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by: Vivien Bradtke V


Marketplace > Texas A&M University > Mathematics (M) > MATH 611 > INTRO ORD PART DIFF EQ
Vivien Bradtke V
Texas A&M
GPA 3.6


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This 2 page Study Guide was uploaded by Vivien Bradtke V on Wednesday October 21, 2015. The Study Guide belongs to MATH 611 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/226055/math-611-texas-a-m-university in Mathematics (M) at Texas A&M University.

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Date Created: 10/21/15
Final Exam Topics The nal exam for M611 will be in the usual classroom EHPH 2067 Wednesday7 Dec 107 1030 am 1230 pm The exam will cover the course material that was not covered on the midterm exam in particular7 distribution theory7 the heat equation7 the wave equation7 and the method of characteristics The exam will consist of ve or six questions7 worth ve to ten points each Two of the questions will ask for explicit calculations and the others will ask for proofs I will provide statements of the system of characteristic equations and of the d7Alembert7 Poisson7 and Kirchhoff solutions to the wave equation You will need to bring your own paper 1 Explicit calculations There will be two questions on the exam involving explicit calculations The basic areas from which l7ll draw these questions are as follows 0 Computing the derivative of a distribution see Problems 4 and 5 from Assignments 8 9 0 Solutions obtained formally by operator methods see Problem 1 from Assignment 12 0 Solutions of the wave equation on R gtlt R1 see Problems 1 and 2 from Assignment 11 0 Solutions of rst order linear7 quasilinear and nonlinear PDE by the method of char acteristics see Problems 2 and 3 from Assignment 12 2 Proofs Three or four questions on the exam will ask you to prove an assertion using techniques discussed in the course The basic areas from which l7ll draw these questions are as follows Prove that a given mapping is a distribution see Problem 3 from Assignments 8 9 Verify properties of distributions see Problems 6 9 from Assignments 8 9 Verify properties of the heat kernel and properties of solutions to the heat equation on R gtlt R1 see Problem 1 from Assignment 10 Verify properties of the heat equation on UT see Evans 25147 though I wouldnt expect you to be as familiar with the proof of Theorem 233 as this problem assumes Derive properties of solutions ofthe wave equation7 especially though not only in cases in which the properties can be obtained from the d7Alembert7 Poisson7 and Kirchhoff integral representations see Problems 2517 and 2518 from Evans 0 Know the properties of the straightening transformation lt13 and its role in our develop ment of the Method of Characteristics 0 Aspects of our development of the Method of Characteristics7 especially regarding our process of bringing everything back to the characteristic equations For exarnple7 show that if agU7 2sgyquot7 and sg solve the characteristic equations with adrnissible initial data q 7g7 for sgij E I gtlt W then F 87j728 7f8 0 for all 577 E I gtlt W


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