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posted Jan 1, 2020, 6:26 AM by Matthew Grenfell
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updated Jan 1, 2020, 10:57 AM
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- 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
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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:
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posted May 14, 2019, 4:20 AM by Matthew Grenfell
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updated Jun 3, 2020, 3:51 AM
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- 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
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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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