MATH 330 Ordinary Differential Equations Fall 2014 Course

MATH 330: Ordinary Differential Equations Fall 2014

Course Topics • • Introduction to differential equations (3 classes) First order differential equations (7 classes) Second and higher order linear differential equations (8 classes) Mechanical and electrical vibrations (3 classes) Series solutions of differential equations (6 classes) Laplace transform solutions of differential equations (5 classes) Systems of first order linear equations (2 classes) Nonlinear equations and numerical methods (3 classes) The tentative schedule of the course has been posted on my website; see http: //home. sandiego. edu/~pruski/m 330 f 14 schedule. html

Course Learning Outcomes Upon successful completion of this course, the student will: 1. Demonstrate a working knowledge of theory of first-order differential equations and second-order linear differential equations, including the knowledge of theorems with assumptions. 2. Be able to: • • 3. apply the standard, calculus-based and algebra-based methods to solve various types of first-order differential equations and linear secondorder equations, apply the power series method, Laplace transform method, and a simple numerical method to solve standard types of differential equations. Demonstrate the ability to: • • solve problems in the topics listed above, including applications from the field of physics and engineering, use a computer environment, such as MATLAB, to solve differential equations and visualize and interpret the solutions, understand simple proofs and write elementary proofs, communicate mathematical ideas clearly.

Proofs Some of you are taking this course as your first upper-division mathematics class. Mathematics is mainly about proving that certain statements are true. We will be doing proofs in class and you will be required to do simple proofs in your assignments and during the exams.

The Textbook Boyce, Di. Prima, Elementary Differential Equations. Tenth Edition. There is not enough time to lecture on everything in class, so that you will have to learn some material on your own. Reading the assigned material is absolutely essential! Pop quizzes will include questions on the assigned reading as a gentle method of enforcing your reading.

MATLAB The course will include a MATLAB component. MATLAB® is a high-level language and interactive environment that enables you to perform computationally intensive tasks, including solving differential equations, analyzing the solutions, and visualizing them. Several homework assignments will contain a MATLAB component. You are also encouraged to use MATLAB, Maple or other resources to avoid tedious computations in your homework assignment exercises.

Office Hours • Mondays 4 -5 • Tuesdays 2: 30 – 4 • Wednesdays 1– 2 • Fridays 12: 30 – 2 and at other times, by appointment. The best way to contact me is by using e-mail (pruski@sandiego. edu). I read e-mail many times a day. I do have voice mail (x. 4035), but I sometimes forget to check it. You may also call our departmental Executive Assistant, Tina, at x. 4706.

Homework Assignments will be assigned and collected weekly. For many of the assigned exercises, a BOB (back of the book) answer will be available. The total homework assignment score will count for 25% of the course grade. Late assignments will not be accepted unless you have a valid reason and you arrange it with me in advance. Mathematics is about an organized, focused, and logical way of thinking. When you solve math problems, the actual answer is less important than the way you arrived at this answer. Therefore, when you submit your homework assignments you should show not just the final answer, but the main steps how you arrived at the answer. Think about your solution being a guide that helps the reader to get from the problem statement to the answer. Your solution is not just a product; it is the process that yields this product.

Research Project A small research project (individual or in pairs) requiring will be assigned in November to be completed by December 10. Each project requires a write-up; volunteers will be solicited to present their projects in class. The project counts for 5% of the course grade.

Pop Quizzes There will be about 10 pop-quizzes (not announced in advance), i. e. , approximately one quiz a week. Quiz questions will refer to the recently covered material and to the new material you were supposed to read. Three lowest quiz scores will be dropped, and the remaining scores will count for 25% of the course grade. Quizzes cannot be made up unless you have a valid reason for not taking the quiz and you notify me in advance of your absence.

Exams The midterm exam will take place on Wednesday, October 22. The exam is of closed-book variety. The test score will count for 15% of the course grade. A test can be made up only if you have an actual emergency and if you notify me in advance about your absence. The final exam (Friday, December 19, 11: 00 – 1: 30) will be cumulative and its score will count for 30% of the course grade. The final exam will also be of closed book type.

Calculator Policy No calculators beyond TI-83/4, smartphones, i. Pods, i. Pads, tablets, etc. , are allowed on quizzes and exams.

Grading Criteria Total percentage Grade ============= 92% and above A 90% - 92% A 88% - 90% B+ 82% - 88% B 80% - 82% B 75% - 80% C+ 65% - 75% C 60% - 65% C 50% - 60% D Below 50% F ============= (Note: I will “curve up” the grades, in the unlikely case that the number of A's and B's falls below, approximately, 40% of the current enrollment)

Academic Integrity Mathematics and Computer Science Department strongly promotes Academic Integrity. I hope issues related to academic integrity will not arise in our course. There have been some cases of cheating in programming courses in the past -- mainly the cases of submitting someone else’s work for homework or programming assignments as well as cases of cheating during exams. Depending on the severity of the case, the possible consequences include: assigning the score of 0 on the given assignment, lowering the course grade, or even assigning F in the course.