**Math 34A**

Calculus for the Social and Life Sciences I

- Paul's Notes: Graphing
Text Introduction to graphs and functions - Paul's Notes: Graphing Functions
Text Examples of sketching graphs - PurpleMath: Graphing Overview
Text General overview of graphing - MathIsFun: Cartesian Coordinates
Text Introduction to the Cartesian plane - MathIsFun: Make Your Own Graphs
Interactive Interactive modules on various graphs/charts - Khan Academy: Reading Line Graphs
Video - 2:20 Interpreting Line Graphs

- Khan Academy: Sum of Consecutive Odd Integers
Video - 4:33 Single variable word problem - Khan Academy: Algebraic Word Problem
Video - 8:02 Single variable word problem - Khan Academy: Basic Rate Problem
Video - 4:08 Introduction to speed = distance/time - Khan Academy: Application problems with equation in one variable
Video - 2:01 Single variable word problem - Khan Academy: Another Percent Word Problem
Video - 6:18 Word problem involving percentages - Khan Academy: Equations of Sequence Patterns
Video - 8:36 Example of getting a line equation from a pattern - Khan Academy: Basic Linear Function
Video - 2:42 Example of a line equation from a word problem - YourMathGal: Percent Mixture Problem #1
Video - 10:20 Example of a mixing problem - YourMathGal: Rate-Time-Distance Problem 1
Video - 5:17 Example of a car problem - CLAS Lee DeAnda's Webpage: "Express in terms of"
Interactive Six examples on express-in-terms-of problems - CLAS Lee DeAnda's Webpage: Car problems
Interactive Example of a car problem - PurpleMath: Geometry Word Problems
Text Lots of word problems with geometry

- Khan Academy: Introduction to Limits
Video - 11:32 Non-rigorous intro to limits - Khan Academy: Limit Examples (part1)
Video - 8:57 Non-rigorous limit examples Continues in next video - Khan Academy: Limits 1
Interactive Limit exercises - Paul's Notes: Limits
Text Catalog List of lectures on limits - MathIsFun: Limits (An Introduction)
Text Catalog Introduction to limits

- MathIsFun: Sigma Notation
Text Explanation of Sigma notation and (finite) summations - Paul's Notes: Sigma Notation
Text Introduction to Sigma notation and summation formulas

- Khan Academy: Linear Equations in Slope Intercept Form
Video - 14:58 Lots of examples on finding slope-intercept form of a line - Khan Academy: Linear Equations in Point Slope Form
Video - 9:38 Lots of examples on finding point-slope form of a line - Khan Academy: Equation of a line 3
Video - 6:42 Graphing a line using slope-intercept - Khan Academy: Linear Functions
Interactive Line exercises - Paul Notes: Lines
Text Summary on equations of lines, parallel/perpendicular lines - PurpleMath: Straight-line equations
Text Line equations

- Khan Academy: Proportionality Constant for Direct Variation
Video - 1:44 "Directly Proportional" example - Khan Academy: Inverse Variation Application
Video - 4:42 "Indirectly Proportional" example - Khan Academy: Direct and Inverse Variation
Interactive Proportionality exercises - PurpleMath: Proportions
Text Introduction to proportions

- Khan Academy: Logarithms
Video Catalog List of videos on logarithms - Khan Academy: Solving Logarithms
Interactive Logarithm exercises - Khan Academy: Operations with Logarithms
Interactive Logarithm properties exercises See videos in lower-right for help - Paul's Notes: Logarithm Function
Text Introduction to logarithms See following pages for solving equations with logs - PurpleMath: Logarithms
Text Introduction to logarithms - PurpleMath: Basic Log Rules
Text Log rules and examples - Base 10 Log Table
Text From Cooper's book - 10^x Graph
Text From Cooper's book - MathIsFun: Working with Exponents and Logarithms
Text Elementary explanation of logarithms

- Khan Academy: Introduction to Exponential Decay
Video - 9:19 Half-life examples - Khan Academy: Exponential Growth Functions
Video - 7:41 Intro to Exponential Growth - Khan Academy: Word Problem Solving- Exponential Growth and Decay
Video - 7:21 Exponential word problems - Khan Academy: Introduction to Compound interest
Video - 6:56 Intro to compound interest (compounding annually) - YourMathGal: Log Application 1 - Compound Interest
Video - 11:16 An example on compound interest (using log) Part 1 of 2 - Paul's Notes: Solving Exponential Equations
Text Solving equations using logarithms - PurpleMath: Solving Exponential Equations
Text Solving equations using logarithms - MathIsFun: Compound Interest Calculator
Interactive Calculates compound interest

- Mathispower4u: Find the Average Rate of Change from a Graph
Video - 3:17 Finding average rate of change from a graph - Mathispower4u: Find the Average Rate of Change Given a Function Rule
Video - 4:37 Finding average rate of change given a function - Mathispower4u: Average Rate of Change Application
Video - 3:23 A word problem on average rate of change - Paul's Notes: Rates of Change and Tangent Lines
Text Derivative, tangent line, and rate of change - Applied Calculus: Average Rate of Change
Interactive Average rate of change examples - Khan Academy: Derivatives 1
Video - 15:43 Derivative intuition - Calculus Applets: Derivative at a Point
Interactive Applet demonstrating the instantaneous rate of change as the limit of average rates of change

- Khan Academy: Power Rule
Video - 3:54 Power rule and some basic differentiation rules - Mathispower4u: Differentiation Techniques: Power Rule
Video - 8:46 Power rule and some basic differentiation rules - Khan Academy: Power Rule Exercises
Interactive Power rule practice - Paul's Notes: Derivative Formulas
Text Power rule and some basic differentiation rules - Wolfram|Alpha
Interactive Do-it-all mathematics tool Type "Derivative of __________" - Calculus Applets: Power Functions
Interactive Interactive derivative plotter for power rule Try examples 6 and 7 - Calculus Applets: Exponential Functions
Interactive Interactive derivative plotter for exponential rule Try using k = e = 2.718

- Paul's Notes: Linear approximations
Text Tangent line approximation with an example - BestDAmnTutoring: Tangent line Approximations Part 1
Video - 4:34 An example on tangent line approximation - Lucid Education: Linear Approximation
Video - 8:20 Example of tangent line approximation - Calculus Applets: Linear Approximations
Interactive Interactive tangent line approximation

- Mathispower4u: Finding relative extrema using the first derivative
Video - 6:18 Finding max/min using first derivative - Mathispower4u: Max/Min Application Problem Ex1
Video - 5:05 Maximizing/Minimizing word problem 34A students may ignore second derivative test - Paul's Notes: Minimum and Maximum Values
Text Finding max/min of a function See next two pages for more examples - Paul's Notes: Optimization
Text Max/min word problems Some examples refer to the second derivative test - Paul's Notes: Business Applications
Text More max/min word problems - Wolfram|Alpha
Interactive Do-it-all mathematics tool Example input: "maximize f(x) = x^2 on [0,2]" - Calculus Applets: Optimization
Interactive Maximization word problem visualization - CLAS Lee DeAnda's webpage: Max and Min's
Text Examples of finding max/min Last method is second derivative test - Paul's Notes: Critical Points
Text Finding critical points + examples Uses some derivative rules that are not covered in 34A

- Mathispower4u: Determining the concavity of a function
Video - 10:02 Second derivative and concavity You do not need to know the second example - Mathispower4u: Summary of the First and Second Derivative of a Function
Video - 11:00 Finding intervals of increasing/decreasing and concave up/concave down - Paul's Notes: Shape of the Graph II
Text Using the second derivative test to find extrema - CLAS Lee DeAnda's webpage: Max and Min's
Text Examples of finding max/min Last method is second derivative test

- How to Calculate Your Grade in a Class
Video - 4:43 How to calculate your grade - NCIS parody- using Newton's Law of Cooling to find time of death
Video - 10:03 High school student calculus project - Math in Daily Life
Text Examples of how 34A level math comes up in daily life