
20162017 Catalog [PAST CATALOG]

MAT 191  Calculus and Analytic Geometry 1 4 credit hours  Four hours weekly; one term. This course meets the Mathematics General Education Requirement.
Learn to find limits, derivatives and integrals of functions. Apply these concepts to explicit, implicit, algebraic, trigonometric and transcendental functions, using derivatives to analyze graphs and to model real situations.
Prerequisite(s): MAT 151 or MAT 142 or equivalent, or completion of three years of high school mathematics including trigonometry and achieving an appropriate score on the mathematics part of the ACT or SAT or the Mathematics Placement Test.
Crosslisted: Also offered as MAT 191H ; credit is not given for both MAT 191 and MAT 191H .
Note: Credit is not given for both MAT 191 and MAT 122 or MAT 191 and MAT 230 .
Course Outcomes Upon successful completion of this course, students will be able to:
 Finds limits of functions algebraically, numerically, and/or graphically and interprets these limits
 Interprets from a graph whether a limit exists and gives its value
 Approximates a limit from a table of values
 Computes limits using limit laws and properties of continuity
 Uses limits to describe asymptotic behavior
 Performs differentiation on functions algebraically, numerically and graphically
 Uses the definition of the derivative to determine the derivative of a function
 Applies rules of differentiation to determine derivatives of functions expressed algebraically
 Approximates a derivative from a table of values
 Approximates a derivative from the graph of a function
 Determines the derivative of an implicit function
 Analyzes graphs and behaviors of functions with regard to rate of change and concavity
 Uses the derivative to determine intervals of increasing and decreasing behavior for a given function
 Determines the extreme values of a function
 Uses the second derivative to determine intervals of concavity and points of inflection
 Approximates zeros of functions using Newton’s method
 Uses technology to investigate the behaviors of graphs of functions and communicates results
 Models problems from the sciences that involve rates of change
 Interprets the derivative as an instantaneous rate of change
 Produces a mathematical model involving related physical quantities and computes optimal values of the model
 Finds indefinite integrals
 Finds the general antiderivative of a function using algebraic and trigonometric rules and the method of substiution
 Finds a specific antiderivative of a function given an initial condition
 Approximates an antiderivative from the graph of a function
 Sketches the graph of a feasible antiderivative from a direction field
 Evaluates definite integrals
 Evaluates a definite integral exactly using the Fundamental Theorem of Calculus
 Approximates a definite integral given a table or a graph using the right endpoint, left endpoint, midpoint, and trapezoidal rules
 Models problems from the sciences that involve definite integrals
 Expresses the limit of a Riemann sum as a definite integral
 Sets up and evaluates definite integrals in area and volume problems using rectangles, discs, washers, and cylindrical shells
 Sets up and evaluates definite integrals in problems involving the total change and physical quantities such as work
Core Competencies Core 1 Communication Core 2 Technology Fluency Core 7 Quantitative Reasoning Core 10 Innovative and Critical Thinking

