| Date | Topic | Reading | Assignments |
|---|---|---|---|
| Week 1 Aug 24-28 |
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 Sept 2) 1.1: 26, 48 1.2: 8, 10, 44 1.3: 11, 14, 18, 27, 29, 30 |
| Week 2 Aug 31-Sept 4 |
Local existence and uniqueness of solutions Separable differential equations Linear first order differential equations |
1.3 1.4 1.5 |
Homework 2 (Due Sept 9) 1.4: 18, 28, 32, 36, 37, 39 1.5: 1, 6, 16, 19, 27, 38 |
| Sept 7 | Labor Day No classes in session |
||
| Week 3 Sept 7-11 |
Differential equations and phase portraits in Mathematica Substitution methods |
Mathematica Notes 1.6 |
Homework 3 (Due Sept 16) Mathematica Project 1.6: 8, 11, 21, 27, 29 |
| Week 4 Sept 14-18 |
Substitution methods and exact equations | 1.6 | Homework 4 (Due Sept 23) 1.6: 33, 37, 38, 44, 47, 57, 58 2.1: 13, 23, 33 |
| Week 5 Sept 21-25 |
Population models Equilibrium solutions and stability Acceleration-velocity models |
2.1 2.2 2.3 |
Homework 5 (Due Oct 7) 2.2: 8, 9, 19, 22 2.3: 9, 10, 19 2.4: 1, 27 3.1: 39, 51, 52, 56 |
| Sept 30 | Midterm I
During lecture time (administered through Blackboard) |
Cumulative 1.1-1.6 and 2.1-2.2 |
Practice exams from previous semesters:
Midterm 1 (Solutions) Midterm 2 (with Solutions) Midterm 3 (Solutions) |
| Week 6 Sept 28-Oct 2 |
Numerical approximation: Euler's method Second order equations with constant coefficients |
2.4 3.1 |
|
| Week 7 Oct 5-9 |
Second order linear equations Nth-order linear equations |
3.1 3.2 |
Homework 6 (Due Oct 14) 3.1: 19, 29, 30, 32, 41, 42 3.2: 8, 19, 27, 36, 38, 43 |
| Week 8 Oct 12-16 |
Nth-order equations with constant coefficients Mechanical vibrations |
3.3 3.4 |
Homework 7 (Due Oct 21) 3.3: 9, 12, 15, 20, 21, 23 3.4: 3, 14, 15 |
| Week 9 Oct 19-23 |
Nonhomogeneous equations Undetermined coefficients Variation of parameters |
3.5 | Homework 8 (Due Oct 28) 3.5: 5, 16, 19, 21, 22, 26, 34, 37, 47, 51 |
| Week 10 Oct 26-30 |
Forced oscillations and resonance Endpoint problems and eigenvalues First order systems |
3.6 3.8 4.1 |
Homework 9 (Due Nov 4) 3.6: 1, 8, 11, 26, 27 3.8: 3, 6, 7, 13 |
| Week 11 Nov 2-6 |
First order systems The elimination method Matrices and linear systems |
4.1 4.2 5.1 |
Homework 10 (Due Nov 18) 4.1: 19, 24 4.2: 4 5.1: 3, 23 5.2: 1, 6, 17, 19 |
| Nov 11 | Midterm II
During lecture time (administered through Blackboard) |
Cumulative (with focus on material after Midterm I) 2.3-2.4, 3.1-3.6, 3.8, and 4.1-4.2 |
Practice exams from previous semesters:
Midterm 1 (Solutions) Midterm 2 (Solutions) Midterm 3 (Solutions) |
| Week 12 Nov 9-13 |
Matrices and linear systems The eigenvalue method for homogeneous systems |
5.1 5.2 |
|
| Week 13 Nov 16-20 |
Complex Eigenvalues Repeated eigenvalues Matrix exponentials and linear systems |
5.2 5.5 5.6 |
Homework 11 (Due Dec 7) 5.5: 13, 16, 20, 33 5.6: 23, 25, 34, 35 5.7: 24, 31 |
| Nov 23-27 | Thanksgiving Break No classes in session |
||
| Week 14 Nov 30-Dec 4 |
Matrix exponentials: examples Nonhomogeneous systems Solution curves of linear systems |
5.6 5.7 5.3 |
|
| Week 15 Dec 7 |
Review | ||
| Dec 11 | Final Exam
2:15-5:00pm (administered through Blackboard) |
Cumulative All sections included in Midterms I, II plus 5.1-5.3, 5.5-5.7 |
Practice exams from previous semesters:
Final 1 (Solutions) Final 2 (Solutions 1 2 3 4) Final 3 (Solutions) |
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