Instructors: Matthew Ellison, Anna Vasenina
Course on canvas.dartmouth.edu.⇗
Course Schedule
Sections refer to Boyce & DiPrima, 11th edition.
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Lectures
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Sections
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Description
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Homework Problems
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Week 1: M Sep 16 |
1.1, 1.2, 1.3
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Introduction to differential equations;
Classificiation of ODEs
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1.1: 5, 6, 7, 18, 20 1.2: 10, 12 1.3: 1, 2, 3, 4, 12 |
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Week 1: W Sep 18
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2.1
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Integrating Factor
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2.1: 9, 12, 20 |
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Week 1: F Sep 20
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2.2, 2.3
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Separable equations;
Modeling with Differential Equations
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2.2: 6, 15, 19 2.3: 2, 6, 11 |
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Week 2: M Sep 23
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2.4
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Differences Between Linear and Nonlinear Equations :
Existence and Uniqueness
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2.4: 4, 8, 12, 16 |
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Week 2: W Sep 25
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2.5
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Autonomous Equations and Population Dynamics
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2.5: 3, 4, 5, 8, 9, 18(b)(c) |
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Week 2: F Sep 27
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2.6
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Exact Equations & Integrating Factor
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2.6: 3, 4, 6, 16, 20, 21 |
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Week 3: M Sep 30
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3.1
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2nd-Order Constant Coefficient Equations:
Distinct Real Roots of the Characteristic Equation
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3.1: 6, 9, 16 |
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Week 3: W Oct 2 |
3.2
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Existence and Uniqueness, Superposition, and the Wronskian
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3.2: 8, 19, 24 |
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Week 3: F Oct 4
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3.3
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Complex Roots of the Characteristic Equation
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3.3: 7, 18, (optional 25, 26) |
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Week 4: M Oct 7
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3.4
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Repeated Roots of the Characteristic Equation & Reduction of Order
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3.4: 5, 8, 12, 19, 22 |
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Monday October 7th
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Midterm Exam 1
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Material through 3.3
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Week 4: W Oct 9
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3.5
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Nonhomogeneous Equations: Undetermined Coefficients
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3.5: 1, 5, 9, 13, 22 |
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Week 4: F Oct 11
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3.6
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Nonhomogeneous Equations:
Variation of Parameters
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3.6: 1, 3, 5, 9, 13 |
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Week 5: M Oct 14
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7.1, 7.2
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Introduction to Matrices and Linear, First-Order Systems of ODEs
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7.1: 1, 2, 5, 19 7.2: 8, 10, 16 (just c, d) |
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Week 5: W Oct 16
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7.3
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Linear Algebra Review: Linear Independence, Eigenvalues, Eigenvectors
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7.3: 3, 5, 9, 14, 15, 18, 19 |
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Week 5: F Oct 18
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7.4
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Basic Theory of First-Order Systems
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7.4: 1, (Optional 10) |
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Week 6: M Oct 21
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7.5
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Homogeneous Systems with Constant Coefficients
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7.5: 1, 4, 5, 9, 12, 18 |
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Week 6: W Oct 23
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7.6
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Complex Eigenvalues
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7.6: 3, 5, 6, 15, 21 |
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Week 6: F Oct 25
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7.7
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Fundamental Matrices
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7.7: 4, 8, 9, 12 |
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Week 7: M Oct 28
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7.8
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Repeated Eigenvalues
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7.8: 1, 2, 3, 14 (Optional: 19, 20, 21) |
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Week 7: W Oct 30
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7.9
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Nonhomogenous Linear Systems
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7.9: 1, 4, 8 |
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Week 7: F Nov 1
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7.9 (ct'd), 9.1
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Nonhomogenous Linear Systems (part 2), The Phase Plane: Linear Systems (summary)
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No additional problems |
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Friday November 1st
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Midterm Exam 2
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Material from 3.4 through 7.8
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Week 8: M Nov 4
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9.2
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Autonomous Systems and Stability
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9.2: 1, 9, 19, 20 |
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Week 8: W Nov 6
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9.3
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Locally Linear Systems
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9.3: 1, 2, 6, 13, 16 |
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Week 8: F Nov 8
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9.4, 9.5
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Competing Species; Predator-Prey Equations
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9.4: 3 [optional: 5, 6] 9.5: 3, 13 |
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Week 9: M Nov 11
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6.1
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Definition of Laplace Transform
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6.1: 4, 6, 12, 17, 19 |
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Week 9: W Nov 13
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6.2
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LT : Solution of Initial Value Problems
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6.2: 2, 10, 14, 16, 17 [Optional: 20, 21] |
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Week 9: F Nov 15
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6.3, 6.4
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LT: Step Functions; Discontinuous Inputs
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6.3: 8, 14 6.4: 3, 6, 11 |
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Week 10: M Nov 18
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6.5
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LT: Impulse Functions
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None |
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Friday November 22nd
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Final Exam
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Exam covers material from the whole course
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