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2009 Spring, Michael Frantz
MATH 315 Differential Equations
Course Designation MATH 315 - Differential Equations: A upper division undergraduate math course required for the B.S. mathematics major, and strongly recommended for the B.A. mathematics major and physics majors. Also recommended for students in chemistry. (4 semester hours) Course Description and Prerequisites This course serves as an introduction to the methods of solution, applications, and theory of ordinary differential equations. Various solution techniques will be examined, including extensive experience with numerical and graphical techniques implemented on computers. Modeling applications for differential equations from various areas of science and engineering will also be discussed. All students enrolling in this course should have passed a complete sequence in the calculus of functions of one variable, up through Taylor series. At the University of La Verne, this means Calculus I, II and III. See the instructor for further information. Goals The goals of this course include the following: to develop proficiency in various methods of solution for first order and higher order ordinary differential equations and linear systems, including exact, separable, homogeneous, linear and Bernoulli equations, utilizing the methods of variation of parameters, undetermined coefficients, power series, Laplace transforms, and numerical approximation; to acquaint the student with the modeling processes used in applying differential equations to solve real problems in the sciences, and expose the student to some of the standard (as well as non-standard) physical problems with solutions governed by differential equations; to develop an operational knowledge of the basic computational algorithms and software used to generate mathematical solutions to differential equations and systems of differential equations; to acquire a depth of understanding of complex concepts and ideas through the exploratory use of sophisticated mathematical software for computing and displaying solutions of differential equations and systems; and to provide a sound mathematical base for the goals listed above, in terms of when solutions are known to exist and whether such solutions are meaningful. Assignments and Tests Daily homework assignments will be made, including a number of exercises to be worked by the student but not turned in, and several problems which must be handed in and graded. Each problem set to be graded will be due by 5pm one week after it is assigned, unless otherwise specified. Note: a key component of this course will be the use of software to assist the student in exploring complex mathematical concepts and models through the interactive graphical display and manipulation of solutions of differential equations. The homework text assignments will frequently include problems requiring the student to use specialized software in the computer lab (Maple, MATLAB, PPLANE, and others). No prior programming experience is required, as the differential equations solver software will be made available and is user-friendly. There will be four one-hour tests and a final exam which will either be comprehensive or will cover the first 3/4 of the course, in the case that the fourth test occurs on the final exam day. Several of the tests will have takehome components in addition to or in place of in-class components. Tests will be announced at least one week in advance, and approximate dates may be inferred from the topics list provided later in this document. Make-up tests will only be given for absences deemed justifiable by the instructor (e.g., illness, family emergency) and may be more difficult than the original test. Note: the fee for a make-up test is $40.00. If you will not be able to attend class the day of a test, please inform the instructor by phone on the day of the test prior to the testing time.
page 2 Evaluation The grade for the course will be based on the homework, computer assignments and projects (15%), the average of the four one-hour tests (60%), and the final exam (25%). If any one-hour exam score (including a test not taken, but excluding the fourth test if it is included on the final exam day) is lower than the final exam score, it will be replaced by the final exam score, so that the final exam may count either 25% or (in this latter case) 40% of the total grade. Late homework assignments (if accepted at all) will receive at least a 20% to 50% reduction in credit, determined at the discretion of the instructor, based on various factors. Final course grades will be determined by the following scale: 100 - 90 89 - 80 79 - 70 69 - 60 0 - 59 B+ C+ D+ F A B C D ABC-
Note 1: If you choose the CREDIT/NO CREDIT grading option (not available for mathematics majors), you must earn at least a "C"- to obtain CREDIT. Note 2: This grading system is minimal in the sense that the student is guaranteed at least as high a grade as indicated by the above scale. A small amount of grade curving may it make possible at times for a 79 to be a "B-", or a 68.5 to be a "C-", for example. Textbook, Blackboard, and Other Resources The text for this course will be Differential Equations and Boundary Value Problems: Computing and Modeling, by Edwards and Penney, fourth edition (2008). The first seven chapters and portions of chapter 8 will be covered in this course. Differential equations solver software will be made available on university computers and to individual students (PPLANE, MATLAB, others). A student Solutions Manual will be available for purchase in the bookstore. There is also a companion website for the text with more resources, located at http://wps.prenhall.com/esm_edwards_bvp_4/ Log in to the ULV Blackboard system and check the course listing there frequently for homework information/solutions and other course information. Academic Honesty and Classroom Etiquette Students are encouraged to help each other on problem assignments to facilitate the learning process. This does not include the practice of copying assignments, and if necessary, points will be deducted accordingly. Any form of dishonest behavior during a test may result in the immediate failure of that test or possible dismissal from the course. Please consult the university catalog for the complete university policy on academic dishonesty. Cell phones, pagers, and any other electronic beeping devices must be turned off while class is in session. If students are found to be in violation of this, the device will be collected for the remainder of the class, or, if s/he feels the need to respond to the call or page, the student will be excused from the classroom until the next time the class meets. Due to the capability of cell phones to transmit text and images, cell phone usage during a test may result in the immediate failure of that test or possible dismissal from the course. Students are expected to be on time for the start of class. You should expect to spend at least two hours studying outside of class for every hour spent in class. Of course, mileage may vary; if you wish to earn the best grade possible, you may have to study more! Each person has different study needs. Office Hours My office number is 155A, located on the middle floor of the Mainiero (MA) building. Office hours will be announced during the first week of class. Feel free to drop by for help any time you are having problems, or simply to talk about mathematics (or whatever!) Office phone number: (909)593-3511, ext. 4609. If I am not available, leave a message on my phone voice-mail after 4 rings, or by e-mail (frantzm@ulv.edu) The Natural Sciences secretary (Sharla, MA152, x4601) is (usually) available between 9am and 5pm.
page 3
Differential Equations Topics
Text: Differential Equations and Boundary Value Problems: Computing and Modeling, by Edwards and Penney, fourth edition (2008). This schedule provides for fifty 50-minute lectures (25 class days), leaving 6 lectures (3 days) free in a typical 56 le...

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