Syllabus for Math 337

Prerequisites: Math 151 and 254

Textbook (optional): Brannan and Boyce: Differential Equations: An Introduction to Modern Methods and Applications. Wiley 2015. ISBN 978-1-118-53177-8

Course Catalog Description: integration of first-order differential equations, initial and boundary value problems for second order equations, series solutions and transform methods, regular singularities.

Student Learning Outcomes:
At the end of this course students will be able to:

1. Solve many linear and nonlinear first and second order differential equations.
2. Understand some qualitative methods for interpreting differential equations.
3. Apply methods from differential equations to solve problems from various fields of science.
4. Perform a geometric analysis to systems of differential equations.
5. Use MatLab and Maple software to study the dynamics of a variety of applications.
6. Interpret graphs from dynamical systems.
7. Apply power series techniques to find the solutions of differential equations
8. Apply Laplace transforms to solve a class of differential equations.
   

Course Objectives and Expectations on Students:

This course is a 3 unit course designed for students who are majoring in mathematics and is considered one of the core fields of applied mathematics. This course is required for a number of the upper division courses in dynamical systems.

Differential equations date back to the studies of Newton and Leibnitz, where the subject of Calculus was developed. The basis of Newtonian physics is the study of motion, which is described by differential equations. Differential equations are central to many sciences, as they describe physical phenomena, such as velocity, rates of reaction, and growth. Thus, differential equations are centered around applications, so key to our studies in dynamical systems at SDSU.

Scope and Purpose of the Course:

The scope and purpose of this course is being developed.

Course Assessment and Grading

Details of the course and timelines are available on the HW Assignment page.

Accommodation Of Disability: Students with disabilities who may need academic accommodations should notify the professor in writing within the first two weeks of instruction. Students need appropriate forms aproved by SDS (Calpulli Center, Suite 3101). All information will be kept confidential. Students that need evacuation assistance during campus emergencies should also meet with the instructor as soon as possible to assure the health and safety of all students. If you encounter a problem accessing anything in this course, please contact me as soon as possible.

Classroom Behavior And Student Code Of Conduct

1. It is expected that students will conduct themselves within the standards outlined in the student code of conduct,
   disciplinary procedure and student due process. Disciplinary action will be taken by the instructor as necessary. See more information at the SDSU Student Ethical & Civic Responsibility Code.
2. Students are expected to come to class in a timely manner, prepared for the day’s work. Full participation for the entire class period in activities, class exercises and discussions is required.
3. Please turn off all cell phones, pagers, etc. You will be released from class with an unexcused absence for making or accepting telephone calls or text messages in the classroom.
4. It is the student’s responsibility to make up missed material. This includes, but is not limited to, obtaining missed lecture notes from another student (not from the instructor), and finding out about any modifications of schedules or assignments announced during class time.
5. WeBWorK assignments are posted with a specific due date. It is the student’s responsibility to complete the assignment on time. There will be a maximum of 2 extensions given during the semester (unless written documentation proves the need for more).
6. Academic dishonesty will result in a grade of zero for the assignment and will be reported to Academic Affairs. It may result in further disciplinary action. Academic dishonesty includes, but is not limited to, cheating, which includes unauthorized collaboration and plagiarism.
7. Missed Exams: Students will receive a ZERO for any missed exam, except for written/documented excuses (illness, personal/family crises, etc.).
8. Even the visual presence of a Cell Phone during an Exam will result in a ZERO for that Exam.

• The instructor will make special arrangements for students with documented learning disabilities and will try to make accommodations for other unforeseen circumstances, e.g., illness, personal/family crises, etc. in a way that is fair to all students enrolled in the class. Please contact the instructor EARLY regarding special circumstances.
• Students are expected and encouraged to ask questions in class.
• Students are expected and encouraged to make use of office hours.

1. Introduction (4-Panel) - Maple Commands
2. Qualitative Methods (4-Panel) - Basic MatLab
   
3. Linear Equations (4-Panel) - MatLab Programming
4. Separable Equations (4-Panel)
5. Exact and Bernoulli Equation (4-Panel)
6. Existence and Uniquess (4-Panel)
7. Numerical Methods (4-panel)
8. 2D Linear Systems A (4-panel)
   
9. 2D Linear Systems B (4-panel)
   
10. 2D Linear Systems Appl (4-panel)
11. Second Order Differential Equations (4-panel)
12. Second Order Differential Equations: Part 2 (4-panel)
13. Laplace Transforms: Part A (4-panel)
14. Laplace Transforms: Part B (4-panel)
15. Power Series (4-panel)