| Jan 23 |
Implicit differentiation (9.6)
Min, max, saddle points, Hessians, second-order Taylor formula (9.9-9.12) |
| Jan 25 |
Finish 9.9-9.12
Lagrange multipliers (9.14) |
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| Jan 30 |
Finish 9.14
Line integrals (10.1-10.4)
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| Feb 1 |
Fundamental theorems of calculus for line integrals (10.10, 10.11, 10.14) |
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| Feb 6 |
Conditions for a vector field to be a gradient (10.15-10.16)
Constructing potential functions (10.17, 10.21) |
| Feb 8 |
Step functions and their integrals (11.1-11.3) |
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| Feb 13 |
Multiple integrals (11.4-11.5)
Double integrals as iterated integrals (11.6-11.8)
Continuous functions are integrable (11.10) |
| Feb 15 |
Double integrals over more general regions (11.11-11.14) |
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| Feb 20 |
More on double integrals; volumes |
| Feb 22 |
Green's theorem and applications (11.19-11.21) |
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| Feb 27 |
Change of variables in double integrals (11.26-11.27, 11.29, 11.30) |
| Mar 1 |
Midterm 1 |
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| Mar 6 |
Extensions to higher dimensions (11.31-11.33) |
| Mar 8 |
Parametric representations of surfaces (12.1)
Fundamental vector product (12.2-12.3) |
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| Mar 13 |
Surface integrals (12.7)
Change of parametrization (12.8) |
| Mar 15 |
Curl and divergence (12.12, 12.14)
Stokes' theorem (12.11) |
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| Mar 20 |
Stokes' theorem continued
Solving curl F = G (12.16) |
| Mar 22 |
Divergence theorem (12.19) |
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| Mar 27 |
Spring break - no class |
| Mar 29 |
Spring break - no class |
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| Apr 3 |
Linear differential equations of order n (6.4)
Existence-uniqueness of solutions (6.5, 6.6) |
| Apr 5 |
Constant-coefficient case (6.7, 6.8) |
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| Apr 10 |
Particular solutions, Wronskians (6.10, 6.11, 6.12) |
| Apr 12 |
Midterm 2 |
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| Apr 17 |
Systems of linear differential equations (7.1)
Calculus of matrix functions (7.2, 7.3)
Matrix exponentials (7.5)
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| Apr 19 |
Matrix exponentials and differential equations (7.6-7.9, 7.16)
Methods for calculating matrix exponentials (7.10) |
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| Apr 24 |
Proof of uniqueness-existence for linear first-order systems (7.21) |
| Apr 26 |
Normed vector spaces
Banach fixed point theorem |
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| May 1 |
Fixed point theorem and differential equations
Review |
| May 3 |
Review |
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| May 8 | Final exam (5:05PM - 7:05PM) |