Math 122 Course Objectives
In successfully completing this course, a well-prepared student should be
able to
- state a definition, equivalent to that used
in the text or class, for each relevant term
- find antiderivatives of a given function
using knowledge of derivative rules and derivatives of specific
functions (power, trigonometric and inverse trigonometric, exponential
and logarithmic)
- find the antiderivatives of a given function using basic
techniques such as substitution, integration by parts, and rewriting
the integrand using algebraic manipulations (including partial
fractions decomposition) or trigonometric identities
- read and use summation notation
- approximate the value of a given definite
integral
- compute the exact value of a given simple definite integral
using the definition of definite integral
- give "easy-to-find" lower and upper bounds for the value of a
given definite integral
- state and use an appropriate interpretation
of definite integral (as area or accumulation)
- state and understand the hypotheses and conclusion of the First
Fundamental Theorem of Calculus
- use the First Fundamental Theorem of Calculus to compute the
value of a given definite integral
- state and understand the hypotheses and conclusion of the
Second Fundamental Theorem of Calculus
- use the Second Fundamental Theorem of
Calculus to compute the derivative of an accumulation function
- sketch the graph of an accumulation function for a given function
- use the polar coordinate system to plot points in a plane
- plot a polar curve for a given polar relationship (i.e., a
relationship between the polar coordinates r and θ)
- compute the average value of a given function for a given interval
- give a statement, equivalent to that used in the text or class, for
the Mean Value Theorem for Integrals
- compute a rectangular, trapezoidal, or Simpson's rule
approximation for the value of a given definite integral within a
given tolerance
- compute an upper bound on the error for a rectangular,
trapezoidal, or Simpson's rule approximation of given definite integral
- set up and evaluate a definite integral to compute an area,
volume, arclength, surface area or other desired quantity (including
non-geometric quantities)
- determine if a given improper integral converges or diverges and,
if it converges, compute the value
- construct and evaluate an improper integral to compute the value
of a desired quantity
- determine if a given sequence converges or diverges and,
if it converges, compute the limit
- state the basic convergence results for p-series and geometric
series
- compute the sum of a given convergent geometric series
- construct and evaluate a geometric series to compute the value of a desired
quantity
- state a comparison (direct or limit) argument to support a
claim that a given series converges or diverges
- use the ratio test to analyze the convergence of a given series
- use the root test to analyze the convergence of a given series
- use the alternating series theorem to analyze the convergence of a
given alternating series
- determine if a given series converges absolutely, converges
conditionally, or diverges and give an
argument to support the conclusion
- determine the interval of convergence for a given power series
- differentiate or integrate a given power series
- construct a Taylor polynomial or Taylor series for a given
function based at a given point
- use a Taylor polynomial to approximate the value of a function
for a given input and compute an upper bound on the error in that
approximation