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Week - 1
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Sums and Sigma Notation. Areas as Limits of Sums. The Definite Integral. |
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Week - 2
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Properties of The Definite Integral. The Fundemental Theorem of Calculus. |
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Week - 3
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The Method of Subsititution. Areas of plane regions. |
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Week - 4
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Integration by Parts. Inverse Subsititution |
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Week - 5
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Integrals of rational functions |
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Week - 6
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Improper integrals |
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Week - 7
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Volume by slicing, Volume by cylindrical shells |
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Week - 8
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Arc Length and Surface Area. |
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Week - 9
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Mass, Moments and Centre of Mass. |
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Week - 10
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Sequences and Convergence. Infinite Series. |
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Week - 11
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Convergence Tests for Positive Series |
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Week - 12
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Absolute and Conditional Convergence |
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Week - 13
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Power Series. Taylor and Maclaurin Series. |
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Week - 14
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Applications of Taylor and Maclaurin Series. The Binomial Theorem and Binomial Series. |