Math-325: Honours Ordinary Differential Equations, Winter 2013

Course Outline

• Coordinates:
  Tues, Thur, 11:30am to 1:00pm in RPHYS 118 starting Tuesday 8th January.
  Prof Humphries, BH-1112, Tel: 398-3821, E-mail: humphries@math.mcgill.ca
  Office Hours: Mon 9:30-10:30, Wed 3:00-4:00, Thurs 4:00-5:00 and by arrangement
  

• Syllabus
  

  First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.

• Contents
  

  The intended contents are:

  • Introduction: Basic, terminology, classification.
  • First Order Equations: Integrating Factors, separable equations, linear and nonlinear equations, exact equations, existence and uniqueness.
  • Second and Higher Order Linear equations: Constant Coefficient homogeneous equations, roots of the characteristic equation, Wronskians, fundamental and general solutions. Cauchy-Euler Equations. Nonhomogeneous equations, undetermined coefficients, variation of constants (parameters), reduction of order.
  • Series Solutions: Regular Points, Regular Singular Points and Frobenius method.
  • The Laplace Transform: Definitions and properties, solving initial value problems, Discontinuities and Impulses, Convolutions.
  • Linear Systems of ODEs: Solutions and stability.
  • Introduction to numerical methods and nonlinear differential equations.

  but are subject to modification during the semester. Applications will be highlighted through examples of differential equations throughout the course.

• References:
  There is no required textbook. Recommended texts include
  • Elementary Differential Equations, 10^th edition, by W.E. Boyce and R.C. DiPrima.
  • Elementary Differential Equations, 6^th edition, by C.H. Edwards and D.E. Penny.
  Previous editions of either book should be just as good. Both books come in two versions, with the more expensive one having an extra chapter on boundary value problems, which are not in the syllabus of this course. I intend to give my own treatment of the material, but it largely follow the texts, but may reorder some of the material and add some embellishments.

• Prerequisites/Restrictions: The course is intended for students in Honours Mathematics, Physics and Engineering programs. It is not open to students who have taken MATH 263 (Engineers version of this course) or MATH 315 (Majors version of this course). The only explicit prerequisite is Math 222 or equivalent.

• Webwork: Webwork assignments will optional, and will not be for credit. I recommend you use them for further practice on the topics when and where you need it.

• Assignments: There will be regular written assignments (about 6 in the semester) . These will count for 20% of the final mark.
• Midterm: The midterm will be in class on Thursday 28^thFebruary, and will be worth 20% of the final mark.

• Final Exam: There will be a formal 3 hour final exam which will count 60% of the final mark.

• Policies:
  • No make up tests will be given.
  • No late homework will be accepted under any circumstances, except for an absence approved in advance by the instructor.
  • Important announcements (including assignment due dates) will be made to registered students by e-mail (via MyCourses to your official McGill e-mail address) and/or posted on MyCourses. You are responsible for reading your McGill e-mail.
  • I attempt to reply to e-mail in a timely fashion, but do not expect immediate responses. I usually will not reply to email sent the day before a test.
  • You are urged to read the textbook; if possible, read ahead! Should you miss a lecture, you are responsible for making up any material covered in class.

• Academic Integrity
  

  The work you hand in should be your own effort; any collaboration must be acknowledged.

  McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/students/srr/honest/ for more information).

• Language
  In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.