| 1 |
Euclidean Geometry in 3 Dimensions
Geometric Proofs |
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| 2 |
Geometric Vectors and Vector Algebra |
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| 3 |
Vector Algebra with Cartesian Coordinates |
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| 4 |
Analytic Geometry in 3 Dimensions |
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| 5 |
Calculus of 1-Variable Vector Functions |
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| 6 |
Calculus of Vector Functions |
Problem set 1 due |
| 7 |
Paths and Curves |
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| 8 |
Scalar Fields
Cylindrical Coordinates |
Problem set 2 due |
| 9 |
Linear Approximation and Differentiability |
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| 10 |
Linear Approximation and Gradient
The Chain Rule |
Problem set 3 due |
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Exam 1 (Covers through Lecture 8) |
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| 11 |
Elimination Method for the Chain Rule |
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| 12 |
Terminology for Point-Sets in Euclidean Spaces
Maximum-Minimum Theorems |
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| 13 |
Two-Variable Test
Constrained Maximum-Minimum Problems |
Problem set 4 due |
| 14 |
Multiple Integrals |
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| 15 |
Iterated Integrals |
Problem set 5 due |
| 16 |
Integrals in Polar, Cylindrical, and Spherical Coordinates |
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| 17 |
Curvilinear Coordinates
Change of Variables |
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| 18 |
Change of Variables (cont.)
Vector Fields |
Problem set 6 due |
| 19 |
Visualizing Vector Fields
Line Integrals |
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| 20 |
Vector Line Integrals
Conservative Fields |
Problem set 7 due |
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Exam 2 (Covers Lecture 9 through 17) |
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| 21 |
Line Integrals (cont.)
Conservative Fields (cont.) |
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| 22 |
Surfaces |
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| 23 |
Surface Integrals |
Problem set 8 due |
| 24 |
Measures |
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| 25 |
Green's Theorem |
Problem set 9 due |
| 26 |
Divergence and the Divergence Theorem |
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| 27 |
Curl and Stokes' Theorem |
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| 28 |
Measures (cont.)
Irrotational Fields |
Problem set 10 due |
| 29 |
Mathematical Applications |
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Exam 3 (Covers Lecture 17 through 29) |
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| 30 |
n-Vectors and Matrices |
Problem set 11 due |
| 31 |
Equation Systems |
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| 32 |
Row Reduction
Determinants |
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| 33 |
Determinants (cont.)
Matrix Algebra |
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| 34 |
Subspaces |
Problem set 12 due |
| 35 |
Multivariable Calculus in Higher Dimensions |
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