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Week 1 | |
| Mon (Mar 31) |
Sec 12.1: Jordan Domain in R^n. Volume of Jordan domains.
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| Homework |
Ex 12.1:
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| Wed (Apr 2) |
Sec 12,1:Continuation of Monday.
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| Homework |
Ex :2($), 3($), 4, 5($), 6, 8($), 9($)
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| Fri (Apr 4) |
Sec 12.1 and 12.2: examples of Jordan regions. Definition of integration on Jordan regions in R^n.
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| Homework |
Ex :
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Week 2 | |
| Mon (Apr 7) |
Sec 12.2 Integration on Jordan regions continued: Continuous functions are integrable.
Linearity properties of integral.
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| Homework |
Ex 12.2: 1, 2($), 3, 4($), 5($), 6(%), 7, 10($), 11($)
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| Wed & Th (Apr 9 & 10) |
Sec 12.2: Comparison theorem and Mean value theorem. Measure zero sets and integrability.
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| Homework |
Ex
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| Fri (Apr 11) |
Sec 12.3: Calculation of multiple integrals. Fubini's theorem.
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| Homework |
Ex 12.3: 1b, 1c($), 2b($), 2d, 3a, 3b($), 3d, 4a($), 4b, 4d, 6($), 7, 9.
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Week 3 | |
| Mon (Apr 14) |
Sec 12.4: Application of the change of variable formula.
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| Homework |
Ex:
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| Wed (Apr 16) |
Sec 12.3: Proof of Fubini's theorem.
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| Homework |
Ex 12.3: 5b($), 7($), 9($).
Ex 12.4: 1a($), 1b, 1c, 2a($), 3a($), 4a($), 4b, 4c($), 5b($), 5d($), 6($), 8b($)
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| Fri (Apr 18) |
Sec 12.4-12.5: Partition of unity and the proof of change of variable formula.
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| Homework |
Ex
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Week 4 | |
| Mon (Apr 21) |
Sec 12.4-12.5: The proof of change of variable formula. (continued)
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| Homework |
Ex
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| Wed (Apr 23) |
No Class
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| Homework |
Ex
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| Fri (Apr 25) |
Midterm 1
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| Homework |
Ex
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Week 5 | |
| Mon (Apr 28) |
Sec 13.1Curves in R^m.
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| Homework |
Ex
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| Wed (Apr 30) |
Sec 13.1 Continued.
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| Homework |
Ex: 3($), 4, 5a($), 5d($), 6b($), 6d($), 7, 8($)
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| Fri (May 2) |
Sec 13.2: Oriented curve. Path integral of a vector field.
Conservative fields and path independence.
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| Homework |
Ex 13.2: 1c($), 1e, 2a($), 2c($), 3a, 3b($), 3c($), 4, 6($)
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Week 6 | |
| Mon (May 5) |
Sec 13.2: More on path independence.
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| Homework |
Ex
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| Wed (May 7) |
Sec 13.3: Surface and their parametrization.
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| Homework |
Ex
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| Fri (May 9) |
Sec 13.3: Smooth parametrization. Surface integrals of scalar functions.
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| Homework |
Ex 13.3: 1a($), 1b($), 1c($), 2a($), 2b, 2c, 3a($), 4, 5, 6($), 7, 8($).
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Week 7 | |
| Mon (May 12) |
Sec 3.4: Oriented surfaces. Flux of a vector field through a surface in R^3.
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| Homework |
Ex
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| Wed (May 14) |
Sec 3.4: More on oriented surface. Algebra of differential forms.
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| Homework |
Ex 3.4: 1a($), 1b, 2a($), 2c($), 2d, 3a($), 3b($) 3c, 4, 5($), 6
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| Fri (May 16) |
Sec 3.4-3.5 Introduction to Green's theorem.
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| Homework |
Ex
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Week 8 | |
| Mon (May 19) |
Sec 13.5 Green's theorem.
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| Homework |
Ex 13.5: 1a, 1b($), 2a($), 2b($), 2c($), 5($), 6a($),
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| Wed (May 21) |
Midterm 2
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| Homework |
Ex
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| Fri (May 23) |
No class.
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| Homework |
Ex
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Week 9 | |
| Mon (May 26) |
Memorial Day
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| Homework |
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| Wed (May 28) |
Sec 13.5
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| Homework |
Ex: Application of Greens theorem.
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| Fri (May 30) |
Sec 13.5-13.6 Grad, Curl and Div. Gauss's divergence theorem.
Stokes theorem for surfaces in R^3.
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| Homework |
Ex 13.5: 3a($), 3b($), 3d($), 4a, 4b($), 4c, 7($), 9($), 10.
Ex 13.6: 1a($), 2a($), 3a($), 3b($),
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Week 10 | |
| Mon (June 2) |
Sec
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| Homework |
Ex
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| Wed (June 4) |
Sec
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| Homework |
Ex
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| Fri (June 6) |
Sec
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| Homework |
Ex
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