Richard Delaware video College Algebra List of Videos

College Algebra (Math 110) Video Course
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Listing of the Videos and Their Contents

College Algebra (Math 110) - Recorded in 1998
Video Professor: Richard Delaware

No reference on the videos is made to a particular text, although the course is based on the instructor's experience and the text: College Algebra Enhanced with Graphing Utilities, by Sullivan & Sullivan, 1st Ed., (1996), Prentice Hall.
Times are approximate.
There are many internal "Stop Tape" pauses for students to work problems or review.

Welcome to the Course
Unit 0 - BASICS: Remembrance of Things Past
Unit 1 - GRAPHS
Unit 2 - FUNCTIONS AND THEIR GRAPHS
Unit 3 - EQUATIONS & INEQUALITIES
Unit 4 - POLYNOMIAL & RATIONAL FUNCTIONS
Unit 5 - EXPONENTIAL & LOGARITHMIC FUNCTIONS
Unit 6 - SYSTEMS OF EQUATIONS
Unit 7 - SOME DISCRETE TOPICS
The X-Y Files: The Proof is in Here - Several Proofs and other topics keyed to the previous Units

PDF copies of all College Algebra pages on the Videos

Welcome to the Course (Accidentally omitted from the tapes)

Welcome to College Algebra.
G.H. Hardy, a famous 19th Century mathematician wrote:

"A mathematician, like a painter or poet, is a maker of patterns.
If his patterns are more permanent than theirs, it is because they are made with ideas..."

This will be a course with emphasis on IDEAS. An idea, like a picture, is worth 1000 words!
With the ideas clear, language & techniques become easier to remember;
they hang together in your mind.

This course will prepare you for further courses, such as
Analytic Geometry, Precalculus, and Calculus.

Please note: A graphing device is appropriate for this course, and will be discussed.
However, I expect YOU to master the basic features of your device yourself.

My recommendations to you:

Replay any tape segment whenever you feel it's necessary!
This is the great advantage of a course on video.

Pay attention to the language I use in speaking about Algebra.
Try to become fluent in this language yourself.

Adopt an organized style of work, as I do.
You need not mimic me exactly, but learn to leave a clear "paper trail",
especially when you use a graphing device.

Don't get behind! Work lots of problems.

Now it's time we roll up our sleeves and get down to the nuts-and-bolts of Algebra!

UNIT 0 - BASICS: Remembrance of Things Past [6 hr. 49 min.]

NUMBERS [1 hr. 14 min.]

Sets of Objects [4 min.]
Natural Numbers [7 min.]
Integers [5 min.]
Rational Numbers [13 min.]
Irrational Numbers [2 min.]
Real Numbers [1 min.]
The Real Line: From Numbers to Points [4 min.]
Real Numbers are Ordered [19 min,]
The Real Line: Distance Between Points [8 min.]
Real Numbers as Decimals [11 min.]

THE LANGUAGE OF MATHEMATICS [27 min.]

Learning to Read Mathematics [7 min.]
Some Symbols of Algebra [9 min.]
Nouns, Pronouns, & The Main Verb of Algebra [4 min.]
Theorems, Corollaries, Lemmas, and All That [7 min.]

THE POWERS THAT BE: EXPONENTS [1 hr. 29 min.]

Integer Exponents [12 min.]
Operations with Integer Exponents [31 min.]
Square Roots: A Pair Of Equal Factors [13 min.]
Nth Roots & Rational Exponents [12 min.]
Operations with Rational Exponents [21 min.]

POLYNOMIAL EXPRESSIONS [3 hr. 2 min.]

What is a Polynomial? [18 min.]
Adding & Subtracting Polynomials [3 min.]
Multiplying Polynomials [19 min.]
A Common Error [5 min.]
Handy Polynomial Products [15 min.]
Un-Multiplying (Factoring) Polynomials [28 min.]
Completing A Perfect Square [10 min.]

Dividing Polynomials: Rational Expressions [24 min.]
The Art of Simplification [14 min.]
Solving Some Polynomial & Rational Equations [46 min.]

MORE NUMBERS [19 min.]

Beyond Real Numbers: Complex Numbers [19 min.]

A LITTLE GEOMETRY [20 min.]

Some Area Formulas [8 min.]
The Pythagorean Theorem & A Visual Proof [12 min.]

UNIT 1 - GRAPHS [3 hr. 53 min.]

GRAPHS [3 hr. 53 min.]

Rectangular Coordinates: Geometry Meets Algebra [11 min.]
Distance Between Points [18 min.]
Midpoint of a Line Segment [7 min.]
Your Graphing Device [17 min.]

Graphs of Equations [25 min.]
Intercepts: Crossing the Axes [12 min.]
Symmetry of Graphs [14 min.]
Lines: Defining "Slope" [34 min.]

Lines & Their Equations [24 min.]
Parallel & Perpendicular Lines [26 min.]
Circles & Their Equations [28 min.]
Some Exercises Explained [16 min.]

UNIT 2 - FUNCTIONS AND THEIR GRAPHS [7 hr. 2 min.]

FUNCTIONS AND THEIR GRAPHS [7 hr. 2 min]

Function: The Central Idea of Mathematics [26 min.]
The Language & Notation of Functions [20 min.]
More On Domains [19 min.]
Function Notation Practice [16 min.]

Visualizing Functions: Graphs of (x, f(x)) Pairs [26 min.]
Increasing & Decreasing Functions [23 min.]
Local Maximums & Local Minimums [18 min.]
Even & Odd Functions [20 min.]

A Library of Important Functions [20 min.]
Piecewise Defined Functions [19 min.]
Some Exercises Explained [11 min.]

Graphing Techniques: Vertical & Horizontal Shifts [28 min.]
Graphing Techniques: Compressions & Stretches [27 min.]
Graphing Techniques: Reflections Across the Axes [17 min.]
Putting It All Together: Moving The Graphs of Functions Around The Plane [36 min.]

The Algebra of Functions [16 min.]
A New Operation Unique To Functions: Composition [24 min.]

Mathematical Models of Real World Problems: Constructing Functions [55 min.]

UNIT 3 - EQUATIONS & INEQUALITIES [7 hr. 16 min.]

EQUATIONS IN 1 VARIABLE [4 hr. 38 min.]

Solving Equations (Approximately) with a Graphing Device & The Intermediate Value Theorem [44 min.]
Solving Linear Equations: The "Linear Formula" or, Graphing [23 min.]
Solving Non-Linear Equations That Lead To Linear Equations [13 min.]

Solving Quadratic Equations: Factoring, or, Graphing [11 min.]
A Complex Reminder & The Principal Square Root of a Negative Number [12 min.]
Solving Quadratic Equations: The "Quadratic Formula" & The Discriminant or, Graphing [50 min.]

Some Linear & Quadratic Equation Exercises Explained [24 min.]

Setting Up Equations: More Mathematical Models [65 min.]

Solving "Radical" Equations [14 min.]
Solving Equations "Quadratic in Form" [15 min.]
Solving Factorable Equations [7 min.]

INEQUALITIES IN 1 VARIABLE [1 hr. 54 min.]

Properties of Inequalities [20 min.]
Solving Inequalities In General [17 min.]
Solving Linear Inequalities [19 min.]

Solving Quadratic Inequalities [17 min.]
Solving Higher-Degree Polynomial Inequalities [14 min.]
Solving Rational Inequalities [27 min.]

EQUATIONS & INEQUALITIES IN 1 VARIABLE [44 min.]

When Absolute Value Appears: Equations [12 min.]
When Absolute Value Appears: Inequalities [17 min.]
More Exercises Explained [15 min.]

UNIT 4 - POLYNOMIAL & RATIONAL FUNCTIONS [5 hr. 23 min.]

POLYNOMIAL FUNCTIONS [2 hr. 30 min.]

Degree 2: Quadratic Functions [19 min.]
Graphing Quadratic Functions [39 min.]
Quadratic Functions As Mathematical Models [25 min.]

Degree "n": General Polynomial Functions [8 min.]
Special Case: Power Functions & Their Graphs [18 min.]
Graphing General Polynomial Functions: Zeros, Multiplicity, Turning Points & End Behavior [40 min.]

LOCATING THE ZEROS OF A POLYNOMIAL FUNCTION [1 hr. 28 min.]

How Many Zeros Are There? [12 min.]
How Many Zeros Are Real? [13 min.]
How Many Real Zeros Are Positive? Negative? [16 min.]
Where (On What Interval) Are All Real Zeros? [22 min.]
How Can You Guess The Location of Real Zeros? [4 min.]
How Can You Reduce The Number of Real Zeros? [21 min.]

Strategy & Tools: A Practical Checklist [14 min.]
Some Polynomial Exercises Explained [22 min.]

RATIONAL FUNCTIONS [1 hr. 25 min.]

General Rational Functions [14 min.]
What Is An Asymptote? [17 min.]
Finding Asymptotes of Rational Functions [35 min.]
Graphing Rational Functions [19 min.]

UNIT 5 - EXPONENTIAL & LOGARITHMIC FUNCTIONS [3 hr. 42 min.]
EXPONENTIAL FUNCTIONS [55 min.]

One-To-One Functions [14 min.]

Exponential Functions & Their Graphs [26 min.]

The Natural Exponential Function [15 min.]

LOGARITHMIC FUNCTIONS [1 hr. 59 min.]

Inverse Functions [23 min.]
Logarithmic Functions & Their Graphs [24 min.]
The Natural Logarithmic Function [4 min.]

Properties of Logarithms [17 min.]
All Logarithms are Natural (or Common)! [15 min.]
Solving Logarithmic Equations [20 min.]
Logarithmic Models: Sound (Loudness) & Fury (Earthquakes) [16 min.]

EXPONENTIAL FUNCTIONS (con.) [47 min.]

Solving Exponential Equations [15 min.]
Exponential Models: Compounded Interest, and Growth & Decay [32 min.]

UNIT 6 - SYSTEMS OF EQUATIONS [2 hr. 44 min.]

SYSTEMS OF LINEAR EQUATIONS [2 hr. 29 min.]

Systems of Linear Equations in General [19 min.]
Solving A System of 2 (or 3) Linear Equations in 2 (or 3) Variables: Substitution [20 min.]
Solving A System of 2 (or 3) Linear Equations in 2 (or 3) Variables: Elimination [36 min.]

Some Exercises Explained [31 min.]
An Application: Writing Proper Rational Functions As Sums of Simpler Proper Rational Functions (Partial Fractions) [43 min.]

SYSTEMS OF NON-LINEAR EQUATIONS [14 min]

Solving (Mostly Graphically) a System of 2 Non-Linear Equations in 2 Variables [14 min.]

UNIT 7 - SOME DISCRETE TOPICS [3 hr. 40 min.]

SEQUENCES [1 hr. 41 min.]

Infinite Sequences: Functions With Domain N [28 min.]
The Factorial Symbol: ! [8 min.]
Adding The First n Terms of a Sequence: nth Partial Sums & Summation Notation [17 min.]

Arithmetic Sequences: Adding Your Way to Infinity [18 min.]
Geometric Sequences: Multiplying Your Way to Infinity [30 min.]

SERIES & INDUCTION [56 min.]

Geometric Series & Their (Infinite) Sums [26 min.]
The Principle of Mathematical Induction [30 min.]

THE BINOMIAL THEOREM [1 hr. 2 min.]

The "Binomial Coefficient" Symbol [11 min.]
Pascal's Triangle [19 min.]
The Binomial Theorem: How to Expand (x+a)ⁿ [32 min.]

THE X-Y FILES: The Proof is in Here [1 hr. 27 min.]

FOR UNIT 0 [29 min.]

A Proof That Ö2 Is Irrational [6 min.]
A Proof That There Are The Same Number of Rational Numbers as Natural Numbers! [9 min.]
A Proof That There Are More Real Numbers Than Natural Numbers! [14 min.]

FOR UNIT 2 [17 min.]

Algebra For Science: Variation [17 min.]

FOR UNIT 4 [21 min.]

How Can You Find Rational Zeros (if any) of a Polynomial Function? [21 min.]

FOR UNIT 7 [19 min.]

A Proof That "e" Is Irrational [19 min.]