MTH 251Z Differential Calculus
This course explores limits, continuity, derivatives, and their applications for real-valued functions of a single variable. These topics will be explored graphically, numerically, and symbolically in real-life applications. This course emphasizes abstraction, problem-solving, modeling, reasoning, communication, connections with other disciplines, and the appropriate use of technology.
Prerequisite
Prerequisite:
MTH 112Z Precalculus II: Trigonometry or equivalent with a grade of C or better.
Notes
Lower Division Transfer (LDT) Course
General Education Requirements
AAOT Math, AAOT Science/Math/CS Non Lab, AAS Math/Computation, AGS Math/Science, AS Quantitative Lit & Analysis
Outcomes
Upon successful completion of this course, students will be able to:
Calculate limits graphically, numerically, and symbolically; describe the behavior of functions using limits and continuity; and recognize indeterminate forms. Apply the definition of the derivative and analyze average and instantaneous rates of change. Interpret and apply the concepts of the first and second derivative to describe and illustrate function features including the slopes of tangent lines, locations of extrema and inflection points, and intervals of increase, decrease, and concavity. Apply product, quotient, chain, and function-specific rules to differentiate combinations of power, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions, as well as functions defined implicitly. Apply derivatives to a variety of problems in mathematics and other disciplines, including related rates, optimization, and L’Hôpital’s rule.