MTH 241 Elementary Calculus

Lecture Hours: 4
Credits: 4

Emphasizes techniques of calculus in applied problem solving. A one-term terminal course with an intuitive approach to differential and integral calculus. Intended for non-math majors.

Prerequisite: Placement into WR 115 (or higher), or completion of WR 090 (or higher); and placement into MTH 241 (or higher), or completion of MTH 111Z (or higher) or equivalent course as determined by instructor; or consent of instructor. (All prerequisite courses must be completed with a grade of C or better.)
Student Learning Outcomes:

Create mathematical models of abstract and real-world situations using first and higher order derivatives and.
Use inductive reasoning to develop mathematical conjectures involving first and higher order derivative and antiderivative function models.
Use deductive reasoning to verify and apply mathematical arguments involving these models.
Use mathematical problem-solving techniques involving first and second derivative and functions and including the use of graphical, symbolic, narrative and tabular representations.
Make mathematical connections to, and solve, problems from other disciplines involving first and second derivative and antiderivative functions.
Use oral and written skills to individually and collaboratively communicate about first and higher order derivative and antiderivative functions models.
Use appropriate technology to enhance mathematical thinking and understanding, to solve mathematical problems involving first and higher order derivative and antiderivative functions, and to judge the reasonableness of results.

Statewide General Education Outcomes:

Use appropriate mathematics to solve problems.
Recognize which mathematical concepts are applicable to a scenario, apply appropriate mathematics and technology in its analysis, and then accurately interpret, validate, and communicate the results.

Content Outline

Functions, Limits, and Rate of Change
- Functions and relations
- Composition with functions
- Slope, rate of change, and linear functions
- Limits, functions, and continuity
- Average and instantaneous rate of change
Differentiation
- The derivative of a function and interpretations
- Product and quotient rule
- Higher-order derivatives
- Chain rule and general power rule
- Implicit differentiation
Applying the derivative
- The first derivative and the behavior of functions
- The second derivative and the behavior of functions
- Applications of the derivative: Optimization
- Applications of the derivative in business and economics
The Natural Exponential and Logarithmic Functions
- The exponential functions
- The natural logarithm functions
- Differentiating the natural logarithm function
- Differentiating the natural exponential function
Integration
- Anti-differentiation and the indefinite integral
- Integration by substitution
- The definite integral
- The definite integral and area
- Improper integral
- Integration by parts