Differential Equations and Mathematical Models

Homework: There will be weekly homework assigned each Thursday, to be completed by the following Thursday. Late assignments will NOT be accepted, but the lowest assignment will be dropped.

Homework 1, due 1/29/15:

Section 1.1: 2, 4, 7, 23

Section 1.2: 2, 7, 12, 13, 15

Section 1.3: 3, 6, 12, 17

We will have a quiz on this material on 1/29/15.

Homework 2, due 2/5/15:

Section 2.1: 13, 14, 18, 19, 30

Section 2.2: 3, 8, 9ac, 17ac

Section 2.3: 2, 3, 4, 14abc, 16

We will have a quiz on this material on 2/5/15.

Homework 3, due 2/12/15:

Section 2.3: 9, 12

Section 2.4: 1, 2, 8, 16, 22, 25

Section 2.6: 4, 7, 8, 19, 25

We will have a quiz on this material on 2/12/15.

Homework 4, due 2/19/15:

Section 2.5: 3, 4, 12, 22

Section 2.7: 2a, 12a

Section 8.3: 3a, compute only y1 and y2

We will have a quiz on this material on 2/19/15.

Homework 5, due 2/26/15:

Section 3.1: 2, 6, 12, 13, 16, 17, 20, 23

Section 3.2: 7, 12, 13

We will have a quiz on this material on 2/26/15.

Homework 6, due 3/6/15:

Section 3.2: 2, 5, 24, 31

Section 3.3: 4, 11, 17, 22

Section 3.4: 6, 11, 23

Homework 7, due 3/19/15:

Section 3.5: 2, 3, 4, 8, 16, 18, 22a, 25a

Section 3.6: 7

We will have a quiz on this material on 3/19/15.

Homework 8, due 3/26/15:

Section 3.6: 10, 13

Section 3.7: 6, 7, 26

Section 3.8: 5, 7ac, 12

We will have a quiz on this material on 3/26/15.

Homework 9, due 4/2/15:

Section 4.1: 3, 13

Section 4.2: 7, 15, 16

Section 4.3: 1, 8, 17

Section 7.1: 2, 8

Section 7.2: 2, 3, 6

We will have a quiz on this material on 4/2/15.

Homework 10, due 4/9/15:

Section 7.3: 3, 5, 7, 8, 16, 17, 23

Section 7.5: 1, 4

We will have a quiz on this material on 4/9/15.

Homework 11, due 4/16/15:

Section 7.5: 15, 16, 18, 29

Section 7.6: 1, 5, 9, 10, 13, 28

Homework 12, due Friday 4/24/15:

Section 7.8: 1c, 2c, 7a, 15 (no comparison), 17

Section 9.1: 1abc, 2abc, 20, 21

Quizzes: We will have a quiz on Thursday of each week on the material covered in the previous week. The quiz will be on the homework material due that week. The lowest quiz grade will be dropped.

Maple: There will be several Maple assignments throughout the semester to illustrate various important concepts and ideas.

Syllabus (subject to change as the course progresses):

Week 1: 1/20, 1/22

Section 1.1: Some basic mathematical models; direction fields/slope fields

Section 1.2: Solutions to some differential equations

Section 1.3: Classification of Differential Equations

Week 2: 1/27, 1/29

Section 2.1: Linear Equations; Integrating factors

Section 2.2: Separable Equations

Section 2.3: Modeling with first order equations

Week 3: 2/3, 2/5

Section 2.3: Modeling with first order equations continued

Section 2.4: Differences between linear and nonlinear equations

Section 2.6: Exact Equations and Integrating Factors

Week 4: 2/10, 2/12

Section 2.5: Autonomous Equations and population dynamics

Section 2.7: Euler's Method

Section 8.1, 8.3: Other Numerical Methods. Maple Lab.

Week 5: 2/17, 2/19

Section 3.1: Homogeneous Equations with Constant Coefficients

Section 3.2: Solutions to Linear Homogeneous Equations; the Wronskian

Week 6: 2/24, 2/26

Section 3.3: Complex Roots of the Characteristic Equation

Week 7: 3/3, 3/5

Exam 1

Section 3.4: Repeated Roots; Reduction of Order

Section 3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients

SPRING BREAK

Week 8: 3/17, 3/19

Section 3.6: Variation of Parameters

Section 3.7: Mechanical and Electrical Vibrations

Section 3.8: Forced Vibrations

Week 9: 3/24, 3/26

Section 4.1: General Theory of nth-Order Linear Equations

Section 4.2: Homogeneous Equations with Constant Coefficients

Section 4.3: Method of Undetermined Coefficients

Section 7.1, 7.2: Review of Matrices

Week 10: 3/31, 4/2

Section 7.3: Linear Algebraic Equations, Linear Independence, Eigenvalues, Eigenvectors

Section 7.4: Basic Theory of Systems of First Order Equations

Section 7.5: Homogeneous Equations with Constant Coefficients

Week 11: 4/7, 4/9

Section 7.6: Complex Eigenvalues

Section 7.8: Repeated Eigenvalues

Week 12: 4/14, 4/16

Section 9.1: The Phase Plane: Linear Systems

Section 9.2: Autonomous Systems and Stability

Section 9.3: Locally Linear Systems

Exam 2

Week 13: 4/21, 4/23

Section 9.4: Competing Species Models

Section 9.5: Predator-Prey Models

Week 14: 4/28, 4/30

Section 5.1: Review of Power Series

Section 5.2, 5.3: Series Solutions Near an Ordinary point

Section 5.4: Euler Equations

Section 6.1: Definition of the Laplace Transform

Section 6.2: Solution of Initial Value Problems