Math Insight

Math Insight contributor Paul Garrett

Paul Garrett
Professor of Mathematics
University of Minnesota
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Paul Garrett contributed material from his Calculus Refresher to Math Insight.

Pages by Paul Garrett

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