| 1 |
Polar Coordinates, draw approximation curves in polar coordinates |
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| 2 |
Calculus, areas and lengths in Polar Coordinates |
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| 3 |
Curves Defined by Parametric Equations and Calculus with Parametric Curves |
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| 4 |
Further examples |
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| 5 |
Three-Dimensional Coordinate Systems, Vectors, Equations of Lines and Planes |
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| 6 |
Standard Quadric Surfaces |
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| 7 |
Vector Functions and Space Curves, Limits, Derivatives and Integrals of Vector Functions and Length |
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| 8 |
Arc Length and Curvature for Space Curves |
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| 9 |
Motion in Space: Velocity and Acceleration |
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| 10 |
Further examples |
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| 11 |
Functions of Several Variables and Limits and Continuity |
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| 12 |
Partial Derivatives and The Chain Rule |
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| 13 |
Directional Derivatives and the Gradient Vector |
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| 14 |
Further examples |
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| 15 |
Maximum and Minimum Values of multivariable functions |
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| 16 |
Lagrange Multipliers method |
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| 17 |
Midterm exam |
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| 18 |
Double Integrals over Rectangles and General Regions |
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| 19 |
Double Integrals in Polar Coordinates |
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| 20 |
Further examples |
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| 21 |
Triple Integrals over Rectangle Cube and General Regions |
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| 22 |
Triple Integrals in Cylindrical and Spherical Coordinates |
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| 23 |
Change of Variables in Multiple Integrals |
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| 24 |
Further examples |
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| 25 |
Vector Fields and Line Integrals |
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| 26 |
The Fundamental Theorem for Line Integrals |
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| 27 |
Green’s Theorem |
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| 28 |
Curl and Divergence and the vector form of Green’s Theorem |
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| 29 |
Parametric Surfaces and Their Areas |
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| 30 |
Surface Integrals |
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| 31 |
Stokes’ and the Divergence Theorems |
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| 32 |
Further examples |
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