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Topics for Calculus 2 Exam

posted May 21, 2018, 9:34 AM by Matthew Grenfell   [ updated May 21, 2018, 9:35 AM ]

  • Numerical Integration.
  • Solving separable differential equations.
  • Finding a Taylor polynomial of a function. 
  • Using Taylor’s inequality when bounding the accuracy of a Taylor Polynomial over a closed interval.
  • Integration by parts.
  • Trigonometric substitution.
  • Improper integrals.
  • Determining conditions for a series to converge.
  • Using he comparison or limit comparison test to determine convergence.
  • Determining conditional or absolute convergence.
  • Being able to recognize a p-series and use it to help determine convergence.
  • Being able to use a root or ratio test to determine convergence.
  • Finding the radius of convergence.
  • Finding the interval of convergence.
  • Using Taylor or Maclauren series when integrating functions that can’t be antidifferentiated.
  • Finding the tangent line to a curve given parametrically at a specific point.
  • Finding the polar coordinates for points of intersection of two polar curves.

  • Recognize a geometric series and to what it converges
  • Arc length of a curve
  • Partial Fraction decomposition of a rational function.
  • Determining the convergence or divergence of a series using various tests.  
  • Understanding when a particular convergence test can be applied
  • Conversion from Cartesian coordinates to polar coordinates and vice versa.
  • Writing the rectangular form of a polar curve.
  • Understanding the application of alternating series when minimizing the degree of a polynomial to approximate a series to within a certain value. 
  • Using known series to find series of other functions; e.g., Find the Maclaurin series of 1/(1-x^3), or of 
  • ln((1-x)/(1+x)) or ...
  • More integrals requiring advanced techniques of integration.
  • Using Taylor’s inequality to find the smallest degree of the Taylor polynomial which will give an estimate within an error of some small value. The Taylor remainder term inequality will be supplied. 
  • Finding the integral which calculates the work done in stretching a spring a certain distance beyond its natural length. 
  • Finding the integral which calculates the work done in pumping water out of a tank.
  • Finding the integral of the area inside one polar curve and outside another polar curve.

Topics for Calculus I Exam

posted Dec 20, 2017, 7:57 AM by Matthew Grenfell

  • Limit rules allowing limit computations.
  • Limit Computations. 
  • Understanding an indeterminate form when regarding limits.
  • Being able to correctly use L’Hôpital’s rule in calculating limits. 
  • Understanding continuity and it implications.
  • Differentiating using the differentiation rules for functions involving algebraic, trigonometric, exponential and logarithmic functions.
  • Understanding how to differentiate implicitly.
  • Being able to compute a tangent line to a differentiable function. 
  • Optimization (maximum-minimum applied questions).
  • Computing areas between curves and bounded by curves.
  • Understanding the use of f’ and f’’ in determining qualities of f. 
  • Understanding what critical numbers of a function are. 
  • Understanding how to solve applied rate of change questions.
  • Understanding the nature of a definite integral, even with a parameter involved.
  • Definite and indefinite integration, including the use of u-substitution.
  • Understanding volumes of revolution 
  • Understanding the interplay between distance, velocity and acceleration of an object.
  • Being able to compute a tangent line to a differentiable function
  • Understanding the difference between displacement and total distance traveled given a velocity function
  • Determining analytically graphical aspects of the graph of a function.
  • Recognizing and using for computation, the limit definition of a derivative to find the derivative of a function.
  • Being able to find vertical and horizontal asymptotes with justification of their answers.
  • Optimization questions.
  • Understanding the Extreme Value Theorem.
  • Average velocity given the position function and instantaneous velocities at a point in time when a given position is attained.
  • Understanding Riemann sums.
  • Working with models of growth and decay.
  • More differentiation using the differentiation rules for functions involving algebraic, trigonometric, inverse trigonometric, exponential and logarithmic functions.
  • More questions using u-substitution for indefinite and definite integration. 
  • Understanding the Fundamental Theorem of Calculus, both parts and using them.

UConn Course Syllabi

posted Sep 4, 2017, 8:41 AM by Matthew Grenfell   [ updated Sep 4, 2017, 8:47 AM ]

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


posted Sep 3, 2017, 5:44 PM by Matthew Grenfell

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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