20222023 College Catalog [ARCHIVED CATALOG]

MAT 220  Calculus I [SUN# MAT 2220] 5 Credits, 5 Contact Hours 5 lecture periods 0 lab periods
Introduction to analytical geometry and calculus. Includes limits and continuity, derivatives, applications of the derivative, and integration.
Prerequisite(s): Within the last three years: MAT 187 or MAT 188 and MAT 189 with a grade of C or better; or required score on the Mathematics assessment exam. 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 certain limits analytically, and estimate other limits numerically and/or graphically. These limits include doublesided, onesided, and limits at infinity.
 Use the definition of continuity to identify points and types of discontinuity of functions defined analytically or graphically.
 Use the definition of the derivative to calculate the exact derivative of certain functions and/or estimate the value of the derivative at a point.
 Sketch the derivative of a function defined graphically.
 Explain the meaning of the derivative in an applied situation using appropriate units.
 Calculate derivatives, explicitly and implicitly, of algebraic combinations of polynomial, radical, exponential, logarithmic, trigonometric, and inverse trigonometric function.
 Determine the linear approximation of a function defined analytically, numerically, or graphically.
 Solve related rates problems.
 Calculate higher order derivatives of algebraic combinations of polynomial, radical, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
 Estimate small changes in a function using differentials.
 Use the 1^{st} derivative to identify critical points and intervals of increase and decrease.
 Identify the type and location of extrema using 1^{st} and/or 2^{nd} derivative tests.
 Use the 2^{nd} derivative to identify intervals of upward and downward concavity and inflection points.
 Sketch graphs of algebraic and transcendental functions using information obtained from derivatives and other analyses.
 Evaluate a variety of indeterminate forms using L’Hopital’s Rule.
 Solve a variety of optimization problems using derivatives.
 Find antiderivatives of polynomial, exponential, and some rational and trigonometric functions.
 Solve applied problems requiring the use of antiderivatives such as acceleration, velocity, and position problems.
 Sketch the graph of a possible antiderivative of a function defined graphically.
 Use finite sums to estimate the definite integral of functions defined numerically, graphically or analytically. Estimate techniques should include some of the following: left/right hand, trapezoid, and midpoint rules.
 Interpret the definite integral in an applied situation using appropriate units.
 Evaluate definite integrals using the Fundamental Theorem of Calculus.
 Calculate the area beneath the graph of a function using the definite integral.
 Use the Fundamental Theorem of Calculus to demonstrate that differentiation and integration are inverse operations.
 Use the technique of “substitution” to evaluate definite and indefinite integrals.
Optional Objectives:
26. Calculate derivatives of hyperbolic functions.
27. Calculate derivatives using logarithmic differentiation.
28. Use calculus to investigate the graphs of and distinguishing characteristics of families of functions.
29. Identify the condition where the Mean Value Theorem and/or the Extreme Value Theorem apply.
30. Estimate the solution of an equation using Newton’s Method.
31. Calculate areas between curves and simple applications problems using definite integrals. Outline:
 Limits and Continuity
 2sided
 1sided
 Limits involving infinity
 Definition of continuity
 Points and types of discontinuity
 Derivatives
 Definition of the derivative
 Estimate the value of the derivative
 Calculate exact derivatives
 Meaning of the derivative
 Differentiation Rules
 Power rule
 Product rule
 Quotient rule
 Chain rule
 Derivatives of transcendental functions
 Trigonometric functions
 Inverse trigonometric functions
 Exponential functions
 Logarithmic functions
 Hyperbolic functions (optional)
 Logarithmic differentiation (optional)
 Implicit differentiation
 Higher order derivatives
 Applications of the Derivative
 Related rates
 Linear approximations
 Differentials
 Curve sketching
 Intervals of increase and decrease
 Extrema
 Intervals of concavity
 Points of inflection
 Families of functions (optional)
 Optimization
 Antiderivatives
 Polynomial functions
 Exponential functions
 Rational functions
 Trigonometric functions
 Applied problems
 L’Hopital’s Rule
 Mean Value Theorem (optional)
 Newton’s Method (optional)
 Integration
 Definition of the definite integral
 Estimate the definite integral
 Fundamental Theorem of Calculus
 Indefinite integrals
 Area under curves
 Integration by substitution
 Area between curves (optional)
