Lecture 1.1: Introduction to Functions.

Lecture 1.2: Trigonometric functions.

Lecture 2.1: Introduction to derivatives.

Lecture 2.2: Differentiation techniques.

Lecture 3.2: Linear approximation (linearization).

Lecture 4.1: Maximum and minimum values.

Lecture 4.2: Shapes of functions. Concavity.

Lecture 5.1: Review of Maximum & Minimum values.

Lecture 5.2: Indetermined limits. L'Hopital's rule. Optimization problems.

Lecture 6.1: Introduction to Integration. Riemann's sum.

Lecture 6.2: Integration techniques: the substitution rule.

Lecture 7.2: Finding areas using Integration

Lecture 8.1: Finding volumes using integration

Lecture 10.1: Integration techniques

• Part 1: Integration by parts
• Part 2: Trigonometric integration
• Part 3: Trigonometric substitution

Lecture 10.2: Integration of rational functions

• Part1: Determining coefficients for partial fractions
• Part 2: Repeating linear fractions & irreducible fractions

Lecture 11.1 | Further applications of integrals

• mean of functions
• evaluating arc length of curves

Lecture 11.2 | Surface of revolution

Lecture 12.1 | Curves defined using parametric equations

Lecture 12.2 | Calculus with parametric equations

Lecture 13.1 | Curves defined in Polar Coordinates. Derivatives.

• change of coordinates
• examples of polar curves
• derivatives of polar equations
• tangent lines to polar curves

Lecture 13.2 | Areas and Arc Lengths of Polar Curves.

• integral formula of finding areas
• example of finding the area of one leaf of a rose
• integral formula for arc length
• example of finding the length of a cardiod