# UBC Math 316: Elementary Differential Equations IIMay–August 2014

This page provides official background information for two courses running in parallel:

• UBC Math 257 — Partial Differential Equations, and
• UBC Math 316 — Elementary Differential Equations II.

## Instructor

Dr. Philip D. Loewen

 Office Mathematics Building, room 207 Email loew@math.ubc.ca (try this first) Office phone 604-822-3082 (urgent cases only, please) URI http://www.math.ubc.ca/~loew/
 Office Hours I'm happy to meet individuals or small groups in room MATH 207, but advance planning is essential. To schedule a conversation, email loew@math.ubc.ca, including your course number (e.g., “264” or “211”) in the subject line.

## Topic Outline

 Topic Hrs Description Review of Series 5 Convergence concepts Geometric series and the ratio test Error control and Shanks Transformation Power series Analytic functions, radius of convergence Linear Ordinary Differential Equations 9 Power Series Solutions near an ordinary point General Solutions Initial-Value Problems Non-homogeneous problems Homogeneous ODE's with Constant Coefficients Non-Homogeneous ODE with Constant Coefficients ODE's of Euler type Change of independent variable Singular points: regular vs irregular Series solutions near a regular singular point (Frobenius method) Linear Operators and Eigenvalue Problems 6 The matrix case Operators and eigenvalues in function space Sample eigenvalue problems Orthogonality and eigenfunction series Eigenfunction-series solutions for Boundary-Value Problems 6 Separation of variables: eigenvalue problems, formal series The Big Four standard eigenvalue problems Propagating coefficients Initialization Special modes; superposition Nonhomogeneous PDE Nonhomogeneous BC More General Eigenfunction Series 5 Eigenvalue Problems Orthogonality and Eigenfunction Series Sturm-Liouville Theory Full Fourier Series Heat Equation in Depth 3 Derivation; BC's and their meanings Transient versus long-run behaviour Splitting methods for nonhomogeneous boundary conditions Laplace's Equation in Depth 4 Derivation and Interpretation Superposition and splitting Neumann problems and consistency conditions Physical solutions are bounded functions Problems in polar coordinates (Euler equations reappear) Wave Equation in Depth 4 Derivation; BC's and their meanings Travelling wave solutions D'Alambert's solution Signal speed; reflections Forcing and resonance Numerical Methods 2 Finite Differences Spreadsheet Implementations Total Hours on Outline 44 (44 lecture-hours + 2 test-hours = 46 meetings this term)

## Course Details

Required Text:
• William F. Trench, Elementary Differential Equations with Boundary Value Problems, 2013. Book 9 in the collection Books and Monographs available free online at http://digitalcommons.trinity.edu/mono/9.

Watch the main course page for writeups customized for this term's experience. In addition, consult the following:

• W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, any edition since about #5. New York: John Wiley & Sons, 1997.
• Froese, Richard G., Partial Differential Equations. UBC M257/316 Lecture notes free on the Web.
• Peirce, Anthony, UBC M257/316 course page for Sep-Dec 2013. Look especially at the section headed “Lecture Notes”.

#### Other Nice Books:

• Churchill, R. V., and J. W. Brown, Fourier Series and Boundary Value Problems. New York: McGraw-Hill, 1993.
• Troutman, John L., Boundary Value Problems of Applied Mathematics. Boston: PWS Publishing Company, 1994.
• Main, Iain G., Vibrations and Waves in Physics, third edition. Cambridge University Press, 1993.

#### Important Dates:

• Tuesday 13 May: Class starts, 14:00 in room LSK 200.
• Thursday 19 June: Midterm test in class. 110 minutes.
• Friday 20 June – Wednesday 2 July: no classes.
• Thursday 3 July: Classes resume after mid-session break.
• Thursday 7 August: Last class of the term.
• Wednesday 13 August: Final exam, 19:00–21:30, room TBA. (This info is unofficial. Please confirm it on the UBC Enrolment Services Exam Schedule.)

#### Evaluation:

• Daily Participation (bring your iClicker to class), 0-2%.
• Weekly Homework (Due every Tuesday), 10%.
• 19 June 2014 (Thursday), Midterm Exam, 38-40%, in class.
• 12–16 August 2014, Final Exam, 50%, scheduled by UBC Enrolment Services.

#### Policies:

• Students may use no resources except for writing equipment on midterm and final examinations. This means no formula sheet and no calculator. Seriously.
• However, students are encouraged to use technology to help with weekly assignments.
• The final course grade is influenced only by what knowledge of the subject students demonstrate in the activities described above.
• There is no supplemental examination in this course.
• Missing a midterm normally results in a mark of 0. Exceptions may be granted in two cases: prior consent of the instructor or a medical emergency. In the latter case, the instructor must be notified within 48 hours of the missed test, and presented with a doctor's note immediately upon the student's return to UBC.
• On both homework and tests, the highest possible standard of academic integrity is expected and will be enforced. In short, students are expected to submit work that represents their own current thoughts and understanding. For details, review the UBC Calendar's sections on Academic Honesty and Standards and Academic Misconduct.

#### Course Web Page (daily details appear here):

http://www.math.ubc.ca/~loew/m316/

Last update: 07 Aug 2014 (Thu), 11:47:48. (Click a graphic to recheck.)