Single Variable Calculus

MIT , Prof.David Jerison

First fundamental theorem of calculus

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Course Description

Derivatives, slope, velocity, rate of change – Limits, continuity Trigonometric limits – Derivatives of products, quotients, sine, cosine – Chain rule Higher derivatives – Implicit differentiation, inverses – Exponential and log Logarithmic differentiation; hyperbolic functions – Hyperbolic functions (cont.) and exam 1 review – Linear and quadratic approximations – Approximations (cont.); curve sketching – Max-min problems – Related rates – Newtons method and other applications – Mean value theorem; Inequalities

Differentials, antiderivatives-Differential equations, separation of variables – Definite integrals – First fundamental theorem of calculus – Second fundamental theorem – Applications to logarithms and geometry – Volumes by disks and shells – Work, average value, probability – Numerical integration – Exam 3 review – Trigonometric integrals and substitution – Integration by inverse substitution – Partial fractions-Integration by parts, reduction formulae – Parametric equations, arclength, surface area – Polar coordinates; area in polar coordinates – Indeterminate forms – L Hospitals rule-Improper integrals – Infinite series and convergence tests – Taylors series

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