# Single Variable Calculus

MIT Course , Fall 2006 , Prof. David Jerison

143 students enrolled

# Overview

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

### Lecture 1: Derivatives, slope, velocity, rate of change

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