Math 161

MEP - Math 161

Lesson 1

Numbers, Inequalities and Absolute Values
Algebralab
Welcome to AlgebraLab, where you can find explanations on a variety of Algebraic functions.

AAAMath
This website allows you to learn, interact and see your results.

ITCCOnline
A tutorial with written exercises on Absolute values and equalities.

Coordinate Geometry and Lines
Cartesian Coordinates
This Java Applet enables you to visualize your geometry and lines

General Coordinates Game
Welcome to the General Coordinates Game. Learn to plot points and read the coordinates

Graphs of Second Degree Equations
Quadratic Equations
The applet helps to understand equations and the usual way to solve them.

Recognize Structures
This applet illustrates the importance of the distinction between "more important" and "less important" properties of mathematical expression.

Quadratic Functions
This java application allows you to input a function and see the resulting graph.

 

Lesson 2

Trigonometry
Name Project
This site contains definitions, formulas, equations and solutions of Trigonometry

Math Tutor
Videos and exercises explaining trigonometry theorem, equations and formulas.

Velocity
HyperPhysics
Definitions, equations and exercises dealing with velocity.

MathWorld
Formulas for velocity

Tangent Problem
Tangent Line
Tutorial with interactive graphs

Graphics
Animation of secants approaching a Tangent

 

Lesson 3

1.1, Ways to represent a function
Function Explained
A wiki page to explain Function in everyday English!

1.2, Mathematical models
Y-Math
Welcome to Y-math a website with an entire range of various mathematical models

 

Lesson 4

1.3, New functions from old functions
New functions from old
A tutorial explaining multiple approaches to changing functions.

Scaled Graph
New functions from Old…: Scaled and Shifted Functions

 

Lesson 5

1.4, Graphing calculators
Calculator
Graphics Calculators – Numerous sites from academia and industry, featuring graphics calculators and what they can do

Calculator 2
Graphing Calculator Help – An interactive site which allows the user to select a graphing calculator model and then enter various topics, tools, functions, etc. for varying results

Graphing Calculator
Top 6 Graphing Calculators – Test the Top Ranking Graphing Calculators, Per about.com and see for yourself what they can do!

1.5, Exponential functions
Applications
Application of Exponential Functions – This site provides a thorough explanation of exponential functions, along with several interactive graphs, to help learn pertinent concepts.

Exponential Fun
College Algebra/Exponential Functions – this site provides practical exponential function problems, along with tips on how to use a graphing calculator. Additional sites are provided for additional help.

MathWorld Exponential
WolframMathWorld’s site for exponential functions – provides interactive plotting experience.

 

Lesson 6

1.6, Inverse Functions and Logarithms
Inverses
Solving Exponential Equations using Logarithms

Inverse Applet
What happens when one function "undoes" what another function does.

Logarithms
Using and Deriving Algebraic Properties of Logarithms with applets.

 

Lesson 7

2.1, Tangent and Velocity Problems
With Graphs
Looking at how the tangent problem relates to velocity.

Velocity Applet
This applet displays the acceleration and velocity vectors in real time.

More Problems
Tangent and Velocity Problems provide the historical basis for the idea of derivative, with short animations.

2.2, Limit of a Function
Whyslopes
Short videos explaining the Limit of a Function

Math.PSU.edu
This applet can be used to examine the limit of the function

Calculus-help
Your personal tutor to limits. With audio and visuals!

 

Lesson 8

2.3, Calculating Limits using Limit Laws
Egghead
California professor posts his lectures and drill problems on Limits .

Hofstra.edu
Numerical and Graphical Approaches to limits.

Stewart Calculus
Calculating limits with JavaScript interactions and audio instructions

 

Lesson 9

2.5, Continuity
Egghead
This California professor posts his lectures and drill problems on Continuity.

HMC.edu
This website shows the important property of continuity and the need of a precise definition

Calculus Help
Your personal tutor to continuity. With audio and visuals!

Lamar.edu
Definition, fact, examples and solutions on Continuity by Prof. Paul!

 

Lesson 10

2.5, Continuity - See Above
2.6, Limits at Infinity
Calculus-Help
Your personal tutor to continuity. With audio and visuals!

Egghead
This California professor posts his lectures and drill problems on Limits at Infinity.

Cool School
A look at the connection between horizontal asymptotes and limits

Wolfram
WolframMathWorld’s site for Infinite Limit at Infinity – provides interactive plotting experience

 

Lesson 11

2.7, Tangents, Velocities, and Other Rates of Change
Cool School
Explores tangents and other rates of change

lamar.edu
Takes a look at two fairly important problems in the study of calculus

Math.UBC
A look at average velocity, average rates of change and secant lines

2.8, Derivatives
Mathworld
WolframMathWorld’s site for Derivatives, packed with examples and useful hyperlinks

Hyper-ad
Explanation of derivatives, their concepts and examples

Calculus-help
Your personal tutor to Derivatives. With audio and visuals!

Math2
Tables of Derivatives and proof of their function .

 

Lesson 12

2.9, Derivative as Function
Math.HWS
Derivative Applet – Interactive site which shows graph of a function of its first derivative. Examples and second derivatives also shown

Hofstra.edu
Derivatives: Algebraic Viewpoint – Tutorial for derivative functions, which interactive examples for computing the derivative algebraically

Montana.edu
Derivatives – Comparing a Function with Its Derivative – A short movie is provided to illustrate graphing the derivative of a function

 

Lesson 13

3.1, Derivatives of Polynomials and Exponential Functions
Coolschool
Finding some simple derivatives: Derivatives of Polynomials and Exponential Functions

MIT.edu
Explaining Polynomials, some of the easiest functions in calculus

Rutgers.edu
Dr Z’s Examples of Derivatives of polynomials and their solutions

3.2, Product and Quotient Rules
WVU.edu
A pdf presentation on products and quotient rules with several good examples

Hofstra.edu
Definitions and examples of the Product and Quotient Rules

 

Lesson 14

3.2, Product and Quotient Rules - See Above

3.3, Rates of Change in the Natural and Social Sciences
UMN.edu
A .pdf presentation/homework on rates of change.

Rutgers.edu
More of Dr Z’s Examples, this time on the Rates of Change in the Natural and Social Sciences

 

Lesson 15

3.4, Derivatives of Trigonometric Functions
IES.CO.JP
An interactive applet makes Derivative of Trigonometric Functions more fun

UTK.edu
Derivatives of Trigonometric Functions explained with the use of Macromedia Flash 5 player .

UBC.ca Trig
More interactive applets with Derivatives of Trigonometric Functions

UBC.ca Trig 2
A look at Derivatives of Trigonometric Functions

 

Lesson 16

3.5, Chain Rule
Calculus Help
The Chain Rule – Informative movie which explains the chain rule in detail

UTK.edu
Visual Calculus – The Chain Rule – Interactive examples, providing one with enough experience to master the Chain Rule.

MIT.edu
World Web Math – The Chain Rule - Detailed explanation of the Chain Rule, along with examples and exercise.

wolfram
WolframMathWorld – Chain Rule - Reputable site for explaining mathematical concepts.

 

Lesson 17

3.6, Implicit Differentiation
Netsoc.tcd.ie
The math is explained in the applet so the user can see where the values came from

Ucdavis.edu
Detailed explanation of Implicit Differentiation along with exercise

Hostsrv
An awesome “type your problem here” and see the answer website

Mit.edu
Explaining Implicit Differentiation with examples and exercises

 

Lesson 18

3.7, Higher Derivatives
Ltcconline
The derivative of the derivative is called the second derivative. A third, fourth, fifth, etc. derivative are called higher. This page gives examples, their solutions and some exercises

Abdn.ac.uk
The derivative of the derivative is called the second derivative. A third, fourth, fifth, etc. derivative are called higher. This page gives examples.

Abdn.ac.uk 2
More from the University of Aberdeen, Scotland..

 

Lesson 19

3.8, Derivatives of Logarithmic Functions
Iteso.mx
The objective of this website is to: learn how to differentiate logarithmic functions with examples and exercises

libraryofmath
The library of Math has an impressive collection of math subjects by topics .

3.9, Hyperbolic Functions
Furman.edu
The objective of this website is to: learn hyperbolic functions with examples and exercises

Mathworld
WolframMathWorld, the web’s most extensive mathematics resource - focusing on Hyperbolic Functions

Ping.be
The objective of this website is to: learn hyperbolic functions with examples

Mcraefamily
Math Help provides tips and techniques and offers one-on-one help for math students using a variety of methods

 

Lesson 20

9.4, Exponential Growth and Decay
Uoguelph.ca Intro
University of Guelph ’s comprehensive site, featuring problem solving help

Uoguelph.ca Q Exp
University of Guelph ’s site featuring equations dealing with exponential growth and decay

regentsprep.org
Oswego City School District Regents Exam Prep Center – spotlights interactive examples of exponential growth and decay

Carleton.edu G and D
Within a comprehensive site compiled by Carleton College – features many components to teaching facts on exponential growth and decay

Carleton.edu Graphs
Graphs of Exponential Growth/Decay – Located on Carleton College’s “Starting Point – Teaching Entry Level Geosciences

 

Lesson 21

3.10 Related Rates
Lamar.edu
Definition, fact, examples and solutions on Related Rates by Prof. Paul!

Dartmouth.edu
U. of Dartmouth site has definitions, applets, examples and exercise as well as videos to explain Related Rates

Tamu.edu
Texas A&M’s Prof Belmonte’s class notes on Related Rates. Loads of examples with nice simple explanations

 

Lesson 22

3.10, Related Rates - See Above

 

Lesson 23

3.11, Linear Approximations and Differentials
Usd.edu
Linear Approximations defined. With animation!

Lamar.edu
Definition, fact, examples and solutions on Linear Approximations by Prof. Paul!

Tamu.edu
Texas A&M’s Prof Belmonte’s class notes on Linear Approximations and Differentials . Loads of examples with nice simple explanations.

 

Lesson 24

4.1, Maximum and Minimum Values
The Math Page max
Maximum and Minimum values explained. With hyperlinks

The Math Page applied
Applications of Maximum and Minimum values explained. With hyperlinks

USD.edu
Maximum and Minimum Values defined. With animations!

 

Lesson 25

4.2, Mean Value theorem
Wolfram
WolframMathWorld, the web’s most extensive mathematics resource – focuses on the Mean-Value Theorem

Dartmouth.edu
The Mean Value Theorem, compiled by Dartmouth – provides interactive examples, applets, videos, quizzes and exercises

You Tube
Calculus Fundamental Theorem part ii proof (1 of 2) – informative youtube tutorial from www.midnighttutor.com (rocket scientists on call) (a 4 youtube star rating)

Calculus Help
Calculus I (AB): Mean ol' Value Theorem – from www.calculus-help.com - problems and solutions provided for various concepts

 

Lesson 26

4.3 How Derivatives Affect the Shape of a Graph
UBC.ca
An interactive website form the University of British Columbia

UWEC.edu
Nice detailed explanations of Derivatives affecting the shape of graphs.

Cool School
Looking at the graphical implications of derivatives

 

Lesson 27

4.3 How Derivatives Affect the Shape of a Graph - See Above

 

Lesson 28

4.4, Indeterminate Forms and L'Hospital's Rule
Wolfram
WolframMathWorld, the web’s most extensive mathematics resource - focusing on Indeterminate Forms and L'Hospital's Rule

Mcrae Family
Math Help provides tips and techniques and offers one-on-one help for math students using a variety of methods .

Sloan Zone
Many tables of functions.

UWEC.edu
Nice detailed explanations on L’Hospital Rule

 

Lesson 29

4.5, Summary of Curve Sketching
Tamu
A very interactive webpage from Texas A&M

You Tube 1
One on one tutor. Clear explanations

You Tube 2
Another one on one tutor. Clear explanations

4.6, Graphing with Calculus and Calculators
HRW.com
An online graphing calculator

Prenhall Graphing
How to program a function on your calculator!

UACCB.edu
Video tutorials on how to program your calculator!

Prenhall Calc 2
How to program your calculator by type.

 

Lesson 30

4.7, Optimization Problems
UIUC.edu
An easy going website from U.of Illinois at Urbana Champaign dealing with several aspects of Optimization

Analyzemath Area
Using Derivatives to solve problems: Area Optimization

Analyzemath Time
Use Derivatives to solve problems: Distance-time Optimization

Temple.edu
Welcome to the COW (Calculus on the Web) from Temple University. A lot of awesome links to every aspects of Calculus!. Explanations and exercises included.

Hopstra
Summary and exercises on Applications of Maxima and Minima

Seminole.cc.fl.us
Great visual help on Optimization ProblemsYou will need to download the free DPGraph Viewer to view the DPGraph animations on this page

 

Lesson 31

4.7, Optimization Problems - See Above

 

Lesson 32

4.9, Newton's Method
Wolfram
WolframMathWorld, the web’s most extensive mathematics resource - focusing on Newton 's Method

Furman.edu
This website’s applet illustrates using Newton's method to approximate solutions to the equation

You Tube
Newton 's Method – informative youtube tutorial (a 5 youtube star rating)

4.10, Antiderivatives
HMC.edu
The nice people at Harvey Mudd University help out with Antideratives

Intmath
An awesome webpage! This is interactive mathematics
where you learn math by playing with it! Includes mini-video lectures

AlgebraLab
Welcome to AlgebraLab. Where you can find explanations on a variety of Algebraic functions. Including Antiderivatives

UNCW.edu
This website has 2 objectives: 1) Distinguish between specific antiderivatives and the general antiderivative and 2) Develop antiderivative rules inductively from known differentiation rules

 

Lesson 33

5.1, Areas and Distance
Lamar.edu
Definition, fact, examples and solutions on optimization by Prof. Paul!

UBC.ca
A math class with tutorial and exercise

5.2, Definite Integral
Wolfram
WolframMathWorld, the web’s most extensive mathematics resource - focusing on Definite Integral

Lamar.edu
Definition, fact, examples and solutions on by Prof. Paul!

UTK.edu
Definite Integral – Provided by the University of Tennessee, Knoxville – an interactive applet featuring examples and animations

Thinkquest.org
An easy-going website on Definite Integral. Has links to interactive pages

 

Lesson 34

5.3 Fundamental Theorem of Calculus
Wolfram
WolframMathWorld, the web’s most extensive mathematics resource – emphasis on fundamental theorems of calculus

UTK.edu
Visual Calculus/Fundamental Theorem of Calculus – Provided by the University of Tennessee, Knoxville – an interactive applet featuring a problem along with graphical visualization

You Tube
Calculus Fundamental Theorem part ii proof (1 of 2) – the midnight tutor strikes again via youtube www.midnighttutor.com (for site information) (a 4 youtube star rating)

You Tube 2
Calculus Fundamental Theorem proof part ii (2 of 2) – a continuation from previous site (a 5 youtube star rating)

HMC.edu
Mathematics- Henry Mudd College – Fundamental Theorem of Calculus – Online tutorial

UTK.edu
Visual Calculus/Fundamental Theorem of Calculus – Provided by the University of Tennessee, Knoxville – an interactive applet featuring examples and animations.

Karls Calculus
Living Backwards -- The Fundamental Theorem of Calculus – provided by http://www.karlscalculus.org/ - Detailed background information on the fundamental theorem of calculus

 

Lesson 35

5.3, Fundamental Theorem of Calculus - See Above

 

Lesson 36

5.4, Indefinite Integrals and the Net Change Theorem
Wolfram
From Wolfram, the web’s most extensive mathematics resource – emphasis on Indefinite Integrals and the Net Change Theorem. An interactive site.

Efunda
Math fundamentals. A “fill in the box- get an answer” webpage

 

Lesson 37

5.5, Substitution Rule
HMC.edu
The nice people at Harvey Mudd University help out with Computing Integrals by Substitution.

Lamar
Definition, fact, examples and solutions on Substitution Rule for Indefinite Integrals by Prof. Paul!