Syllabus for Math 308Differential EquationsFall 2010Sections 503 and 504Instructor: Volodymyr NekrashevychOffice: Milner 223Office hours: Office hours: Monday 1:00–2:00 and Wednesday 2:00–3:00 PM or by appointment.e-mail: [email protected]: http://www.math.tamu.edu/˜nekrashTelephone: (979) 845 24 50Class hours:Section 503: MWF 10:20–11:10 AM BLOC 128Section 504: MWF 11:30–12:20 PM BLOC 128MATH 308 web page: The web page of the course ishttp://www.math.tamu.edu/˜nekrash/teaching/10F/M308.htmlThe Mathematics Department has a web page for Math 308. Its URL address ishttp://calclab.math.tamu.edu/docs/math308/You can find there: Weekly schedule of the course, suggested homework problems, math department computerhelp, help session schedule and other information.Text. J. R. Brannan and W. E. Boyce, Differential Equations: An Introduction to Modern Methods & ApplicationsJohn Wiley & Sons, Inc, ISBN-13 978-0-471-65141-3.I will provide handouts with introduction to MatLab. The following book might be helpful:J. C. Polking, D. Arnold Ordinary Differential Equations using MATLAB, Pearson, ISBN 0-13-145679-2.A 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 Oct. 6 Nov. 12 Dec. 14, 8–10 am504 weekly Oct. 6 Nov. 12 Dec. 15, 10:30–12:30I 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.8/30 Section 1.1. Some Basic Mathematical Models; Direction Fields9/1 Section 1.2. Solutions of Some Differential Equations9/3 Section 2.1. Linear Equations; Method of Integrating Factors9/6 Section 2.2. Seperable Equations9/8 Section 2.3. Modeling with First Order Equations9/10 Basic commands of MATLAB. Section 2.4. Differences Between Linear and Nonlinear Equations9/13 Section 2.5. Autonomous Equations and Population Dynamics, Section 2.6. Exact Equations and Integrat-ing Factors9/15 Section 3.1. Systems of Two Linear Algebraic Equations9/17 Section 3.2. Systems of Two First Order Linear Differential Equations9/20 Section 3.3. Homogeneous Linear Systems with Constant Coefficients9/22 Section 3.4. Complex Eigenvalues9/24 Section 3.6. A Brief Introduction to Nonlinear Systems; Solving equations with MATLAB9/27 Section 7.1. Autonomous Systems and Stability9/29 Section 7.2. Almost Linear Systems10/1 Section 7.3. Competing Species, Section 7.4. Predator-Prey Equations10/4 Section 4.1. Definitions and Examples, Section 4.2. Theory of Second Order Linear Homogeneous Equa-tions210/6 Exam Review10/8 First exam10/11 Section 4.3. Linear Homogeneous Equations with Constant Coefficients10/13 Section 4.4. Characteristic Equations with Complex Roots10/15 Section 4.6. Nonhomogeneous Equations: Method of Undetermined Coefficients10/18 Section 4.7. Forced Vibrations, Frequency Response, and Resonance10/20 Section 4.8. Variation of Parameters10/22 Section 5.1. Definition of the Laplace Transform10/25 Section 5.2. Properties of the Laplace Transform10/27 Section 5.3. The Inverse Laplace Transform10/29 Section 5.4. Solving Differential Equations with Laplace Transforms11/1 Section 5.5. Discontinuous Functions with Laplace Transforms11/3 Section 5.6. Differential Equations with Discontinuous Forcing Functions11/5 Section 5.7. Impulse Functions11/8 Section 5.8. Convolution Integrals and Their Applications11/10 Overview.11/12 Second exam11/15 Section A.1. Matrices; Section A.2. Systems of Linear Algebraic Equations, Linear Independence, andRank11/17 Section A.3. Determinants and Inverses ; Section A.4. The Eigenvalue Problem11/19 Section 6.1. Definitiions and Examples11/22 Section 6.2. Basic Theory of First order Linear Systems11/24 Section 6.3. Homogeneous Linear systems with Constant Coefficients311/29 Section 6.4. Complex Eigenvalues12/1 Section 6.5. Fundamental Matrices and the Exponential of a Matrix12/3 Section 6.6. Nonhomogeneous Linear Systems12/6 OverviewMake-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. 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