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Sep 07, 2024
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M 171M - Calculus I Credit(s): 5
Prerequisite(s): grade of “C” or better in M 122 , appropriate placement test score, or Math Department consent. This is the first of three standard courses in calculus, the others are M 172 and M 273 . The course includes limits and continuity, derivatives, applications of derivatives and integration. The types of functions studied include algebraic, trigonometric, exponential, and logarithmic. (Fall and Spring Semesters)
Course Learning Outcomes: Upon completion of the course, students will be able to - Use mathematical techniques to problem solve.
- Define limits and the limit definition of continuity, compute limits in elementary cases, and determine the limits of transcendental, rational and piecewise defined functions.
- Understand infinite limits, limits at infinity, asymptotes, indeterminate forms and how to use ‘Hospital’s Rule.
- Understand the limit definition of the derivative of a function, how it relates to the function itself, and how to use it to compute derivatives.
- Utilize derivatives to find tangent lines to curves and velocity for particle motion and understand how to use the derivative to solve challenging related rate and optimization problems.
- Understand and apply the power, sum, product and quotient rules for differentiation.
- Understand the derivatives of exponential, logarithmic, trigonometric and hyperbolic functions as well as implicit and logarithmic differentiation.
- Analyze functions graphically, including using continuity and differentiation to determine local and global extrema, concavity and inflection points.
- Understand the Riemann integral, areas under graphs, antiderivatives, the Fundamental Theorem of Calculus, and integration using the method of substitution.
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