# 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 1-variable 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 piece-wise defined functions;

Course Documents