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Study Guide for Math 120: Introductory Calculus
Brenton LeMesurier
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Contents
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Front Matter
Copyright Page
Introduction
1
Functions and Models
Four Ways to Represent a Function (omitted)
Mathematical Models: A Catalog of Essential Functions (omitted)
New Functions from Old Functions (omitted)
Exponential Functions
Inverse Functions and Logarithms
2
Limits and Derivatives
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using Limit Laws
The Precise Definition of a Limit
Continuity
Limits at Infinity: Horizontal Asymptotes
Derivatives and Rates of Change
The Derivative as a Function
3
Differentiation Rules
Derivatives of Polynomial and Exponential Functions
The Product and Quotient Rules
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Derivatives of Logarithmic Functions
Rates of Change in the Natural and Social Sciences
Exponential Growth and Decay (omitted)
Related Rates of Change
Linear Approximations and Differentials
Hyperbolic Functions (omitted)
4
Applications of Differentiation
Maximum and Minimum Values
The Mean Value Theorem
How Derivatives Affect the Shape of a Graph
Indeterminate Forms and l'Hospital's Rule
Summary of Curve Sketching
Graphing with Calculus
and
Calculators (omitted)
Optimization Problems
Newton's Method
Antiderivatives
5
Integrals
Areas and Distances
The Definite Integral
The Fundamental Theorem of Calculus
Indefinite Integrals and the Net Change Theorem
The Substitution Rule
Authored in
Study Guide for Math 120: Introductory Calculus
Brenton LeMesurier
Department of Mathematics
College of Charleston
Charleston, South Carolina
lemesurierb@cofc.edu
Fall 2019
Copyright Page
Introduction