Syllabus for Math 308Differential EquationsFall 2011Sections 503 and 505Instructor: Volodymyr NekrashevychOffice: Milner 223Office hours: Office hours: Monday and Wednesday 2:00–3:00 PM or by appointment.e-mail: [email protected]: http://www.math.tamu.edu/˜nekrashClass hours:Section 503: MWF 10:20–11:10 AM BLOC 128Section 505: MWF 12:40–1:30 PM BLOC 128MATH 308 web page: The web page of the course ishttp://www.math.tamu.edu/˜nekrash/teaching/11F/M308.htmlThe Mathematics Department has a web page for Math 308. Its URL address ishttp://www.math.tamu.edu/courses/math308/?semester=2011CYou can find there: Weekly schedule of the course, suggested homework problems, math department computerhelp, help session schedule and other information.Text. Boyce, DiPrima Elementary Differential Equations 9th edition, Wiley, ISBN 978-1-118-13371-2.I will provide handouts with introduction to MatLab. The following book might be helpful:Hunt, Lipsman, Osborn, Rosenberg Differential Equations with Matlab 2nd edition, Wiley, ISBN 978-0471718123A personal copy of MatLab is useful, but not necessary, since you will be able to work remotely on Calclabcomputers.Topics covered. This is a course in differential equations. Topics include linear ordinary differential equationsand systems of linear differential equations, second order linear equations, solutions using Laplace transforms,numerical methods.Grading. Your grade will be determined by homework, two midterm exams and a cumulative final exam. Theweights of each of these are as follows.1Section Homework Exam I Exam II Final Exam Total20 pt 25 pt 25 pt 30 pt 100503 weekly Sept. 30 Oct. 28 Dec 9, 3-5 pm505 weekly Sept. 30 Oct. 28 Dec 12, 3:30-5:30 pmI may curve any grade and will then compute the course grade by the following rule: A for at least 90 points,B for at least 80 points, C for at least 70 points, D for at least 60 points and F for less than 60 points.Plan of lectures.8/29 1.1. Basic mathematical models, direction fields. 1.2. Solutions of some differential equations.8/31 1.2. Solutions of some differential equations. 1.3. Classification of differential equations.9/2 2.1. Linear equations; Method of integrating factors.9/5 2.2. Separable equations.9/7 2.3. Modelling with first order equations.9/9 2.4. Differences between linear and non-linear equations. 2.5. Autonomous equations and populationdynamics.9/12 2.6. Exact equations and integrating factors.9/14 3.1. Homogeneous equations with constant coefficients.9/16 3.2. Solutions of linear homogeneous equations; the Wronskian.9/19 3.3. Complex roots of the characteristic equation.9/21 3.4. Repeated roots; reduction of order.9/23 3.5. Non-homogeneous equations; Method of undetermined coefficients.9/26 3.6. Variation of parameters.9/28 3.7. Mechanical and electric vibrations.9/30 Exam I.10/3 3.8. Forced vibrations.10/5 6.1. Definition of the Laplace transform.210/7 6.2. Solution of initial value problems.10/10 6.3. Step functions.10/12 6.4. Differential equations with discontinuous forcing functions.10/14 6.5. Impulse functions.10/17 6.6. The convolution integral.10/19 7.1, 7.2. Introduction and review of matrices.10/21 7.3. Linear algebraic equations: linear independence, eigenvalues, eigenvectors.10/24 7.4. Basic theory of systems of first order linear equations.10/26 7.5. Homogeneous linear systems with constant coefficients.10/28 Exam II.10/31 7.6. Complex eigenvalues.11/2 7.7. Fundamental matrices.11/4 7.8. Repeated eigenvalues.11/7 7.9. Nonhomogeneous linear systems.11/9 5.1. Review of power series.11/11 5.2. Series solutions near an ordinary point, part I.11/14 5.3. Series solutions near an ordinary point, part II.11/16 5.4. Euler equations; Regular singular points.11/18 5.5. Series solution near a regular singular point, part I.11/21 5.6. Series solution near a regular singular point, part II.11/23 8.1. The Euler or tangent line method.11/28 8.2. Improvements of the Euler method.11/30 8.3. The Runge-Kutta method.312/2 8.4. Multistep methods.12/5 Overview.Make-up policy: Make-ups for missed quizzes and exams will only be allowed for a university approved excusein writing. Wherever possible, students should inform the instructor before an exam or quiz is missed. Consistentwith University Student Rules , students are required to notify an instructor by the end of the next working dayafter missing an exam or quiz. Otherwise, they forfeit their rights to a make-up.Scholastic dishonesty: Copying work done by others, either in-class or out of class, is an act of scholasticdishonesty and will be prosecuted to the full extent allowed by University policy. Collaboration on assignments,either in-class or out-of-class, is forbidden unless permission to do so is granted by your instructor. For moreinformation on university policies regarding scholastic dishonesty, see University Student Rules.Remember the Aggie Code of Honor: “An Aggie does not lie, cheat, or steal or tolerate those who do.”Copyright policy: All printed materials disseminated in class or on the web are protected by Copyright laws.One xerox copy (or download from the web) is allowed for personal use. 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