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