Mar 03, 2024
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.
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 anti-derivative 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 1 Communication Core 2 Technology Fluency Core 7 Quantitative Reasoning Core 10 Innovative and Critical Thinking