Thread: Calculus Refresher A brief review of the concepts of single variable calculus Preliminaries Introduction to Calculus Refresher Polynomial inequalities Domain of functions Lines (and other items in Analytic Geometry) Elementary limits Limits with cancellation Limits at infinity Limits of exponential functions at infinity Differentiation The idea of the derivative of a function Derivatives of polynomials Derivatives of more general power functions The quotient rule The product rule The chain rule Tangent and normal lines Critical points, monotone increase and decrease Minimization and maximization refresher Local minima and maxima (First Derivative Test) An algebra trick for finding critical points Linear approximations: approximation by differentials Implicit differentiation Related rates Intermediate Value Theorem, location of roots Newton's Method Derivatives of transcendental functions L'Hospital's rule Exponential growth and decay: a differential equation The second and higher derivatives Inflection points, concavity upward and downward Another differential equation: projectile motion Graphing rational functions, asymptotes Integration Basic integration formulas The simplest integration substitutions Integration substitutions Area and definite integrals Length of curves Numerical integration Averages and weighted averages Centers of mass (centroids) Volumes by cross sections Volume of surfaces of revolution Integration by parts Partial fractions Trigonometric integrals Trigonometric substitution Taylor polynomials Historical and theoretical comments: Mean Value Theorem Taylor polynomials: formulas Classic examples of Taylor polynomials Computational tricks regarding Taylor polynomials Prototypes: More serious questions about Taylor polynomials Determining tolerance/error in Taylor polynomials. How large an interval with given tolerance for a Taylor polynomial? Achieving desired tolerance of a Taylor polynomial on desired interval Integrating Taylor polynomials: first example Integrating the error term of a Taylor polynomial: example