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

### Course Curriculum

 Derivatives, slope, velocity, rate of change Details 51:33 Limits, continuity Trigonometric limits Details 52:47 Derivatives of products, quotients, sine, cosine Details 49:55 Chain rule Higher derivatives Details 46:3 Implicit differentiation, inverses Details 49:1 Exponential and log Logarithmic differentiation; hyperbolic functions Details 47:57 Hyperbolic functions (cont.) and exam 1 review Details 50:53 Linear and quadratic approximations Details 46:48 Approximations (cont.); curve sketching Details 51:44 Max-min problems Details 49:42 Related rates Details 49:56 Newtons method and other applications Details 53:23 Mean value theorem; Inequalities Details 49:42 Differentials, antiderivatives Details 48:53 Differential equations, separation of variables Details 45:25 Definite integrals Details 47:14 First fundamental theorem of calculus Details 48:15 Second fundamental theorem Details 49:31 Applications to logarithms and geometry Details 50:17 Volumes by disks and shells Details 49:58 Work, average value, probability Details 48:36 Numerical integration Details 50:30 Exam 3 review Details 49:19 Trigonometric integrals and substitution Details 46:45 Integration by inverse substitution Details 48:29 Partial fractions Details 48:38 Integration by parts, reduction formulae Details 51:24 Parametric equations, arclength, surface area Details 45:25 Polar coordinates; area in polar coordinates Details 49:23 Exam 4 review Details 49:7 Indeterminate forms – L Hospitals rule Details 48:43 Improper integrals Details 49:27 Infinite series and convergence tests Details 50:12 Taylors series Details 47:31 Final review of Single Variable Calculus Details 39:14

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