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Functions and single-variable calculus
A course resource for Math 218
Ellen Goldstein, Aaron Greicius
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\(\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\C}{\mathbb C} \DeclareMathOperator{\range}{range} \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\id}{id} \newcommand{\abs}[2][]{\left\lvert #2\right\rvert_{#1}} \newcommand{\anpoly}{a_nx^n+a_{n-1}x^{n-1}\cdots +a_1x+a_0} \newcommand{\anmonic}{x^n+a_{n-1}x^{n-1}\cdots +a_1x+a_0} \newcommand{\bmpoly}{b_mx^m+b_{m-1}x^{m-1}\cdots +b_1x+b_0} \newcommand{\bnpoly}{b_nx^n+b_{n-1}x^{n-1}\cdots +b_1x+b_0} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Front Matter
0
How to Learn Mathematics
0.1
How to Read Mathematics
Learning Goals
General "Do’s" for Reading Math
Definitions, Examples, and Theorems
Summary
0.2
How to Problem-Solve
Learning Goals
Why Problem Solving?
Problem-Solving Framework
Some Myths of Problem-Solving
Examples of Worked Problems
References and Notes:
0.3
How to Study Math
1
Math 218-1
1.1
What is a function?
Learning goals
Definition of a function
Set-builder notation and intervals
Implied domain and range
Tables and graphs
Vertical line test
Functions and relations
Modeling with functions
Exercises
1.2
Linear and quadratic functions
Learning Goals
Definitions of linear and quadratic functions
Properties of linear functions
Vertex form
Exercises
1.3
Modeling with Linear and Quadratic Functions
Learning Goals
The Mathematical Modeling Process
Average rate of change
Using Linear Functions as Models
Modeling with quadratic functions: falling objects
Cost, Revenue, and Profit
Exercises
1.4
Algebraic functions
Learning Goals
Power functions
Polynomial functions
Rational functions
Algebraic functions
Exercises
1.5
Algebraic functions: continued
Learning objectives
Power functions
Polynomials
Rational functions
1.6
Transformations and symmetry
Learning Goals
Transformations
Symmetry
Vertex form of a quadratic function
Exercises
1.7
Function composition
Learning Goals
Motivation and Examples
Function composition
Implied domain of compositions
1.8
Solving inequalities
Elementary inequality rules
Sign diagram technique
1.9
Domains of algebraic functions
1.10
Piecewise-defined functions and absolute value
Piecewise-defined functions
An Application of Piecewise-defined Functions
Absolute value and distance
Graphs of absolute values
1.11
Introduction to limits
Informal definition of the limit
One-sided limits
1.12
Limit rules
Limit rules
1.13
Limits: algebraic technique
1.14
Limits: formal definition
1.15
Continuity
Continuous functions
Intermediate value theorem
1.16
Limits at infinity
1.17
Infinite limits
Backmatter
A
Notation
B
Definitions
C
Theory
D
Examples
Colophon
Colophon
Colophon
©2020–2024 Ellen Goldstein
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit
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