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MATH 4027 - Ordinary Differential Equations - LSU Study Resources
  • 10 Pages FinalExamPractice
    FinalExamPractice

    School: LSU

    Course: Ordinary Differential Equations

    Final Exam Practice Problems Math 4027 The nal exam will be comprehensive. You should review both the statements of all existence and uniqueness theorems and the various techniques employed for nding solution of dierential equations. As with the second ex

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    School: LSU

    Course: Ordinary Differential Equations

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    Course: Ordinary Differential Equations

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    Course: Ordinary Differential Equations

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    Course: Ordinary Differential Equations

  • 1 Page Ordinary Differential Equations
    Ordinary Differential Equations

    School: LSU

    Course: Ordinary Differential Equations

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    DE14

    School: LSU

    Course: Ordinary Differential Equations

  • 3 Pages ExerciseSet4s07a
    ExerciseSet4s07a

    School: LSU

    Course: Differential Equations

    Exercise Set 4 Math 4027 Due: February 15, 2007 For each of the following matrices A, do all of the following calculations: (a) Compute the eigenvalues of A. For convenience, the characteristic polynomial cA () = det(A I ) is given. (b) Find all of the ei

  • 6 Pages ExerciseSet5s07a
    ExerciseSet5s07a

    School: LSU

    Course: Differential Equations

    Exercise Set 5 Math 4027 Due: March 1, 2007 From Waltman, Section 7. 1. Find eAt where (a) A = 11 . 01 Solution. The matrix A is triangular, so the eigenvalues are the diagonal entries, i.e., 1 = 2 = 1. From Theorem 7.1, we need to solve the system of die

  • 2 Pages ExerciseSet6s07a
    ExerciseSet6s07a

    School: LSU

    Course: Differential Equations

    Exercise Set 6 Math 4027 Due: March 21, 2007 Find the general solution of the given dierential equation. 1. 4y + y = 0 Solution. The characteristic polynomial is p() = 42 + = (4 + 1) so the roots of p() = 0 are 1 = 0 and 2 = 1/4 so the solution of the die

  • 2 Pages ExerciseSet7s07a
    ExerciseSet7s07a

    School: LSU

    Course: Differential Equations

    Exercise Set 7 Math 4027 Due: April 10, 2007 From Waltman, Page 107. 6. Locate the critical points of the following systems. (a) cfw_(n, 0) : n Z (b) (0, 0) and (1, 1) (c) cfw_(0, y ) : y R (d) (0, 0) and (1 2, 1) (e) (0, 0), (1, 1), and (1, 1) (f) cfw_(

  • 4 Pages ExerciseSet8s07a
    ExerciseSet8s07a

    School: LSU

    Course: Differential Equations

    Exercise Set 8 Math 4027 Due: April 19, 2007 1. Consider the three systems (a) x y = 2x + y = y + x2 (b) x y = 2x + y = y + x2 (c) x y = 2x + y = y x2 All three have a critical point at the origin (0, 0). Which two systems have the same qualitative struct

  • 5 Pages Exam 1
    Exam 1

    School: LSU

    Course: Differential Equations

    Name: Exam 1 Instructions. Answer each of the questions on your own paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each

  • 5 Pages Exam 2
    Exam 2

    School: LSU

    Course: Differential Equations

    Name: Exam 2 Instructions. Answer each of the questions on your own paper, except for problem 2, where you may record your answers in the box provided. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given f

  • 3 Pages Exam1Reviews07a
    Exam1Reviews07a

    School: LSU

    Course: Differential Equations

    Math 4027 Exam 1 Review Sheet Review Exercises for Exam 1 Answers 1. (a) y (t) = ce2t (b) y (t) = ce2t + et (c) y (t) = cet + 1 e3t 2 2 (d) y (t) = cet + (e) y (t) = ct3 t 1 2 3 cos t 2. (a) y (t) = 5te2t e2t (b) y (t) = 2e3t cos 2t + e3t (c) y (t) = t4

  • 6 Pages Exam2Reviews07a
    Exam2Reviews07a

    School: LSU

    Course: Differential Equations

    Math 4027 Exam 2 Review Sheet Exam 2 will be on Tuesday, April 24, 2007. The syllabus for this exam consists of Sections 9 (Elementary Stability) and 11 (Scalar Equations) of Chapter 1 and Sections 1 6 and 8 of Chapter 2 in Waltman. You will be allowed (

  • 4 Pages ExerciseSet2s07a
    ExerciseSet2s07a

    School: LSU

    Course: Differential Equations

    Exercise Set 2 Math 4027 Due: January 25, 2007 1. Find the solution of the initial value problems: (a) y + 2y = x, y (0) = 1, Solution. Multiply by e2x to get (e2x y ) = xe2x and then integrate to get e2x y = x 2x 1 2x e e + C. 2 4 Solve for y and substit

  • 4 Pages ExerciseSet3s07a
    ExerciseSet3s07a

    School: LSU

    Course: Differential Equations

    Exercise Set 3 Math 4027 Due: February 6, 2007 Pages 1314. 7. Construct the inverse of each of the given matrices. You may use any of the techniques that you learned in linear algebra for the computation of the inverse A1 of a square matrix. The two most

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    School: LSU

    Course: Ordinary Differential Equations

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    DE8

    School: LSU

    Course: Ordinary Differential Equations

  • 5 Pages Exercise Set 5
    Exercise Set 5

    School: LSU

    Course: Ordinary Differential Equations

    Exercise Set 5 Math 4027 Due: May 5, 2005 1. Solve the following dierential equations: (a) y = x2 /y . Solution. The equation is separable, so rewrite it in the form yy = x2 or in dierential form y dy = x2 dx and integrate to get an implicit equation y2 x

  • 3 Pages Exercise Set 4
    Exercise Set 4

    School: LSU

    Course: Ordinary Differential Equations

    Exercise Set 4 Math 4027 Due: April 7, 2005 1. Find the general solution of each of the following dierential equations. (a) 2x2 y + xy y = 0 Solution. The indicial equation q (r) = 2r(r 1) + r 1 = (2r + 1)(r 1) has roots 1 and 1/2. Hence y = c1 x + c2 |x|

  • 4 Pages Exercise Set 3
    Exercise Set 3

    School: LSU

    Course: Ordinary Differential Equations

    Exercise Set 3 Math 4027 Due: March 15, 2005 1. Verify that the function 1 (x) is a solution of the given dierential equation, and nd a second linearly independent solution 2 (x) on the interval indicated. (a) y 2x2 y = 0 (b) y 4xy + (4x2 2)y = 0 (c) (1 x

  • 3 Pages Exercise Set 2
    Exercise Set 2

    School: LSU

    Course: Ordinary Differential Equations

    Exercise Set 2 Math 4027 Due: February 10, 2005 1. Determine, with justication, whether each of the following lists of functions is linearly dependent or linearly independent. (a) 1 (x) = ex , 2 (x) = ex+2 Solution. These functions are linearly dependent

  • 3 Pages Exercise Set 1
    Exercise Set 1

    School: LSU

    Course: Ordinary Differential Equations

    Exercise Set 1 Math 4027 Due: February 1, 2005 1. Find the solution of the initial value problems: (a) y + 2y = x, y (0) = 1, Solution. Multiply by e2x to get (e2x y ) = xe2x and then integrate to get x 2x 1 2x e e + C. 2 4 Solve for y and substitute y (0

  • 5 Pages Exam 2
    Exam 2

    School: LSU

    Course: Ordinary Differential Equations

    Name: Exam 2 Instructions. Answer each of the questions on your own paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each

  • 6 Pages Exam 1
    Exam 1

    School: LSU

    Course: Ordinary Differential Equations

    Name: Exam 1 Instructions. Answer each of the questions on your own paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each

  • 2 Pages Exam 1 Solutions
    Exam 1 Solutions

    School: LSU

    Course: Ordinary Differential Equations

  • 12 Pages Exam2Practice
    Exam2Practice

    School: LSU

    Course: Ordinary Differential Equations

    Exam II Practice Problems Math 4027 The syllabus for the second exam will consist of Chapter 3 (Sections 1 8) and Chapter 4 (Sections 1 4, 6 8). Here are a few sample problems similar to previously assigned problems. 1. Find a basis for the solution set o

  • 2 Pages Diff Eq.
    Diff Eq.

    School: LSU

    Course: Ordinary Differential Equations

    Math 4027 Differential Equations Spring 2005 TTh 10:40 - 12:00 Lockett 113 Instructor: William A. Adkins 350 Lockett Hall Tel: 578-1601 E-mail: adkins@math.lsu.edu Class Web Site: http:/www.math.lsu.edu/~adkins/m4027.html Office Hours: 9:40 - 10:30 A.M. M

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    Course: Ordinary Differential Equations

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    Course: Ordinary Differential Equations

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    DE7

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    Course: Ordinary Differential Equations

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    DE6

    School: LSU

    Course: Ordinary Differential Equations

  • 4 Pages Homework Solution 2
    Homework Solution 2

    School: LSU

    Course: Differential Equations

    Exercise Set 2 Math 4027 Due: January 25, 2007 1. Find the solution of the initial value problems: (a) y + 2y = x, y (0) = 1, Solution. Multiply by e2x to get (e2x y ) = xe2x and then integrate to get e2x y = x 2x 1 2x e e + C. 2 4 Solve for y and substit

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