All the Tools You Need to Excel at Calculus

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Course Curriculum

Functions, trig Details
Limits: theory and polynomial examples Details
Continuity, differentiability, trig limits Details
Trig limits (continued), how to solve differentiation problems, trig derivatives, simple harmonic motion Details
Implicit differentiation, related rates Details
Exponentials, review of topics so far Details
Inverse functions, inverse trig functions, linearization Details
More on the differential, extrema, Rolle/Mean Value Theorem, critical points and the second derivatives (Note: The lecture stops suddenly but is made up at the beginning of the next video.) Details
Classifying critical points, sketching graphs Details
Optimization, L’Hôpital’s Rule Details
Sigma notation, Riemann sums, integration, introduction to the Fundamental Theorems Details
Fundamental Theorems, integration by substitution Details
Substitution revisited, integration by parts, integrals involving trig limits Details
Partial fractions Details
Trig integrals, trig substitutions, and summary of integration techniques Details
Volumes of revolution, arc lengths, and surface areas Details
Improper integrals, part 1 Details
Improper integrals, part 2 Details
Sequences and series, part 1 Details
Sequences and series, part 2, introduction to power Details
Estimation using Taylor series, the remainder/error term, radius of convergence of power series Details
More about power and Taylor series, introduction to complex numbers Details
Complex numbers, separable first-order differential equations Details
First order linear differential equations, first/second order constant coefficient linear differential equations Details

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