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/m330f14schedule.html

Course Learning OutcomesUpon successful completion of this course, the student will:1. Demonstrate a working knowledge of the theory of first-order differential

equations and second-order linear differential equations, including the knowledge of theorems with assumptions.

2. Be able to: • apply the standard, calculus-based and algebra-based methods to solve

various types of first-order differential equations and linear second-order equations,

• apply the power series method, Laplace transform method, and a simple numerical method to solve standard types of differential equations.

3. 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, DiPrima, Elementary Differential Equations. Tenth Edition.

There is not enough time to lecture oneverything in class, so that you will have tolearn some material on your own. Readingthe assigned material is absolutelyessential! Pop quizzes will include questions onthe assigned reading as a gentle method ofenforcing your reading.

MATLAB

The course will include a MATLAB component. MATLAB® is a high-level language and interactiveenvironment that enables you to performcomputationally intensive tasks, including solvingdifferential equations, analyzing the solutions, andvisualizing them. Several homework assignmentswill contain a MATLAB component. You are alsoencouraged to use MATLAB, Maple or otherresources to avoid tedious computations in yourhomework assignment exercises.

Office Hours

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

Homework AssignmentsHomework 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 onequiz a week. Quiz questions will refer to therecently covered material and to the new materialyou were supposed to read. Three lowest quizscores will be dropped, and the remaining scoreswill count for 25% of the course grade. Quizzescannot be made up unless you have a validreason for not taking the quiz and you notify mein 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, iPods, iPads, tablets, etc., are allowed on quizzes and exams.

Grading CriteriaTotal percentage Grade==========================92% and above A90% - 92% A-88% - 90% B+82% - 88% B80% - 82% B-75% - 80% C+65% - 75% C60% - 65% C-50% - 60% DBelow 50% F==========================(Note: I will “curve up” the grades, in the unlikely case that the numberof 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 toacademic integrity will not arise in our course. There havebeen some cases of cheating in programming courses inthe past -- mainly the cases of submitting someone else’swork for homework or programming assignments as wellas cases of cheating during exams. Depending on theseverity of the case, the possible consequences include:assigning the score of 0 on the given assignment, loweringthe course grade, or even assigning F in the course.