Instructor: Dr. Jessica M. Conway.

Lectures: MWF 1-2pm, Henn 200.

Office hours: Mathematics Annex, Room 1110 - Wednesdays 4-6pm + by appointment.

OFFICE HOURS DURING FINAL EXAMS (DEC 6-20): Tuesdays/Thursdays from 3-5pm; Saturday Dec 18/Sunday Dec 19 from 4-7pm.

Email: conway (at) math (dot) ubc (dot) ca OR math255s104.fall2010 (at) gmail (dot) com

Phone: (604)822-6754

The Mathematics Department offers

Schedule and locations available at http://www.math.ubc.ca/Ugrad/ugradTutorials.shtml.

We will cover chapters 1-3, 6, 7, and 9.

On material up to and including lecture on Wed Sept 22 (up to and including section 3.1 of textbook).

Practice midterm AND solutions (in problem 2, don't worry about non-zero right hand side).

Note that these are meant to be just a guide; if you're having trouble with a concept, do more problems!

Midterm and solutions

On material in sections 3.1-3.8 of textbook (second part of lecture on Wed. Sept. 22 to first part of lecture on Mon. Oct. 18).

Midterm and solutions

On Laplace transforms and solving linear systems (up to undetermined vectors only). Note that sketching of phase planes will not be tested on this midterm.

Practice midterm A AND solutions

Practice midterm B AND solutions

Table of Laplace transforms. This will be the table included with your midterm exam. Note that it's identical to the one in your textbook.

Midterm and solutions

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(2) Problems from problem session (27 Sept 2010): here

(3) Reduction of order example

(4) Method of undetermined coefficients table of trial expressions

(5) Variation of parameters example

(6) Forced Oscillations example

(7) Summary of the method of partial fractions expansion (excerpt from Nagle, Saff, and Snider's

(8) Discontinuous Forcing Functions example

(9) SAME Discontinuous Forcing Functions example solved using convolution integrals. Includes details on integrating over step functions.

(10)

(11) Problems from problem session (3 Nov 2010): here. Please inform me immediately if you find any typos. UPDATED 13 Nov 2010 (one typo corrected).

(12) Summary of linear systems in the plane - characterization of critical points and phase portraits (excerpt from Nagle, Saff, and Snider's

(13) Examples of how to compute eigenvalues and eigenvectors of a matrix.

(14) Problems from problem session (15 Nov 2010): here. Please note that these are the problems I had prepared in advance. At the problem session based on questions some slightly different problems were computed, with emphases placed on different concepts.

Week | Topic | Reading | Suggested Problems | Lecture Notes |
---|---|---|---|---|

September 6 | I. Introduction: what is a DE, order, linear and nonlinear, solution, general
solution, particular solution.II. First Order Equations: solution of linear ODE, direction field |
9th ed.:Chap. 1, 2.1. 8th ed.:Chap. 1, 2.1. |
9th edition:p.15: 1(a), 3, 4, 8, 13, 15, 17, 18; p.24: 18, 20. p.39: 5, 11, 14, 21, 24, 32; p.99: 13. 8th edition:p.15: 1(a), 3, 4, 8, 13, 15, 17, 18; p.24: 18, 20. p.39: 5, 11, 14, 21, 24, 32; p.99: 13. |
Lecture 2 |

September 13 | II. First Order Equations: existence and uniqueness, integrating factors, separable
equations, symmetry, homogeneous equations, applications |
9th ed.:2.2 - 2.6. 8th ed.:2.2 - 2.6. |
9th edition:p.75: 3, 25, 27; p.47: 1, 6, 30, 34; p.59: 8, 9, 10, 16, 18, 32; p.88: 15, 20, 22, 24 , 28. 8th edition:p.75: 3, 25, 27; p.47: 1, 6, 30, 34; p.59: 8, 9, 10, 16, 18, 32; p.88: 15, 20, 22, 24 , 28. |
Lecture 3 Lecture 4 Lecture 5 |

September 20 | III. Second order linear equations: linear operator, existence and uniqueness, linear
independence, linear homogeneous equation, linear nonhomogeneous equation |
9th ed.:3.1, 3.2. 8th ed.:3.1, 3.2. |
9th edition:p.144: 1, 9, 13, 17, 23, 28; p.155: 1, 2, 46, 51. 8th edition:p.142: 1, 9, 13, 17, 23, 28; p.151: 1, 2, 33, 38. |
Lecture 6 Lecture 7 Lecture 8 |

September 27 | III. Second order linear equations: Wronskians and linear
independence (fundamental set of solutions), constant coefficient
linear homogeneous equations (characteristic equation: real roots,
double roots, complex roots), linear nonhomogeneous equation (method
of undetermined coefficients when the homogeneous equations has
constant coefficients) |
9th ed.:3.2, 3,3, 3.4, 3.5. 8th ed.:3.2, 3,3, 3.4, 3.5, 3.6. |
9th edition:p.163: 2, 7, 17, 25, 29, 32, 34; p.171: 1, 14, 23; p.183: 1, 8, 17, 28, 29. 8th edition:p.164: 2, 7, 17, 25, 29, 32, 38; p.172: 1, 14, 23; p.184: 1, 8, 17, 28, 29. |
Lecture 9 Lecture 10 Lecture 11 |

October 4 | III. Second order linear equations: linear nonhomogeneous equation (method
of undetermined coefficients when the homogeneous equations has
constant coefficients), linear nonhomogeneous equation (method of variation
of parameters), applications to electrical circuits and mechanical vibrations MIDTERM |
9th ed.:3.5, 3.6, 3.7. 8th ed.:3.6, 3.7, 3.8. |
9th edition:p.189: 1, 5, 19, 21, 28, 29; p.202: 5, 15, 16, 19, 20, 30. 8th edition:p.190: 1, 5, 19, 21, 28, 29; p.203: 5, 15, 16, 19, 20, 30. |
Lecture 12 Lecture 13 |

October 11 | III. Second order linear equations: applications to electrical circuits and mechanical vibrations |
9th ed.:3.7, 3.8. 8th ed.:3.8, 3.9. |
9th edition:p.215: 1, 5, 17. 8th edition:p.214: 1, 5, 17. |
Lecture 14 Lecture 15 |

October 18 | IV. Laplace Transform: definition and examples, solution of initial value problems, discontinuous functions |
9th ed.:6.1, 6.2, 6.3. 8th ed.:6.1, 6.2, 6.3. |
9th edition:p.311: 5, 6, 14, 18, 26, 27; p.320: 2, 11, 20, 24, 27(a,b), 28, 30, 37; p.328: 13, 25, 29, 30, 33, 34. 8th edition:p.312: 5, 6, 14, 18, 26, 27; p.322: 2, 11, 20, 24, 27(a,b), 28, 30, 37; p.329: 7, 19, 23, 24, 27, 28. |
Lecture 16 Lecture 17 Lecture 18 |

October 25 | IV. Laplace Transform: discontinuous functions, impulse functions |
9th ed.:6.4, 6.5. 8th ed.:6.4, 6.5. |
9th edition:p.336: 1, 10, 19; p.343: 1, 25. 8th edition:p.337: 1, 10, 19; p.344: 1, 25. |
Lecture 19 Lecture 20 |

November 1 |
IV. Laplace Transform:impulse functions, convolutions
V. Systems of first order linear equations: homogeneous case |
9th ed.:6.5, 6.6, 7.5. 8th ed.:6.5, 6.6, 7.5. |
9th edition:p.350: 1, 7, 13, 21, 22, 29; p.398: 1, 15, 29, 32, 33. 8th edition:p.351: 1, 7, 13, 21, 22, 29; p.398: 1, 15, 29, 32, 33. |
Lecture 21
Lecture 22 Lecture 23 |

November 8 |
V. Systems of first order linear equations: homogeneous case, non-homogeneous case | 9th ed.:7.6, 7.8, 7.9, 9.1. 8th ed.:7.6, 7.8, 7.9, 9.1. |
9th edition:p.409: 1, 26, 28; p.428: 1; p.439: 1, 3; p.494: 1(a-c), 17, 20, 21. 8th edition:p.410: 1, 26, 28; p.428: 1; p.439: 1, 3; p.492: 1(a-c), 17, 20, 21. |
Lecture 24
Lecture 25 Lecture 26 Example from Lecture 26 |

November 15 | V. Systems of first order linear equations: non-homogeneous caseVI. Nonlinear Systems: introduction, example of simple pendulumMIDTERM |
9th ed.:7.9, 9.1, 9.2. 8th ed.:7.9, 9.1, 9.2. |
9th edition:p.506: 1, 3, 17, 21, 23. 8th edition:p.501: 1, 3, 17, 21, 23. |
Lecture 27
Lecture 28 |

November 22 | VI. Nonlinear Systems: introduction, example of simple pendulum. |
9th ed.:9.3, 9.4, 9.5. 8th ed.:9.3, 9.4, 9.5. |
9th edition:p.516: 1-6, 19, 21, 22, 27. 8th edition:p.511: 1-6, 17, 19, 20, 25. |
Lecture 29
Lecture 30 Lecture 31 |

November 29 | VI. Nonlinear Systems: critical points (type/stability), phase portraits, applications. VII. Catch Up? And/or Review?: may be used for lectures to catch-up on schedule otherwise for review |
9th ed.:9.3, 9.4, 9.5. 8th ed.:9.3, 9.4, 9.5. |
. | Lecture 32
Lecture 33 Lecture 34 |

Section 102 (Nec)

Section 103 (Schoetzau)

Section 105 (Dridi)

Jessica M. Conway / Department of Mathematics / University of British Columbia