MAT 275 Homework

MAT 275 – Spring 2009
Modern Differential Equations

Homework

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Equations Credit: James Clerk Maxwell

January

Tuesday

Thursday

22	Read §1.1 Differential Equations and Mathematical Models Read the course syllabus. WeBWorK (optional): Introduction to WeBWorK WeBWorK (required): Integration Review

27	Read §1.2 Integrals as General and Particular Solutions WeBWorK: Introduction to Differential Equations §1.1 #28, 36, 46 (see Example 7) §1.2 #39, Write a paragraph justifying the assumption of constant deceleration in problems 30-32.

29	Read §1.4 Separable Equations and Applications §1.4 #64, 69

February

Tuesday

Thursday

3	Read §1.3 Slope Fields and Solution Curves WeBWorK: Separable Equations

5	Read §1.5 Linear First-Order Equations WeBWorK: Slope Fields Lab 1 (requires dfield7.m)

10	Read §2.4 Numerical Approximation: Euler's Method WeBWorK: First Order Linear ODEs §1.5 #29, 38, 42

12	Read §2.5 A Closer Look at the Euler Method WeBWorK: Euler's Method §1.3 #15, 16, Use dfield7.m to plot a slope field for this ODE. Describe what you see geometrically that explains your answers to these two questions.

17	Read §2.6 The Runge-Kutta Method Read §3.1 Introduction: Second Order Linear Equations No homework due. Study the handout on error anlayses in numerical methods. Work on Lab 2.

19	Read §3.3 Homogeneous Equations with Constant Coefficients Read §3.4 Mechanical Vibrations Lab 2 (requires euler.m, impeuler.m, and rk.m)

24	Read §3.5 Nonhomogeneous Equations and Undetermined Coefficients WeBWorK: Second Order Linear ODEs (homogeneous constant coefficient) §3.4 #1, 10, 11

26	Test 1 - Chapters 1 & 2 WebWorK Extra Credit: Exact Equations WebWorK Extra Credit: Riemann Integral Models

March

Tuesday

Thursday

3	Read §3.6 Forced Oscillations and Resonance WeBWorK: Undetermined Coefficients

5	Read §3.7 Electrical Circuits WeBWorK: Spring-Mass Systems §3.6 #21, 22, 24

10	Spring Break

12	Spring Break

17	Read §7.1 Laplace Transforms and Inverse Transforms Read §7.2 Transformations of Initial Value Problems §3.7 #1, 4, 8

19	Read §7.3 Translation and Partial Fractions Read §7.4 Derivatives, Integrals, and Products of Transforms Lab 3: Linear and nonlinear second order ODEs

24	Read §7.5 Periodic and Piecewise Continuous Functions WeBWorK: Laplace 1

26	Read §7.6 Impulses and Delta Functions WeBWorK: Laplace 2

31	Test 2 - Chapters 3 & 7 WebWorK Extra Credit: Laplace Practice (due 3/29)

April

Tuesday

Thursday

2	Read §4.1 Introduction to Systems of Differential Equations

7	Re-Read §4.1 Introduction to Systems of Differential Equations §4.1 #24, 26, 27, 30, For each problem also derive the corresponding first-order system.

9	Read §5.1 Matrices and Linear Systems WeBWorK: Systems 1 Draft of Modeling Project Paper

14	Lab 4: Exploration of Linear Systems

16	Read §5.2 The Eigenvalue Method for Homogeneous Systems WeBWorK: Linear Systems

21	Read §5.3 Second-Order Systems and Mechanical Applications §5.2 #28, 30 §5.3 #2, 16, 17, 18, 19

23	Read §6.1 Stability and the Phase Plane §6.1 #3, 5, 8, 9, 24, 26

28	Test 3 - Chapters 4 & 5

30	Read §6.2 Linear and Almost Linear Systems Read §6.3 Ecological Models: Predators and Competitors §6.2 # 31, 32 §6.3 # 3, 8, 9, 10

May

Tuesday

Thursday

5	Read §6.4 Nonlinear Mechanical Systems Lab 5: Exploration of Non-Linear Systems Final Version of Modeling Project Paper

12	Cumulative Final Exam 12:10-2:00 pm