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 case VI. Nonlinear Systems: introduction, example of simple pendulum MIDTERM |
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 |