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Week - 1 |
A Summary of Fundamental Integration Concepts: Riemannian Integral, Sets of Measure Zero, Fubini Theorem, Change of Variables Theorem. |
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Week - 2 |
Algebraic Preliminaries I: Tensors and Alternating Tensors. |
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Week - 3 |
Algebraic Preliminaries II: Wedge Product, Determinant, Orientation. |
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Week - 4 |
Vector Fields on R^n, Differential Forms and Exterior Derivative. |
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Week - 5 |
Pullback Map, Closed and Exact Forms, Poincaré Lemma. |
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Week - 6 |
Singular Cubes, Chains, Boundary Operator and Integration on Chains. |
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Week - 7 |
Stokes Thorem on Chains and Its Applications. |
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Week - 8 |
Exam |
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Week - 9 |
Manifolds |
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Week - 10 |
Vector Fields on Manifolds, Forms and Orientation. |
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Week - 11 |
Integration on Manifolds and Stokes Theorem. |
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Week - 12 |
Volume Element, Arc Length, Surface Area and Flow. |
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Week - 13 |
Classical Theorems: Green, Divergence and Stokes Theorems. |
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Week - 14 |
Applications and General Assessment. |