Week - 1 |
Sums and Sigma Notation.
Areas as Limits of Sums.
The Definite Integral
The Method of Substitution
Areas of Plane Regions.
Properties of Definite Integral
The fundamental theorem of Calculus |
Week - 2 |
Integration by Parts
Integrals of Rational Functions
Inverse Substitutions
Improper Integrals. |
Week - 3 |
Volume by Slicing-solids of revolution
More volumes by slicing. |
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 |
Infinite series
|
Week - 7 |
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. |
Week - 10 |
Partial Derivative
Hİgher Order Derivatives. |
Week - 11 |
The Chain Rule
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. |