Calculus

Limits

Limit introduction, squeeze theorem, and epsilon-delta definition of limits

Taking derivatives

Calculating derivatives. Power rule. Product and quotient rules. Chain Rule. Implicit differentiation. Derivatives of common functions.

Derivative applications

Minima, maxima, and critical points. Rates of change. Optimization. Rates of change. L'Hopital's rule. Mean value theorem.

Indefinite and definite integrals

Indefinite integral as anti-derivative. Definite integral as area under a curve. Integration by parts. U-substitution. Trig substitution.

Solid of revolution

Using definite integrals with the shell and disc methods to find volumes of solids of revolution.

Sequences, series and function approximation

Sequences, series and approximating functions. Maclaurin and Taylor series.

Double and triple integrals

Volume under a surface with double integrals. Triple integrals as well.

Partial derivatives, gradient, divergence, curl

Thinking about forms of derivatives in multi-dimensions and for vector-valued functions: partial derivatives, gradient, divergence and curl.

Line integrals and Green's theorem

Line integral of scalar and vector-valued functions. Green's theorem and 2-D divergence theorem.

Surface integrals and Stokes' theorem

Parameterizing a surface. Surface integrals. Stokes' theorem.

Divergence theorem

Divergence theorem intuition. Divergence theorem examples and proofs. Types of regions in 3D.