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Week - 1 |
Multiple Integrals: Sets of zero measure, Double and triple integrals |
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Week - 2 |
Multiple Integrals: Properties of multiple integrals, Fubini's Theorem |
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Week - 3 |
Change of Variables Theorem: Change of variables theorem, Coordinate transformations, Polar coordinates |
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Week - 4 |
Change of Variables Theorem: Spherical coordinates, Cylindrical coordinates |
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Week - 5 |
Area and Volume Calculations, Volume of the n-dimensional sphere |
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Week - 6 |
Improper multiple integrals |
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Week - 7 |
Parametric integrals, Gamma and Beta functions |
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Week - 8 |
Some Applications of Multiple Integrals |
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Week - 9 |
Vector Fields, Integral curves |
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Week - 10 |
Gradient Fields, Divergence, Curl |
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Week - 11 |
Line Integrals: Parametric curves, Arc length, Line integrals of scalar functions, Fundamental Theorem |
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Week - 12 |
Line Integrals: Line integrals of vector fields, Green's Theorem |
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Week - 13 |
Surface Integrals: Parametric surfaces, Surface area, Surface integrals of scalar functions |
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Week - 14 |
Surface Integrals: Oriented surfaces, Surface integrals of vector fields, Stokes' Theorem, Divergence Theorem, Some applications |