Week - 1 |
Sums and Sigma Notation. Areas as Limits of Sums. The Definite Integral.Properties of The Definite Integral. The Fundemental Theorem of Calculus.The Method of Subsititution. Areas of plane regions. |
Week - 2 |
Integration by Parts. Inverse Subsititution. Integrals of rational functions. Improper integrals |
Week - 3 |
Volume by slicing, Volume by cylindrical shells |
Week - 4 |
Arc Length and Surface Area.Polar Coordinates and Polar Curves. Slopes, Areas, and Arc Lengths for Polar Curves |
Week - 5 |
Sequences and Convergence |
Week - 6 |
Sequences and Convergence |
Week - 7 |
Infinite Series. Convergence Tests for Positive Series. Absolute and Conditional Convergence. |
Week - 8 |
Power Series. Taylor and Maclaurin Series. |
Week - 9 |
Functions of Several Variables. Limits and Continuity. Partial Derivatives. Higher Order Derivatives. The Chain Rule. |
Week - 10 |
Gradients and Directional Derivatives. |
Week - 11 |
Gradients and Directional Derivatives. |
Week - 12 |
Double Integrals |
Week - 13 |
Iteration of Double Integrals in Cartesian Coordinates. Improper Integrals and a Mean Value Theorem |
Week - 14 |
Double Integrals in Polar Coordinates |