
20222023 College Catalog [ARCHIVED CATALOG]

MAT 212  Topics in Calculus [SUN# MAT 2212] 3 Credits, 3 Contact Hours 3 lecture periods 0 lab periods
Introductory topics in differential and integral calculus to include limits, continuity, differentiation, and integration of functions with particular emphasis on business applications. Microsoft Excel and/or graphing calculators will be used as tools for further understanding of these concepts.
Prerequisite(s): Within the last three years: MAT 151 or MAT 187 or MAT 188 with a grade of C or better, or satisfactory score on the mathematics assessment exam. Information: A graphing calculator (technology) is required. See your instructor for details. GenEd: Meets AGEC  MATH; Meets CTE  M&S.
Course Learning Outcomes
 Evaluate limits of functions.
 Differentiate functions and apply derivatives.
 Determine antiderivatives of functions and apply the Fundamental Theorem of Calculus.
Performance Objectives:
 Evaluate limits of algebraic functions.
 Use the definition to determine continuity of a function.
 Use the definition to determine the derivative of algebraic functions.
 Use techniques of differentiation on powers, sums, products, quotients, exponential, logarithmic, composite, and implicit functions. Calculate higher order derivatives.
 Use the first and second derivatives to determine intervals where a function is increasing, decreasing, concave up, concave down; find points of inflection, relative and absolute extrema; and graph the function.
 Use derivatives to solve a variety of application problems including optimization and rates of change with an emphasis in business. Explain the meaning of the derivative in the applications using appropriate units.
 Find antiderivatives of polynomials, exponential functions and some rational functions.
 Use finite sums to estimate the definite integral of functions defined numerically, graphically, or analytically. Estimation techniques should include left and right hand sums.
 Evaluate indefinite integrals. Use the integration technique of substitution. Use the fundamental Theorem of Calculus to evaluate definite integrals.
 Use integration to solve applications problems including area between two curves and consumer and producer surplus. Interpret the meaning of the integral in the applications using appropriate units.
Outline:
 Limits
 Definition and notation
 Evaluation of limits
 Continuity
 Definition
 Continuity at a point
 Continuity on an interval
 Differentiation
 Definition of derivative
 Rules for derivatives
1. Power rule
2. Product rule
3. Quotient rule
4. Exponential/Logarithmic rules
I. Chain Rule
 Implicit Differentiation
 Higher order derivatives
 Applications of the derivative
 Intervals of increase or decrease
 Relative and absolute extrema
 Concavity
 Points of Inflection
 Graphs of Functions
 Mathematical modeling with the derivative
 Optimization
 Marginal cost, marginal revenue, marginal profit
 Interpretation of mathematical models
 Antiderivatives
 Rules for antiderivatives
 Antiderivatives of polynomial and rational functions
 Antiderivatives of exponential functions
 Approximation of definite integrals
 Area under a graph
 Left hand sum
 Right hand sum
 Integration
 Indefinite integral
 Fundamental Theorem of Calculus
 Definite integral
 Integration by substitution
 Applications of integration
 Area between two curves
 Consumer and producer surplus
 Interpretation of mathematical models

