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2019/2020 - Topics for the Calculus I Final Exam

posted Jan 1, 2020, 6:26 AM by Matthew Grenfell   [ updated Jan 1, 2020, 10:57 AM ]

  • Calculating limits algebraically, using limit laws, and using graphs
  • Continuity
  • Limit definition of the derivative
  • Graphs of functions vs. their derivatives
  • Equations of tangent lines
  • Product/Quotient/Chain Rules
  • Trig function derivatives
  • Implicit differentiation
  • Absolute max/min values
  • The Mean Value Theorem
  • Inflection points
  • L'Hospital's Rule
  • Antiderivatives
  • Relationship of position/velocity/acceleration
  • Integrals as area
  • Fund Thm of Calculus, evaluating definite integrals
  • u-substitution
  • Area between curves
  • Volumes using disks
  • Horizontal and vertical asymptotes
  • Other limits at infinity
  • Types of discontinuities
  • Logarithmic differentiation
  • Related Rates
  • Optimization
  • Graphing functions using their derivatives
  • Riemann sums
  • Interpreting values of definite integrals and/or Net Change Thm

UConn Course Syllabi

posted Sep 5, 2019, 12:55 PM by Matthew Grenfell

Although only one of these are applicable for the fall semester, I am posting the syllabi for both UConn courses for this year. They can be found in the "Forms and Docs" section of this site, or by clicking the links below:

    Calculus I

2019/2020 - Topics for the Calculus 2 Final Exam

posted May 14, 2019, 4:20 AM by Matthew Grenfell   [ updated Jun 3, 2020, 3:51 AM ]

  • Use integration by parts to evaluate integrals
  • Evaluate trigonometric integrals (e.g., integrate sin^3(x), sec^2(x)tan^2(x), and so on)
  • Evaluate integrals by making trig substitutions
  • Evaluate integrals using partial fractions
  • Determine the convergence/divergence of improper integrals and evaluate if convergent
  • Use various tests to determine the convergence/divergence of series, including the integral test, comparison tests, and ratio test
  • Determine the convergence/divergence of a geometric series or alternating series
  • Determine a power series representation of a given function
  • Determine the radius of convergence and interval of convergence for a power series
  • Determine a Maclaurin or Taylor series representation of a function
  • Determine a Taylor polynomial of a certain degree for a given function
  • Determine the solution of a separable differential equation
  • Graph curves defined by parametric equations
  • Determine the derivative at a point on a parametric curve
  • Describe and work with points and curves in polar coordinates
  • Determine areas of common regions using polar coordinates
  • More integration by parts
  • Approximate integration techniques (Midpoint Rule, Trapezoidal Rule, Simpson's Rule)
  • Sequences
  • More power series/Taylor series (preferably deriving a Taylor series from scratch)
  • Approximating error of an integration technique or Taylor polynomial
  • More on parametric curves and calculus with parametric equations


posted Sep 3, 2017, 5:44 PM by Matthew Grenfell   [ updated May 14, 2019, 4:24 AM ]

Most of our homework will be done using the WeBWork server; click the following link to get started: http://webwork.grenfellmusic.net

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