**Coordinates**:

Tues, Thur, 2:30pm to 4:00pm in MAASS-10 starting Tuesday 9th January.

Prof Humphries, BH-1112, Tel: 398-3821, E-mail: humphries@math.mcgill.ca

Office Hours: Mon 11:30-12:30 and Thurs 4:00-5:00pm in BH-1112, 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.*Differential Equations and Boundary Value Problems*, 8^{th}edition, by D.G Zill and W.S Wright.*Elementary Differential Equations*, by W.F. Trench. The pdf of this book is available online for free and legal download.

**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. However, it is an Honours course that will be taught at an honours level and will assume a corresponding level of mathematical sophistication. I recommend that you only take this course if you are registered or considering registering in an honours program or have the standing to do so.**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:**There will be a midterm which will be worth 20% of the final mark. This is provisionally scheduled to be in the normal class slot on Thursday 1st March - but this is subject to room availability.**Final Exam:**There will be a formal 3 hour final exam which will count 60% of the final mark.**Policies:**- Make up tests will not be given,
and late homework will not be accepted, except for an
absence approved
*in advance*by the instructor. - Important announcements (including posting of assignments and due dates)
will be made to registered students
by e-mail (via MyCourses)
and/or posted on
**MyCourses**. - 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.

- Make up tests will not be given,
and late homework will not be accepted, except for an
absence approved
**Copyright**

Instructor generated course materials (e.g., handouts, notes, summaries, exam questions, etc.) are protected by law and may not be copied or distributed in any form or in any medium without explicit permission of the instructor. Note that infringements of copyright can be subject to follow up by the University under the Code of Student Conduct and Disciplinary Procedures.**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.