Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists)Community Questions
Limit introduction, squeeze theorem, and epsilon-delta definition of limits
Calculating derivatives. Power rule. Product and quotient rules. Chain Rule. Implicit differentiation. Derivatives of common functions.
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.
AP Calculus practice questions
Sample questions from the A.P. Calculus AB and BC exams (both multiple choice and free answer).
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 intuition. Divergence theorem examples and proofs. Types of regions in 3D.