MATH 23: Differential
Equations
SpringTerm, 2003
Scott Pauls
Text: Elementary Differential Equations and Boundary Value Problems, 7th edition. Boyce and DiPrima
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Course Details
x-hour Thursday
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Instructor Information
Phone: 646-1047 email: scott.pauls@dartmouth.edu Office Hours:
Tuesday 2-4pm, Thursday 1-3pm |
Overview
In this course we will cover some of the techniques used to solve
differential equations, building on the techniques covered in math 3,
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
midterm exam on April 28th. There will
also be a final exam, scheduled by registrar Saturday, May 31, 10:30 am-12:30 pm.
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.
Grading
The course grade breaks down roughly as follows:
Midterm: 100 points
Final Exam: 150 points
Homework: 100 points
Rough Syllabus
Week 1: First and second order linear ODEs, review of separable equations, constant coefficientmethods, 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: Review
of necessary linear algebra, techniques for homogeneous linear system
with constant coefficients. (Chapter 7)
Week 4: More
complicated systems of linear equations, phase planes (parts of
chapters 9 and 10)
Week 5: Chapter
5, power series and series solutions. Be
prepared – review series and power series!
Week 6: More series solutions - singular points
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