Dec 02, 2022
MTH 251 - Calculus 1 (Differential Calculus)5 Credit(s)
MTH 251 is a first-term calculus course that includes a selective review of precalculus followed by development of the derivative from the perspective of rates of change, slopes of tangent lines, and numerical and graphical limits of difference quotients. The limit of the difference quotient is used as a basis for formulating analytical methods that include the power, product, and quotient rules. The chain rule and the technique of implicit differentiation are developed. Procedures for differentiating polynomial, exponential, logarithmic, and trigonometric functions are formulated. Analytical, graphical, and numerical methods are used to support one another in developing the course material. Opportunities are provided for students to work in groups, verbalize concepts with one another, and explore concepts and applications using technology.
Prerequisite: MTH 112 or equivalent course with a grade of C- or better completed within the past five years, or placement test.
Upon successful completion of this course, the student should be able to:
- Understand the definition of the derivative as the limit of the difference quotient for a function.
- Be able to use the definition of the derivative to find derivatives of certain elementary functions.
- Find derivatives numerically utilizing technology.
- Visualize and interpret derivatives graphically.
- Understand and use the derivative of a function as a function in its own right.
- Understand the development and use of procedures for differentiating polynomial, exponential, logarithmic, and trigonometric functions, including the inverse sine & inverse tangent functions.
- Use the power, product, quotient, and chain rules to find derivatives of functions.
- Use the technique of implicit differentiation to find derivatives of implicitly defined functions.
- Find equations of tangent lines to the graphs of functions at specific points.
- Understand local linearity and that the tangent line to the graph of a function at a specific point is the best linear approximation for the function at that point.
- Use linear approximation to estimate function values.
- Use the methods and techniques of differential calculus to solve a variety of application problems, including optimization and related rate problems.
- Use a programmable graphing calculator as an effective tool in confirming analytical work and obtaining numerical and graphical results related to differential calculus.
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