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posted May 14, 2019, 4:20 AM by Matthew Grenfell
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updated May 14, 2019, 5:15 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
- Work (draining a tank, for example)
- More on parametric curves and calculus with parametric
equations
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posted Dec 20, 2018, 4:36 PM by Matthew Grenfell
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updated May 14, 2019, 4:22 AM
]
- Use
various techniques to evaluate limits, including algebraic manipulation,
graphs, and tables of values
- Use
limit laws to evaluate limits, including sums and products of limits
- Use
the definition of continuity to determine if a function is continuous at a
point or to determine ways to make a function continuous at a point
- Understand
and describe discontinuities on a graph
- Evaluate
limits at infinity and determine equations of horizontal asymptotes
- Understand
the definition of a derivative as a limit of a difference quotient
- Interpret
the derivative at a point on a graph and use the derivative of a function
to determine the equation of a tangent line at a given x-value
- Determine
the derivative of various functions using the general power rule, product
rule, quotient rule, chain rule, etc.
- Compute
derivatives of exponential, logarithmic, and trigonometric functions
- Compute
derivatives using implicit differentiation and logarithmic differentiation
- Use
the concept of related rates to determine the rate of change of related
variables or quantities
- Determine
the critical numbers (x-values) of a function
- Use
the Extreme Value Theorem to determine the absolute maximum and minimum
values of a function on an interval
- Use
properties of the first and second derivatives of a function to
algebraically or geometrically determine critical numbers, intervals where
the function is increasing or decreasing, intervals where the function is
concave up or down, the shape of the graph, etc.
- Use
L'Hospital's Rule to evaluate limits and determine when a limit has
indeterminate form
- Use
calculus to solve optimization problems involving an unknown quantity and
a constraint
- Use
Riemann sums to approximate the area under a curve or to approximate the
value of a definite integral
- Evaluate
definite integrals using the Fundamental Theorem of Calculus
- Use
an appropriate substitution to evaluate definite integrals when needed
- Determine
the area between two curves
- Determine
the volume of a solid of revolution using the method of disks/washers
- Evaluating
limits and using the limit laws
- Determine
the derivative of various functions using the general power rule, product
rule, quotient rule, chain rule, etc.
- Compute
derivatives of exponential, logarithmic, and trigonometric functions
- Compute
derivatives using implicit differentiation and logarithmic differentiation
- Derivatives
of inverse trigonometric functions (particularly arctangent, which is most
useful)
- Exponential
growth and decay models (population growth, half-life decay, Newton's law
of cooling)
- Sketching
the graph of a function using information about the function, the first
derivative, and the second derivative
- Evaluate
definite integrals using the Fundamental Theorem of Calculus
- Determine
antiderivatives and indefinite integrals
- Use
an appropriate substitution to evaluate definite integrals when needed
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posted May 21, 2018, 9:34 AM by Matthew Grenfell
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updated May 14, 2019, 4:23 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.
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posted Dec 20, 2017, 7:57 AM by Matthew Grenfell
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updated May 14, 2019, 4:23 AM
]
- 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.
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posted Sep 4, 2017, 8:41 AM by Matthew Grenfell
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updated May 14, 2019, 4:23 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:
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posted Sep 3, 2017, 5:44 PM by Matthew Grenfell
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updated May 14, 2019, 4:24 AM
]
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