Rob Thompson Hunter College Fall 2018

Tuesdday/Thursday 4:10-5:25 Room: 506 HW

**e-mail:**
robert.thompson@hunter.cuny.edu

**Office: ** 902 HE **Hours:** TTh 3:00-4:00 and by appointment

- Use differential equations to model population growths, compounding interest, spring oscillations, predator-prey systems and other problems from natural sciences.
- Find general and specific solutions to first-order, second-order, and higher-order homogeneous and non-homogeneous differential equations.
- Select and apply appropriate methods to solve differential equations; these methods will include undetermined coefficients, variation of parameters, Laplace and inverse Laplace transforms and power series.

**Prerequisites:**MATH 250 or the equivalent.**Required Textbook:**Elementary Differential Equations (Sixth Edition)}, by C. Henry Edwards, David E. Penney, David Calvis**Exams:**There will be two midterm exams and a comprehensive final exam. The first exam will be approximately a third of the way through the course, the second exam will be approximately three fourths of the way. The final exam will be after the last class meeting, on the date scheduled by Hunter College for this particular section.**Grading:**Homework will count for 20% of your course grade. The midterm exams will be worth 25% each and the final exam will count for 30% of your course grade. If you stop attending the course and do not withdraw, you will receive a grade of WU. You may elect to take the course on a credit/no credit basis if you are eligible, but this is subject to the College's rules, which means you that you will not be eligible for credit/no credit grading unless you have attended most class periods, taken all the exams, including the Final Exam, and completed most of the homework.

- Assignment One, due Tuesday 9/4:

1.1/1,3,8,10,14,15,34,35

1.4/1,4,5,11,12,23,33,35

1.8/2,3 - Assignment Two, due Thursday, 9/13:

1.3/11,13,14,17,18. For these problems refer to this addendum on the Existence and Uniqueness Theorems, which are more thorough than the theorem in the book.

1.4/43,49,55,56,62,65.

(Note: I think there's a typo in problem 55. It should say "...the tank of Problem 54...", not "...the tank of Problem 48...". - Assignment Three, due Thursday 9/20:

1.5/1,4,5,13,16,33,34,36,41. - Assignment Four, due Thursday 10/4:

1.6/8,13,22,31,35,38,40,56

1.7/10,16,19

1.8/4,5,20,21

1.3/21,22,23 (For these slope field problems, instead of doing them by hand, use some sort of computer software, or better yet, just use an online slope field calculator.) - Assignment Five, due Tuesday 10/16:

2.1/20,21,22,23,24,25

2.2/21,23

2.3/3,5,8,23,21

2.4/3,4,5,6,15,17,18

- 1.1 Differential Equations and Mathematical Models
- 1.2 Integrals as General and Particular Solutions
- 1.3 Slope Fields and Solution Curves
- 1.4 Separable Equations and Applications
- 1.5 Linear First-Order Equations
- 1.6 Substitution Methods and Exact Equations
- 1.7 Population Models
- 1.8 Acceleration-Velocity Models

- 2.1 Introduction: Second-Order Linear Equations
- 2.2 General Solutions of Linear Equations
- 2.3 Homogeneous Equations with Constant Coefficients
- 2.4 Mechanical Vibrations
- 2.5 Nonhomogeneous Equations and Undetermined Coefficients
- 2.6 Forced Oscillations and Resonance
- 2.7 Electrical Circuits

- 3.1 Introduction and Review of Power Series
- 3.2 Series Solutions Near Ordinary Points
- 3.3 Regular Singular Points
- 3.4 Method of Frobenius: The Exceptional Cases

- 4.1 Laplace Transforms and Inverse Transforms
- 4.2 Transformation of Initial Value Problems
- 4.3 Translation and Partial Fractions
- 4.4 Derivatives, Integrals, and Products of Transforms

- 5.1 First-Order Systems and Applications
- 5.2 The Method of Elimination