Math 1314 Online Lectures
University of Houston Department of
Mathematics
Copyright 2009
Instructions:
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# | Lecture Outlines | Flash Lectures |
0 |
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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 | |
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Definition of a Limit |
Flash |
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Evaluating Limits - Substitution |
Flash |
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Indeterminate Forms |
Flash |
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Limits at Infinity |
Flash |
2 |
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One-Sided Limits | Flash | |
Continuity at a Point and Continuity on an Interval | Flash | |
Examples and Applications | Flash | |
3 |
The Derivative | |
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The Limit Definition of the Derivative |
Flash |
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Four Step Process for Finding the Derivative |
Flash |
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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 |
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The Product Rule | Flash | |
The Quotient Rule | Flash | |
6 |
The Chain Rule | |
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The Chain Rule |
Flash |
The Chain Rules for Exponential and Logarithmic Functions |
Flash | |
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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) | |
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Example 1 |
Flash |
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Example 2 |
Flash |
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Example 3 |
Flash |
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Example 4 |
Flash |
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Example 5 |
Flash |
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Example 6 |
Flash |
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Example 7 |
Flash |
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Example 8 |
Flash |
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Example 9 |
Flash |
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Example 10 |
Flash |
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Example 11 |
Flash |
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Example 12 |
Flash |
Example 13 | Flash | |
Example 14 | Flash | |
Example 15 | Flash | |
Example 16 | Flash | |
8 |
Some Basic Applications of the Derivative | |
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Equations of Tangent Lines |
Flash |
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Horizontal Tangent Lines, etc. |
Flash |
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Rates of Change - Example 7 |
Flash |
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Rates of Change - Example 8 |
Flash |
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Rates of Change - Example 9 |
Flash |
Velocity and Acceleration | Flash | |
9 |
Marginal Functions in Economics and Other Applications | |
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Marginal Cost |
Flash |
Marginal Cost Example | Flash | |
Average Cost | Flash | |
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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 | ||
Introduction | Flash | |
Example 4 | Flash | |
Example 5 | Flash | |
Example 6 | Flash | |
Application | Flash | |
14 | ||
Introduction | Flash | |
Example 2 | Flash | |
Example 3 | Flash | |
Example 4 | Flash | |
Example 5 | Flash | |
Example 6 | Flash | |
15 | ||
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 | ||
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 |