Math 180 Course Objectives
The objectives most relevant to Part A of the final exam are highlighted in
green.
In successfully completing this course, a well-prepared student should be
able to
- understand and use algebra, trigonometry, and geometry with
mastery at the high school level
- state a definition, equivalent to that used
in the text or class, for each relevant term (for example,
limit, continuity, derivative, antiderivative, definite
integral,...)
- determine the domain, range, and rule for a given function
- determine the domain, range, and rule for the inverse of a given
function
- build a function that models a given real-world situation
- understand and articulate what a given limit statement tells us
about the relevant function or functions
- understand and articulate the similarities and differences among limit, one-sided
limit, and limit at infinity
- conjecture a given limit using an input/output table or a graph
- evaluate a simple given limit using
informal reasoning
- evaluate a given limit problem using formal reasoning and tools
such as algebraic manipulation, change of variable, relating to
known limits, and L'Hopital's rule
- use the Sandwich Theorem to prove a given limit statement
- relate limits at infinity to horizontal asymptotes and infinite
limits to vertical asymptotes
- analyze continuity for a given function
- give a geometric interpretation of a difference quotient
- compute a derivative starting from the definition
- sketch a qualitatively correct plot of the graph of a derivative
given a plot of the graph of a function
- state the derivative of each basic function (constant, power, sin,
cos, exp, ln)
- state each rule for computing derivatives (constant multiple, sum,
difference, product, quotient, chain)
- use results for basic functions and rules for combinations of
functions to differentiate a given function
- compute higher derivatives of a given function
- state and use an appropriate interpretation of derivative (as rate
of change or slope of tangent line)
- determine the equation of a tangent line for
a given function at a given point
- find the location of horizontal tangent lines for a given function
- compute and use a derivative given an
implicit relation involving two variables
- use implicit differentiation to find the derivative of an inverse
function knowing the derivative of the original function
- solve applied problems that involve relating two or more rates of
change
- compute and use the linear approximation for
a given function at a given point
- use Euler's method with a given step size to approximate the
solution for a given differential equation and initial condition
- understand the language and notation of differentials
- use differentials to relate the error (or percentage error) in a
measured quantity to the error (or percentage error) in a computed
quantity
- state conditions under which a function on a stated domain is
guaranteed to have a global minimum and a global maximum
- find the global minimum and global maximum of a
given function on a given domain or show that one or both of these do
not exist
- find and classify (as local minimum, local maximum, or neither)
all critical points for a given function on a given domain
- use the second derivative to understand
concavity (including classifying a critical input as a local minimum or
local maximum)
- use limits to understand relevant aspects of the graph of a
function
- find all inputs for which a given function is positive and all
inputs for which the function is negative
- find all inputs for which a given function is increasing and all
inputs for which the function is decreasing
- find all inputs for which a given function is concave up and all
inputs for which the function is concave down
- use calculus techniques to plot the graph of a given function in a
window that shows all essential features of the graph
- state and understand the hypotheses and
conclusion of the Mean Value Theorem
- apply the Mean Value Theorem to relate an average rate of change
to an instantaneous rate of change
- apply the Mean Value Theorem to justify conclusions about the
number of zeros for a given function
- set up and solve applied problems that involve minimizing or
maximizing a specified quantity
- find antiderivatives of a given function using knowledge of
derivative results and rules
- use differentiation to go from position to
velocity to acceleration and use antidifferentiation to go from
acceleration to velocity to position
- read and use summation notation
- estimate the value of a given definite integral
- compute the exact value of a given simple definite integral using
the definition of definite integral (as limit of a Riemann sum)
- state and understand the hypotheses and conclusion of the Second
Fundamental Theorem of Calculus
- use the Second Fundamental Theorem of Calculus to compute the
value of a given definite integral
- set up and evaluate an appropriate definite integral to compute
the area of a given region
- set up and evaluate an appropriate definite integral to compute
the accumulated change for a given rate of change and interval