MSUB Mathematics Department
M 171 Calculus I
Course Description
4 credits
Prerequisite: M 122
Covers differentiation and presents applications to the approximation of functions, root finding, and 1variable optimization. Introduces integration.
Learning Outcomes

Demonstrate the understanding of the general behavior of one variable functions, including transcendentals,

understand the definition of limit, compute it in elementary cases, and determine the limits of transcendental, rational and piecewise defined functions,

define infinite limits, limits at infinity, asymptotes, indeterminate forms and how to use Hopital's Rule,

explain the limit definition of continuity,

explain the limit definition of the derivative of a function, how it related to the function itself, and how to use it to compute derivatives,

use derivatives to find tangent lines to curves and velocity for particle motion,

apply the power, sum, product, quotient and chain rules of differentiation,

use the derivatives of exponential, logarithmic , trigonometric and hyperbolic functions,

explain implicit and logarithmic differentiation,

apply the Intermediate and Mean Value Theorems,

graphically analyze functions including using continuity and differentiation to determine local and global extrema, concavity, and inflection points,

use the derivative to solve challenging related rate and optimization word problems,

explain and apply Newton's Method for estimating zeros of a function, and
 find antiderivatives of fundamental functions.Explain and apply the concept of limit, infinite limits, limits at infinity, asymptotes and how to solve limit problems involving rational and piecewise defined functions;
Course Documents