| Date | Topic | Reading | Assignments | |
|---|---|---|---|---|
| General reminders |
In general, Homework assignments are due in the recitation of the week after next (e.g., Homework 1 is due on Week 3). | |||
| Week 1 Aug 28-Sept 1 |
Syllabus Differential equations and mathematical models Integrals as general and particular solutions Slope fields and solutions curves |
1.1 1.2 1.3 |
Homework 1 (Due Week 3) 1.1: 26, 48 1.2: 8, 10, 44 1.3: 11, 14, 18, 27, 29, 30 |
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| Week 2 Sept 4-8 |
Local existence and uniqueness of solutions Separable differential equations Linear first order differential equations |
1.3 1.4 1.5 |
Homework 2 (Due Week 4) 1.4: 18, 28, 32, 36, 37, 39 1.5: 1, 6, 16, 27, 38 |
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| Week 3 Sept 11-15 |
Differential equations and phase portraits in Mathematica Substitution methods |
Mathematica Notes 1.6 |
Homework 3 (Due Week 5) Mathematica Project 1.6: 8, 11, 21, 27, 29 Homework 1 is due |
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| Week 4 Sept 18-22 |
Substitution methods and exact equations | 1.6 | Homework 4 (Due Week 6) 1.6: 4, 19, 33, 37, 38, 44, 47, 57, 58 Homework 2 is due |
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| Week 5 Sept 25-29 |
Population models Equilibrium solutions and stability Acceleration-velocity models |
2.1 2.2 2.3 |
Homework 5 (Due Week 8) 2.1: 13, 23, 33 2.2: 8, 9, 19, 22 2.3: 9, 10, 19 2.4: 1, 11 Homework 3 is due |
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| Week 6 Oct 2-6 |
Numerical approximation: Euler's method Review |
2.4 | Homework 4 is due | |
| Midterm I Thursday, October 5, 10:00-11:20am (during lecture time) |
Cumulative 1.1-1.6 and 2.1-2.4 |
Practice exam Do not expect that the actual exam will contain exactly these kinds of problems! |
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| Week 7 Oct 9-13 |
Fall Break Tuesday, October 10, no classes in session |
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| Second order linear equations | 3.1 | Homework 6 (Due Week 9) 3.1: 11, 15, 19, 29, 30, 32, 37, 39 |
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| Week 8 Oct 16-20 |
Nth-order equations with constant coefficients | 3.2 3.3 |
Homework 7 (Due Week 10) 3.2: 8, 19, 36, 38, 43 3.3: 9, 12, 15, 21, 23 Homework 5 is due |
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| Week 9 Oct 23-27 |
Mechanical vibrations Nonhomogeneous equations Undetermined coefficients |
3.4 3.5 |
Homework 8 (Due Week 11) 3.4: 3, 14, 15 3.5: 2, 5, 9, 16, 17 Homework 6 is due |
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| Week 10 Oct 30-Nov 3 |
Variation of parameters Forced oscillations and resonance |
3.5 3.6 |
Homework 9 (Due Week 12) 3.5: 21, 22, 26, 34, 37, 47, 51 3.6: 1, 8 Homework 7 is due |
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| Week 11 Nov 6-10 |
Endpoint problems and eigenvalues First order systems |
3.8 4.1 |
Homework 10 (Due Week 14) 3.6: 11, 27 3.8: 3, 6, 7, 13 4.1: 19, 24 4.2: 4 Homework 8 is due |
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| Week 12 Nov 13-17 |
Midterm II
Tuesday, November 14, 10:00-11:20am (during lecture time) |
Cumulative (with focus on material after Midterm I) 3.1-3.6 and 3.8 |
Practice exam Do not expect that the actual exam will contain exactly these kinds of problems! |
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| The elimination method Matrices and linear systems |
4.2 5.1 |
Homework 9 is due | ||
| Week 13 Nov 20-24 |
Matrices and linear systems The eigenvalue method for homogeneous systems |
5.1 5.2 |
Homework 11 (Due Week 15) 5.1: 3, 23 5.2: 6, 17, 19 5.5: 13, 16, 20, 33 |
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| Thanksgiving Break Thursday, November 23, no classes in session |
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| Week 14 Nov 27-Dec 1 |
The eigenvalue method for homogeneous systems Repeated eigenvalues |
5.2 5.5 |
Homework 10 is due | |
| Week 15 Dec 4-8 |
Repeated eigenvalues Matrix exponentials |
5.5 5.6 |
Practice Homework (not to turn in) 5.6: 23, 25, 34, 35 Homework 11 is due |
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| Dec 18 | Final Exam
Monday, December 18, 11:15am-1:45pm Classroom: Javits Lecture Hall 110 (different from lectures!) |
Cumulative All sections included in Midterms I, II plus 4.1-4.2, 5.1-5.2, 5.5-5.6 |
Practice exam Do not expect that the actual exam will contain exactly these kinds of problems! |
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