Math 1314 Online Lectures

University of Houston Department of Mathematics
Copyright 2009

 

 

Instructions:

  1. To access a lecture outline:  Click on a section in the “Lecture Outlines” column. Print the outline before viewing the lecture so that you can take notes on it when you view the lectures for that section.
    Note:  You must have the free Adobe Reader  to view the worksheets.

  1. To view a lecture:  Turn up the sound on your computer. Go to the "Flash Lectures" column, select "Flash, and then maximize your viewing window so that you can see the entire screen. The control bar for the Flash video (stop, play, rewind, etc.) can be found by scrolling down to the bottom of the screen.
    Note:  You must have the free Adobe Flash Player  to view the lectures.

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# Lecture Outlines Flash Lectures

0

Prerequisites

 
            Writing Equations of Lines Flash
            Solving an Equation for a Given Variable Flash
            Using Interval Notation Flash
            Finding the Domain of a Function Flash
            Finding Information from a Graph Flash
            Multiplying Polynomials Flash
            Function Notation Flash
            Factoring Flash
            Using the Rules of Exponents Flash
            Simplifying Radicals Flash
 

          Exponential Functions, Logarithmic Functions and

               the number e

Flash
 

          Comparing Numbers

Flash
            Solving Equations Flash
            Graphing Flash
            Solving Systems of Equations Flash
            Simplifying Expressions Flash
          Synthetic Division Flash

1

Limits  

 

          Definition of a Limit

Flash

 

          Evaluating Limits - Substitution

Flash

 

          Indeterminate Forms

Flash

 

          Limits at Infinity

Flash

2

One-Sided Limits and Continuity

 
            One-Sided Limits Flash
            Continuity at a Point and Continuity on an Interval Flash
            Examples and Applications Flash

3

The Derivative  

 

          The Limit Definition of the Derivative

Flash

 

          Four Step Process for Finding the Derivative

Flash

 

          Example 2

Flash
            Example 3 Flash
            Example 4 Flash
            Example 5 Flash

4

Basic Rules of Differentiation  
            Constant Rule and Power Rule Flash
            Constant Multiple Rule and Sum/Difference Rule Flash
 

          Derivatives of the Exponential Function and the

               Natural Log Function

Flash
            Derivative of f(x) = a^x Flash 

5

The Product and Quotient Rules

 
            The Product Rule Flash
            The Quotient Rule Flash

6

The Chain Rule  

 

          The Chain Rule

Flash
 

          The Chain Rules for Exponential and Logarithmic

               Functions

Flash

 

          Chain Rule with Product or Quotient Rule:

               Examples 9-10

Flash
 

          Chain Rule with Product or Quotient Rule:

               Example 11

Flash
7 Higher Order Derivatives  
            Higher Order Derivatives Flash

4,5,6,7

Mixed Examples, Derivatives (Lessons 4-7)  

 

          Example 1

Flash

 

          Example 2

Flash

 

          Example 3

Flash

 

          Example 4

Flash

 

          Example 5

Flash

 

          Example 6

Flash

 

          Example 7

Flash

 

          Example 8

Flash

 

          Example 9

Flash

 

          Example 10

Flash

 

          Example 11

Flash

 

          Example 12

Flash
            Example 13 Flash
            Example 14 Flash
            Example 15 Flash
            Example 16 Flash

8

Some Basic Applications of the Derivative  

 

          Equations of Tangent Lines

Flash

 

          Horizontal Tangent Lines, etc.

Flash

 

          Rates of Change - Example 7

Flash

 

          Rates of Change - Example 8

Flash

 

          Rates of Change - Example 9

Flash
            Velocity and Acceleration Flash

9

Marginal Functions in Economics and Other Applications  

 

          Marginal Cost

Flash
          Marginal Cost Example Flash
            Average Cost Flash

 

          Marginal Revenue

Flash
          Marginal Profit Flash
            Example 7 Flash
10 Applications of the First Derivative  
            Increasing and Decreasing Functions,
               Graph of  f
Flash
            Increasing and Decreasing Functions,
               A Functional Approach,
                    Example 4
Flash
                      Example 5 Flash
                      Example 6 Flash
 

          Critical Numbers, Relative Extrema and the First

          Derivative Test

Flash
            Relative Extrema by Analyzing the Sign of  f '
                    Example 7
Flash
                      Example 8 Flash
                      Example 9 Flash
            Application - Example 10 Flash
11 Applications of the Second Derivative  
 

          Concavity

Flash
            Example 2 Flash
            Example 3 Flash
            Example 4 Flash
            Inflection Points Flash
 

          Example 6

Flash
 

          Example 7

Flash
 

          Example 8

Flash
 

          Second Derivative Test - Example 9

Flash
 

          Example 10

Flash
12 Curve Sketching  
            Rational Zeros:  Example 1 Flash
            Example 2 Flash
            Example 3 Flash
            Example 4 Flash
            Example 5 Flash
            Example 6 Flash
            Example 7 Flash
            The Guide to Curve Sketching Flash
            Example 8 Flash
            Example 9 Flash
          Example 10 Flash
          Example 11 Flash
          Example 12 Flash
          Example 13 Flash
13

Absolute Extrema

 
            Introduction Flash
            Example 4 Flash
            Example 5 Flash
            Example 6 Flash
          Application Flash
14

Optimization

 
            Introduction Flash
            Example 2 Flash
            Example 3 Flash
            Example 4 Flash
            Example 5 Flash
            Example 6 Flash
15

Applications with Exponential Functions

 
            Interest Problems Flash
            Exponential Functions Flash
            Exponential Growth Example 3 Flash
            Exponential Growth Example 4 Flash
            Exponential Decay Example 5 Flash
            Exponential Decay Example 6 Flash
16

Antiderivatives

 
            Introduction Flash
            The Basic Rules of Integration:
               Integration of a Constant, The Power Rule
Flash
            The Basic Rules of Integration:
               Constant Multiple Rule, Sum/Difference Rule
Flash
            The Basic Rules of Integration:  Integrating
               the Exponential Function and  f (x) = 1/x
Flash
            Applying the Rules Flash
            Differential Equations Flash
17 Integration by Substitution  
            Example 1 Flash
            Example 2 Flash
            Example 3 Flash
            Example 4 Flash
            Example 5 Flash
            Example 6 Flash
            Example 7 Flash
            Example 8 Flash
18 Area Under a Curve:  Riemann Sums  
          Introduction to Riemann Sums Flash
            Example 5 Flash
          Example 6 Flash
            Example 7 Flash
            The Definite Integral Flash
19 The Fundamental Theorem of Calculus  
            Example 1 Flash
            Example 2 Flash
            Example 3 Flash
            Example 4 Flash
            Example 5 Flash
            Example 6 Flash
            Example 7 Flash
            Example 8 Flash
            Example 9 Flash
            Example 10 Flash
            Click here for a proof of the Fundamental Theorem  
20 Evaluating Definite Integrals  
            Properties and Example 1 Flash
            Example 2 Flash
            Example 3 Flash
            Example 4 Flash
            Example 5 Flash
            Applications Flash
            Average Value Flash
21 Area Between Two Curves  
            Introduction and Example 1 Flash
            Example 2 Flash
            Example 3 Flash
            Example 4 Flash
            Example 5 Flash
            Example 6 Flash
            Example 7 Flash
            Example 8 Flash
22 Functions of Several Variables  
            Evaluating Functions of Several Variables Flash
            Domain Flash
            Level Curves Flash
23 Partial Derivatives  
            Example 1 Flash
            Example 2 Flash
            Example 3 Flash
            Example 4 Flash
            Example 5 Flash
            Example 6 Flash
            Example 7 Flash
            Example 8 Flash
24 Relative Extrema  
            Example 1 Flash
            Example 2 Flash
            Example 3 Flash
            Example 4 Flash
            Example 5 Flash