitutes fair use under the Copyright Act. As a UT Dallas stu-dent, you are required to follow the institutions copyright policy (Policy Memorandum 84-I.3-46). For more information about the fair use exemption, see the following website for details.http://www.utsystem.edu/ogc/intellectualproperty/copypol2.htm

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Email Use

The University of Texas at Dallas recognizes the value and efficiency of communication between

faculty/staff and students through electronic mail. At the same time, email raises some issuesconcerning security and the identity of each individual in an email exchange. The universityencourages all official student email correspondence be sent only to a students U.T. Dallas emailaddress and that faculty and staff consider email from students official only if it originates froma UTD student account. This allows the university to maintain a high degree of confidencein the identity of all individual corresponding and the security of the transmitted information.UTD furnishes each student with a free email account that is to be used in all communicationwith university personnel. The Department of Information Resources at U.T. Dallas provides amethod for students to have their U.T. Dallas mail forwarded to other accounts.

Withdrawal from Class

The administration of this institution has set deadlines for withdrawal of any college level courses.These dates and times are published in that semesters course catalog. Administration proce-dures must be followed. It is the students responsibility to handle withdrawal requirementsfrom any class. In other words, I cannot drop or withdraw any student. You must do the properpaperwork to ensure that you will not receive a final grade of F in a course if you choose notto attend the class once you are enrolled.

Student Grievance Procedures

Procedures for student grievances are found in Title V, Rules on Student Services and Activities,of the universitys Handbook of Operating Procedures. In attempting to resolve any studentgrievance regarding grades, evaluations, or other fulfillments of academic responsibility, it is theobligation of the student first to make a serious effort to resolve the matter with the instructor,supervisor, administrator, or committee with whom the grievance originates (hereafter calledthe respondent). Individual faculty members retain primary responsibility for assigning gradesand evaluations. If the matter cannot be resolved at that level, the grievance must be submittedin writing to the respondent with a copy of the respondents School Dean. If the matter is notresolved by the written response provided by the respondent, the student may submit a written

appeal to the School Dean. If the grievance is not resolved by the School Deans decision, thestudent may make a written appeal to the Dean of Graduate or Undergraduate Education, andthe deal will appoint and convene an Academic Appeals Panel. The decision of the AcademicAppeals Panel is final. The results of the academic appeals process will be distributed to allinvolved parties. Copies of these rules and regulations are available to students in the Office ofthe Dean of Students, where staff members are available to assist students in interpreting therules and regulations.

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the absence. A student who fails to complete the exam or assignment within the prescribedperiod may receive a failing grade for that exam or assignment. If a student or an instructordisagrees about the nature of the absence [i.e., for the purpose of observing a religious holy day]or if there is similar disagreement about whether the student has been given a reasonable timeto complete any missed assignments or examinations, either the student or the instructor mayrequest a ruling from the chief executive officer of the institution, or his or her designee. Thechief executive officer or designee must take into account the legislative intent of TEC 51.911(b),and the student and instructor will abide by the decision of the chief executive officer or designee.

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

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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 courses homepage you will see a link titled Login to MuchLearning. Click on it.

4. At User Association, click For Students button.


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

create an anonymous account on MuchLearning.


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6. Click on login to finish the process.

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


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


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

eLearning course.

Documents

UT Dallas Syllabus for math2420.0u1.11u taught by Zalman Balanov (zxb105020)