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.