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U of U MATH 2280 - MATH 2280 syllabus

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MATHEMATICS 2280-1Introduction to Differential EquationsSYLLABUSSpring semester 2010when:where:MTWF 8:35-9:25LCB 215instructor:office:telephone:email:office hours:problem session:Prof. Nick KorevaarLCB [email protected] 2:10-3:00, and by appointment, LCB 204Th 8:35-9:35 problem session, JTB 120.course home page: www.math.utah.edu/ ∼korevaar/2280springtext: Differential Equations and Boundary Va lue Problems, Computing and Modelingby C.Henry Edwards and David E. PenneyISBN = 9780131561076 (4thedition)prerequisites: A grade of at least “C” in Math 227 0 (linear algebr a), and any of 126 0, 1280, or2210 (i.e. calculus through multivariable Calculus).course outline: Math 2280 is an introduction to ordinary an d partial differential equations, andhow th ey are used to model problems a rising in engineering and scien ce. It is the second semesterof the year long sequence 2270-228 0, which is an in-depth introduction to linear mathematics. Thelinear algebra which you learned in Math 2270 will provide a surprising amount of the frameworkfor our discussions in Math 2280, alt hough this will no t be apparent at first.The semester begins with first order differential equations: their origins, geometric meaning(slope fie lds), analytic and numerical solutions, in Chapter s 1-2. The logist ic e quation and variou svelocity and acceleration models are studied closely. The next topic area, in Chapter 3, is lineardifferential equations of higher order, with the principal application being mechanical vibrations(friction, forced oscillations, resonance). This is about the time your linear algebra kn owledge willstart being helpful.Next we show how models of more complicat ed dynamical system s lead to first and second or-der systems of differential equations (Chapt er 4), and study Euler ’s method for numerical solutionsto help underst and existence and uniqueness of solutions. We use eigenvalues a nd eigenvectors, ma -trix e xponentials and general vector spac e theor y, to explicitly solve these problems in Chapter 5.The concepts of phase plane, stability, periodic orbits and dynamical-system chaos are intro ducedwith various ecological and mechanical models, in Ch apter 6. The study of ordinary differentialequations concludes with an introduction to the Laplace transform, in Chapter 7.The fin al portion of Math 2280 is an introduction to the classical partial d ifferential equations:the heat, wave and Laplace equations, and to the use of Fourier series and separation of variableideas to solve th ese equations in special cases. This material is covered in Chapter 9 of the text.1homework: when assigned from the text , homework will be collected each week on Fridays, anda large proportion of the problems will be graded. You will know the assignment due on Friday byMonday of the same week, at the latest. You are encouraged to make friends and st udy group s fordiscussing and working homework, althou gh you will each hand in your own pa pers (and copyingsomeone elses work won’t be productive for actually learning the mathematics).A portion of your homework will be in the form of computer pr ojects, u sually using the softwarepackage MAPLE. You will be encourag ed to do the computer projects in groups of 2-3 people andeach grou p may hand in a single solution. The subject of differential equ ations is driven by itsapplications, an d the computer allows you to st udy interesting problems which are conceptuallyclear bu t computationally difficult.The Math tutoring center is in the Rushing Student Center, in the basement between LCBand JWB on President’s Circle. You will be able to find tuto rs the re who can help with Math2280 ho mewor k (8 a .m.- 8 p.m. Monday-Thursday and 8 a.m.- 4 p.m. on Fridays). The pagewww.math.utah.edu/ugra d/mathcenter.html has more information .problem sessions: I will lead (optional) problem sessions each Thursday from 8:35-9:35, in JTB120.exams: There will be two in-class midterms (closed book, scientific calculat or only), as well as afinal exam. The date s are as follows:exam 1: Friday February 19. Pro bable course material is chapters 1-3.exam 2: Friday April 2. Probable course material is chapters 4-6.Final Exam: 8-10 a.m. Thursday May 6 in our classroom LCB 215. The exam will cover theentire course. This is the University-scheduled time.grading: Each midterm will count for 20% of your grade, the book homework and the projectswill count for a t otal of 30%, and the final exam will make up the remaining 30% of your grade .The value of ca refully working the homework problems and p rojects is that mathematics (likeanything) must be practiced and experienced to really be lea rned. Note: In order to receive agrade of at least “C” in the course you must earn a grade of at least “C” on the final exam.University date s to keep in mind: Monday January 18 is the last day to add this class,Wednesday January 20 is the last day to drop it. Friday Mar ch 5 is the last day to withdraw. (Allof these dates are easy to find from the University home page.)ADA statement: The American with Disabilities Act requ ires th at reasonable accomodationsbe p rovided for students with physical, sen sory, cognitive, systemic, learning, and psychiatricdisabilities. Please contact me at the beginning of the se mester to disc uss any such accommodationsfor the co urse.2Tentative Daily Scheduleexam dates fixed,daily subject mat ter approximatedMTWFMTWFMTWFMTWFMTWFMTWFMTWFMTWFMTWF11 Jan12 Jan13 Jan15 Jan18 Jan19 Jan20 Jan21 Jan25 Jan26 Jan27 Jan29 Jan1 Feb2 Feb3 Feb5 Feb8 Feb9 Feb10 Feb12 Feb15 Feb16 Feb17 Feb19 Feb22 Feb23 Feb24 Feb26 feb1 Mar2 Mar3 Mar5 Mar8 Mar9 Mar10 Mar12 Mar1.11.21.31.4none1.4-1.51.52.12.22.32.32.4-2.62.4-2.63.1-3.23.33.3-3.43.43.43.53.6none3.63.7Exam 14.14.1-4.34.35.1-5.25.1-5.25.35.3-5.45.45.4-5.55.55.65.6introduct ion to differential equationsintegral and general and particular solutionsslope fields and solution curvesseparable differential equationsMartin Luther King Dayand linear first order equationslinear DEspopulation mod elsequilibrium solutions and stab ilityacceleration-velocity modelscontinuednumerical solution approximationscontinuedintroduct ion to linear differential equationshomogeneous equations with constant coefficientsand mechanical vibrationscontinuedcontinuedparticular solutions to nonhomogeneous equationsforced oscillations and resonancePresident’s Daycontinuedelectrical circuitschapters 1.1-1.5,2,3.1-3.7first order


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