MATH 23: Differential Equations
Dr. S. Pauls
Text: Elementary Differential Equations and Boundary Value Problems, 7th edition. Boyce and DiPrima
MWF , Bradley 103
x-hour Tuesday , Bradley 103
Office: 404 Bradley
Office Hours: Monday 3-4pm, Tues 2-3pm, Friday 10-11am
In this course we will cover
some of the techniques used to solve differential equations, building on the
techniques covered in math 5, 8, and 13.
These include but are not limited to separation of variables, constant
coefficient methods, the method of undetermined coefficients, variation of
parameters, applications of linear algebraic methods to systems of equations,
series solutions, Fourier series solutions and
transform methods. The objective of
mastering these techniques is to apply them to differential equations which
model physical or “real world” situations.
Although we will see numerous applications of this type throughout the
semester, the main goal of the course is to apply the techniques to three of
the most important differential equations in physics: the
Course Structure and Expectations
Exams: This course will have one take home midterm
exam handed out
Reading Assignments: There will be regular reading assignments for the course. You are expected to read the relevant sections before coming to the class in which we discuss this material.
Homework: There will be regular homework assignments. Usually, there will be problems assigned at the end on one class period which will be due at the beginning of the next class.
Quizzes: I reserve the right to give an unspecified number of quizzes throughout the term. These quizzes may or may not be announced. Unannounced quizzes tend to correlate inversely to the amount of assigned reading the class is completing.
The course grade breaks down roughly as follows:
Midterm: 100 points
Final Exam: 150 points
Homework: 100 points
Quizzes/Misc: 50 points
Total: 400 points
Depending on the number of quizzes, the contribution of quizzes to the final grade may be raised or lowered. If a change occurs, I will explain the change completely in class.
Week 1: First and second order linear ODEs, review of separable equations, constant coeef methods, modeling of physical systems, etc. (Chapter 2 and the beginning of chapter 3)
Week 2: End of chapter three and chapter 4, including method of undetermined coefficients and variation of parameters. Applications to physical systems associated to vibrations.
Week 3: Chapter 5, power series and series solutions. Be prepared – review series and power series!
Week 4: More series solutions and beginning of systems of equations (chapter 7)
Week 5: Review of necessary linear algebra, techniques for homogeneous linear system with constant coefficients. (More of chapter 7)
Week 6: More complicated systems of linear equations, phase planes (parts of chapters 9 and 10)
Week 7: Fourier series, introduction to partial differential equations and separation of variables (Chapter 10)
Week 8: Applications of separation of variables to the Heat and Wave equations.
Week 9: More wave equation and applications to
Week 10: Supplemental topics and/or catch-up.