Math 1314 Online Lectures
University of Houston Department of
Mathematics
Copyright 2009
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Instructions:
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| # | Lecture Outlines | Flash Lectures |
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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 | |
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Exponential Functions, Logarithmic Functions and the number e |
Flash | |
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Comparing Numbers |
Flash | |
| Solving Equations | Flash | |
| Graphing | Flash | |
| Solving Systems of Equations | Flash | |
| Simplifying Expressions | Flash | |
| Synthetic Division | Flash | |
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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 |
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2 |
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| One-Sided Limits | Flash | |
| Continuity at a Point and Continuity on an Interval | Flash | |
| Examples and Applications | Flash | |
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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 | |
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4 |
Basic Rules of Differentiation | |
| Constant Rule and Power Rule | Flash | |
| Constant Multiple Rule and Sum/Difference Rule | Flash | |
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Derivatives of the Exponential Function and the Natural Log Function |
Flash | |
| Derivative of f(x) = a^x | Flash | |
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5 |
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| The Product Rule | Flash | |
| The Quotient Rule | Flash | |
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6 |
The Chain Rule | |
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The Chain Rule |
Flash |
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The Chain Rules for Exponential and Logarithmic Functions |
Flash | |
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Chain Rule with Product or Quotient Rule: Examples 9-10 |
Flash |
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Chain Rule with Product or Quotient Rule: Example 11 |
Flash | |
| 7 | Higher Order Derivatives | |
| Higher Order Derivatives | Flash | |
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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 | |
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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 | |
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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 | |
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Increasing
and Decreasing Functions, Graph of f |
Flash | |
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Increasing and Decreasing Functions, A Functional Approach, Example 4 |
Flash | |
| Example 5 | Flash | |
| Example 6 | Flash | |
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Critical Numbers, Relative Extrema and the First Derivative Test |
Flash | |
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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 | |
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Concavity |
Flash | |
| Example 2 | Flash | |
| Example 3 | Flash | |
| Example 4 | Flash | |
| Inflection Points | 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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Second Derivative Test - Example 9 |
Flash | |
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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 | |
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The Basic Rules of Integration: Integration of a Constant, The Power Rule |
Flash | |
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The Basic Rules of Integration: Constant Multiple Rule, Sum/Difference Rule |
Flash | |
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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 | |