Presents concepts of limits, derivatives,
differentiation of
various types of functions and use of differentiation rules,
application of
differentiation, antiderivatives, integrals and applications of
integration.
Credit will not be awarded for both MTH 261: Applied Calculus I
and MTH 263 -
Calculus I. This is a Passport and UCGS transfer course. Lecture
4 hours. Total
4 hours per week.
General Course Purpose
The general purpose of this first course in a
three-course
sequence is to prepare students for further study in calculus
with analytic
geometry by providing them with the necessary competencies in
finding limits,
differentiation and integration.
Course Prerequisites/Corequisites
Prerequisite: Completion of MTH 167 or MTH
161/162 or
equivalent with a grade of C or better.
Course Objectives
Limits
Differentiate between the limit
and the value of a function at a point
Find the limit of a function by
numerical, graphical and analytic methods
Apply Limit Laws
Calculate one-sided limit of a
function
Prove the existence of a limit
using precise definition of the limit
Determine the continuity of a
function
Calculate Vertical and Horizontal
asymptotes using limits
Derivatives and Differentiation
Rules
Define Derivatives and Rates of
Change
Compute derivatives of basic
functions using the definition of the derivative
Differentiate polynomial,
rational, radical, exponential and logarithmic functions
Find equation of a tangent line
using derivative
Differentiate trigonometric
functions
Apply product, quotient, chain
rules
Apply implicit differentiation
and find derivatives of inverse trigonometric functions
Apply concept of rates of change
to natural and social sciences
Apply the concept of related
rates
Define hyperbolic functions and
their derivatives
Find linear approximation of a
function at a given point
Applications of Differentiation
Calculate local and absolute
maximum and minimum values of a function
Apply Rolle's Theorem and Mean
Value Theorem to study properties of a function
Find critical points, and
intervals of increasing and decreasing values of a function
Find points of inflection and
intervals of different concavities
Sketch a curve for a given
function
Apply rules of differentiation to
solve optimization problems
Find antiderivatives for basic
functions using knowledge of derivatives
Integrals
Relate areas to definite
integrals using sigma notation, Riemann Sums, and limits.
[Note: L'Hopital’s Rule is in Calc II but may be used for
instructional purposes here.]
Apply Fundamental Theorem of
Calculus to find definite integrals and derivatives
Find indefinite integrals of
polynomials and basic trigonometric and exponential function
Apply Net Change Theorem
Perform integration using
substitution
Find areas between curves
Find average value of a function
Major Topics to Be Included
Limits
Derivatives and Differentiation
Rules
Applications of Differentiation
Integrals
page revised 01/16/26
Contact Dr. Goral at dgoral@nvcc.edu