MATH 3319: Differential Equations and Linear Algebra Section 003 Spring 2015

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1 MATH 3319: Differential Equations and Linear Algebra Section 003 Spring 2015 Time: Tue. & Thur. 5:30 6:50 PM Classroom: Pickard Hall 107 Instructor: Prof. Barbara Shipman Office: Pickard Hall 437 Phone: (817) Office Hours: Tue. & Thur. 10:30 11:30 AM Website: at Student Center, Math 3319 Prerequisite: C or better in MATH 2426 or concurrent enrollment in MATH Textbook (required): Differential Equations and Linear Algebra, 3 rd Edition. Stephen W. Goode and Scott A. Annin. ISBN: Learning Outcomes: On successful completion of this course, students will be able to explain what an ordinary differential equations (ODE) is and how specific ODEs arise in physical phenomena such as oscillations and population dynamics, think critically about when and how to apply various techniques for solving ordinary differential equations, interpret solutions of ordinary differential equations physically and mathematically, explain how concepts of linear algebra apply to solving differential equations, read and understand mathematical writing at the level of the textbook, and be confident about the correctness of their mathematical solutions and reasoning. Course Content: Introductory course on ordinary differential equations with emphasis on solution techniques, in particular those involving linear algebra. Topics include ordinary differential equations, vector spaces, linear transformations, matrix and vector algebra, eigenvectors, the Laplace Transform, and systems of differential equations. Expectations of the Student for Success in the Course: Attendance policy: At the University of Texas at Arlington, taking attendance is not required. Each faculty member is free to develop his or her own methods of evaluating students academic performance, including course-specific policies on attendance. In this class, your instructor takes attendance and counts it towards your course grade as described below. You are expected to attend every class, arrive on time, and remain in class for the whole period. Participation: Prepare all assigned study problems and bring your work to class; these will be needed for in-class presentations and discussions. 9 hours per week outside of class. Spend at least 9 hours per week outside of class studying for this course, including work on the study problems. Course notebook. Keep a neat, up-to-date, and organized binder with correct solutions to all problems assigned or discussed in class. MavMail and Announcements: Keep an activated MavMail account and check it regularly. You are responsible for all information that I send to your MavMail account and all announcements made in class or on the course website. Ask for help when needed. Ask for help on material that you may not be grasping fully. You may work with your classmates, come to office hours, or send me an with specific questions. Personal responsibility. You carry the ultimate responsibility for your learning. Be sure to attend every class, keep up daily with the assignments, put in the expected hours, keep your course notebook up-to-date, and ask for help when needed.

2 Study Problems and Participation: Study problems will be assigned daily as posted on the course website. Selected study problems will be discussed in class as time permits. At every class, be prepared to explain (at the board or from your seat) your solution to any problem assigned so far. You may also be asked to explain your reasoning to other questions that arise during class. You are expected to work out correct solutions to all study problems, resolve any questions that you have on them, keep your correct solutions organized in your class binder, and bring these solutions to every class. Scoring for Prepared Attendance and Participation: At every class, you will receive an attendance and participation score according the following scheme: 2, for being present during the entire period with good participation and preparation. 0 1, if you are not present during the entire period, are inadequately prepared, or do not fully participate. If you arrive late, your score will be recorded as 0; if you would like consideration for raising this to 1, please inform me after class on the same day. 0, for missing class for any reason. This number records that the in-class active learning experience for that day has been lost. Quizzes: Zero to two short quizzes will be given each week; these will take the place of longer midterm exams and will provide you with frequent feedback. Quizzes are cumulative and may involve any material assigned or discussed up to that point. You are expected to come to every class prepared for a possible quiz; the dates of the quizzes will be unannounced. A missed quiz cannot be made up for any reason. Two lowest quiz scores will be dropped. Here are some tips on preparing for the quizzes: Regularly review all class notes and study problems. Re-work study problems and problems discussed in class without resorting to notes. Consult notes only after a solid effort to re-work the problems on your own. Set aside ample time to work out all study problems carefully before the next class. Form study groups with classmates and work on coursework together. Pinpoint the specific question if you get stuck. This may help you see how to solve it. Meet with your instructor to settle remaining questions that you may have. Final Exam: There will be a comprehensive final exam on Tuesday, May 12 from 5:30--8 PM, in the same room as the class. A missed final exam cannot be made up. Grading: Your work will be graded on correctness, completeness, and clarity. Attendance and Participation: 15% Quiz Average: 45% Final Exam: 40% Course average 100% Your course average determines your final grade. A: %; B: 80 89%; C: 70 79%; D: 60 69%; F: 0 59%. Students are expected to keep track of their performance throughout the semester and seek guidance from available sources (including the instructor) if their performance drops below satisfactory levels.

3 Course Schedule: The day-by-day outline is approximate; the instructor may adjust this schedule in any way that better serves the educational needs of the students enrolled in this course. Week 1 Jan 20 Jan 22 ODEs in classic physical examples, initial value problems, basic principles and terminology, separable ODEs, population dynamics Week 2 Jan 27 Integrating factors, modeling problems Jan 29 Change of variables, exact ODEs, notes on higher order ODEs Week 3 Feb 3 Feb 5 Systems of linear equations, matrix formulation, solution by Gaussian elimination, invertibility of matrices Week 4 Feb 10 Feb 12 More on solving linear systems; determinants and applications of determinants Week 5 Feb 17 Feb 19 Determinants, continued Vector spaces, examples, spanning sets Week 6 Feb 24 Snow Day no class Feb 26 Spanning sets of vector spaces Week 7 Mar 3 Linear independence Mar 5 Snow Day no class Week 8 Mar 17 Basis and dimension Mar 19 Eigenvectors and eigenvalues of linear transformations Week 9 Mar 24 Homogeneous and nonhomogeneous linear differential equations Mar 26 Method of undetermined coefficients Week 10 Mar 31 Complex-valued trial solutions; Oscillationg mechanical systems Apr 2 Apr 3 More on oscillating systems, damping, resonance Last day to drop a class Week 11 Apr 7 Apr 9 Circuit problems First order linear systems of differential equations and matrix form Week 12 Apr 14 Solutions techniques for first order linear systems defective and Apr 16 nondefective coefficient matrices Week 13 Apr 21 Applications of linear systems Apr 23 Applications, matrix exponential, phase plane Week 14 Apr 28 Apr 30 Laplace transform and its inverse transform The Laplace transform and initial-value problems Week 15 May 5 Shifting theorems, May 7 impulsive driving terms in the Laplace transform Final May 12 Final Exam 5:30 8 PM (Tuesday)

4 Policies of the University of Texas at Arlington: Drop Policy: Students may drop or swap (adding and dropping a class concurrently) classes through self-service in MyMav from the beginning of the registration period through the late registration period. After the late registration period, students must see their academic advisor to drop a class or withdraw. Undeclared students must see an advisor in the University Advising Center. Drops can continue through a point two-thirds of the way through the term or session. It is the student's responsibility to officially withdraw if they do not plan to attend after registering. Students will not be automatically dropped for non-attendance. Repayment of certain types of financial aid administered through the University may be required as the result of dropping classes or withdrawing. For more information, contact the Office of Financial Aid and Scholarships ( Americans with Disabilities Act: The University of Texas at Arlington is on record as being committed to both the spirit and letter of all federal equal opportunity legislation, including the Americans with Disabilities Act (ADA). All instructors at UT Arlington are required by law to provide "reasonable accommodations" to students with disabilities, so as not to discriminate on the basis of that disability. Any student requiring an accommodation for this course must provide the instructor with official documentation in the form of a letter certified by the staff in the Office for Students with Disabilities, University Hall 102. Only those students who have officially documented a need for an accommodation will have their request honored. Information regarding diagnostic criteria and policies for obtaining disability-based academic accommodations can be found at or by calling the Office for Students with Disabilities at (817) Title IX: The University of Texas at Arlington is committed to upholding U.S. Federal Law Title IX such that no member of the UT Arlington community shall, on the basis of sex, be excluded from participation in, be denied the benefits of, or be subjected to discrimination under any education program or activity. For more information, visit Academic Integrity: Students enrolled all UT Arlington courses are expected to adhere to the UT Arlington Honor Code: I pledge, on my honor, to uphold UT Arlington s tradition of academic integrity, a tradition that values hard work and honest effort in the pursuit of academic excellence. I promise that I will submit only work that I personally create or contribute to group collaborations, and I will appropriately reference any work from other sources. I will follow the highest standards of integrity and uphold the spirit of the Honor Code. UT Arlington faculty members may employ the Honor Code as they see fit in their courses, including (but not limited to) having students acknowledge the honor code as part of an examination or requiring students to incorporate the honor code into any work submitted. Per UT System Regents Rule 50101, 2.2, suspected violations of university s standards for academic integrity (including the Honor Code) will be referred to the Office of Student Conduct. Violators will be disciplined in accordance with University policy, which may result in the student s suspension or expulsion from the University. Electronic Communication: UT Arlington has adopted MavMail as its official means to communicate with students about important deadlines and events, as well as to transact university-related business regarding financial aid, tuition, grades, graduation, etc. All students are assigned a MavMail account and are responsible for checking the inbox regularly. There is no additional charge to students for using this account, which remains active even after graduation. Information about activating and using MavMail is available at Student Feedback Survey: At the end of each term, students enrolled in classes categorized as lecture, seminar, or laboratory shall be directed to complete an online Student Feedback Survey (SFS). Instructions on how to access the SFS for this course will be sent directly to each student through MavMail approximately 10 days before the end of the term. Each student s feedback enters the SFS database anonymously and is aggregated with that of other students enrolled in the course. UT Arlington s effort to solicit, gather, tabulate, and publish student feedback is required by state law;

5 students are strongly urged to participate. For more information, visit Review Week: A period of five class days prior to the first day of final examinations in the long sessions shall be designated as Final Review Week. The purpose of this week is to allow students sufficient time to prepare for final examinations. During this week, there shall be no scheduled activities such as required field trips or performances; and no instructor shall assign any themes, research problems or exercises of similar scope that have a completion date during or following this week unless specified in the class syllabus. During Final Review Week, an instructor shall not give any examinations constituting 10% or more of the final grade, except makeup tests and laboratory examinations. In addition, no instructor shall give any portion of the final examination during Final Review Week. During this week, classes are held as scheduled. In addition, instructors are not required to limit content to topics that have been previously covered; they may introduce new concepts as appropriate. Emergency Exit Procedures: Should we experience an emergency event that requires us to vacate the building, students should exit the room and move toward the nearest exit, which is located just outside of the classroom door on the left (facing the front of the room); after exiting the classroom, go through the glass doors to the left, and exit the building. When exiting the building during an emergency, one should never take an elevator but should use the stairwells. Faculty members and instructional staff will assist students in selecting the safest route for evacuation and will make arrangements to assist individuals with disabilities. Student Support Services: UT Arlington provides a variety of resources and programs designed to help students develop academic skills, deal with personal situations, and better understand concepts and information related to their courses. Resources include tutoring, major-based learning centers, developmental education, advising and mentoring, personal counseling, and federally funded programs. For individualized referrals, students may visit the reception desk at University College (Ransom Hall), call the Maverick Resource Hotline at , send a message to resources@uta.edu, or view the information at Student Disruption: The University reserves the right to impose disciplinary action for an infraction of University policies. This includes engagement in conduct, alone or with others, that obstructs, disrupts, or interferes with any function of class activities. Emergency Phone Numbers: In case of an on-campus emergency, call the UT Arlington Police Department at (non-campus phone), (campus phone). You may also dial 911.

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