Difference between revisions of "Course schedule"
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|Linear and nonlinear equations - existence and uniqueness | |Linear and nonlinear equations - existence and uniqueness | ||
Revision as of 10:29, 7 January 2015
This schedule is tentative and may change slightly as the term progresses.
Not included on this schedule: There will be a weekly worksheet handed in during each tutorial session, starting during the second week of class. Pre-lecture WeBWorK assignments will be due before each lecture and a post-lecture assignment will be due each week.
Regarding textbook references below: These references are to Boyce and DiPrima (from last year). I will start add corresponding refs to the new textbook (Diffy Qs).
| Week | Chapters/sections (Diffy Qs) | Chapters/sections (Boyce and DiPrima) | Topics | |
|---|---|---|---|---|
| 1: Jan 3 | / Jan 5 | 0.2 | 1.1 | Intro to differential equation models |
| 0.2 | 1.2 | Introduction to solutions of differential equations | ||
| -- | 1.3 | Classification of DEs. | ||
| 1.4 | 2.1 | First order linear equations - Method of Integrating Factors | ||
| 1.3 | 2.2 | First order separable equations | ||
| 2: Jan 10 | / Jan 12 | -- | 2.3 | Modeling with First Order DEs |
| 1.2.2 | 2.4 | Linear and nonlinear equations - existence and uniqueness | ||
| -- | 2.5 (skip for now) | Autonomous equations, the phase line and applications | ||
| -- | 3.1 | Second order linear equations - Homogeneous equations with constant coefficients (real roots of the characteristic equation) | ||
| -- | 3.2 | Second order linear equations - The Wronskian | ||
| 3: Jan 17 | / Jan 19 | -- | 3.3 | Second order linear equations - Complex root of the characteristic equation |
| -- | 3.4 | Repeated roots; Reduction of order | ||
| -- | 3.5 | Nonhomogeneous equations; method of undetermined coefficients | ||
| 4: Jan 24 | / Jan 26 | -- | 3.6 (skip) | Variations of parameters |
| -- | 3.7 | Mechanical and electrical vibrations | ||
| -- | 3.8 | Forced vibrations | ||
| 5: Jan 31 | -- | Catch-up/Review | ||
| Feb 2 | -- | Midterm 1 | ||
| 6: Feb 7 | / Feb 9 | -- | 7.1 | Introduction to systems of first order linear equations |
| -- | 7.2 | Review of matrices | ||
| -- | 7.3 | Systems of linear equations;linear independence, eigenvalues, eigenvectors | ||
| -- | 7.4 | Basic theory of systems of first order linear equations | ||
| -- | 7.5 | Homogeneous linear systems with constant coefficients | ||
| -- | 7.6 | Complex eigenvalues | ||
| Feb 14 | / Feb 16 | -- | Reading break | |
| 7: Feb 21 | / Feb 23 | -- | 7.8 | Repeated roots |
| -- | 7.9 | Summary of homogeneous 2x2 systems. Nonhomogeneous linear systems (Method of Undetermined Coefficients, constant vector only) | ||
| 8: Feb 28 | / Mar 2 | -- | 6.1 | Definition of the Laplace Transform |
| -- | 6.2 | Solution of IVPs | ||
| -- | 6.3 | Step functions | ||
| -- | 6.4 | DEs with discontinuous forcing fucntions | ||
| 9: Mar 7 | / Mar 9 | -- | 6.5 | Impulse functions |
| -- | 6.6 | The convolution integral | ||
| -- | 10.2 | Fourier series | ||
| 10:Mar 14 | -- | 10.3 | The Fourier convergence theorem | |
| -- | 10.4 | Even and odd functions | ||
| Mar 16 | -- | Midterm 2 | ||
| 11: Mar 21 | / Mar 23 | -- | 10.5 | Heat conduction in a rod - Fourier series and separation of variables |
| -- | 10.7 | The wave equation - vibrations of an elastic string | ||
| 12: Mar 28 | / Mar 30 | -- | 10.6 | Other heat conduction problems |
| Apr 4 | -- | Catch-up/Review |
