Math 110: College Algebra

Video Lectures

Displaying all 39 video lectures.
I. Unit 0 - Basics: Remembrance of Things Past
Lecture 1
Numbers
Play Video		 Numbers

In this video lecture, Professor Richard Delaware discusses set of objects, natural numbers, real numbers and how to find distance between two points.Topics discussed are:



- Sets of Objects

- Natural Numbers

- Integers

- Rational Numbers

- Irrational Numbers

- Real Numbers

- The Real Line: From Numbers to Points

- Real Numbers are Ordered

- The Real Line: Distance Between Points

- Real Numbers as Decimals
Lecture 2
Language of Mathematics
Play Video		 Language of Mathematics

In this video lecture, Prof. Richard Delaware gives an overview of the Language of Mathematics.Topics included are:



- Learning to Read Mathematics

- Some Symbols of Algebra

- Nouns, Pronouns, & The Main Verb of Algebra

- Theorems, Corollaries, Lemmas, and All That
Lecture 3
The Powers That Be: Exponents
Play Video		 The Powers That Be: Exponents

In this video lecture, Prof. Richard Delaware discusses powers, exponents, operations with integer and rational exponents, square roots and nth roots. Topics discussed are:



- Integer Exponents

- Operations with Integer Exponents

- Square Roots: A Pair Of Equal Factors

- Nth Roots & Rational Exponents

- Operations with Rational Exponents
Lecture 4
Polynomial Expressions (Part I)
Play Video		 Polynomial Expressions (Part I)

Topics discussed are:



- What is a Polynomial?

- Adding & Subtracting Polynomials

- Multiplying Polynomials

- A Common Error

- Handy Polynomial Products

- Un-Multiplying (Factoring) Polynomials

- Completing A Perfect Square
Lecture 5
Polynomial Expressions (Part II)
Play Video		 Polynomial Expressions (Part II)

In this video lecture, Prof. Richard Delaware discusses dividing polynomials and rational expressions. Topics covered are:



- Dividing Polynomials: Rational Expressions

- The Art of Simplification

- Solving Some Polynomial & Rational Equations
Lecture 6
More Numbers and Geometry
Play Video		 More Numbers and Geometry

In this video lecture, Prof. Richard Delaware teaches about complex numbers, some area formulae and the Pythagorean theorem.Topics discussed are:



- Beyond Real Numbers: Complex Numbers

- Some Area Formulas

- The Pythagorean Theorem & A Visual Proof
II. Unit 1 - Graphs
Lecture 7
Graphs (Part I)
Play Video		 Graphs (Part I)

In this video lecture, Prof. Richard Delaware teaches about the graphs of equations, intercepts, symmetry and slopes. Topics discussed are:



- Rectangular Coordinates: Geometry Meets Algebra

- Distance Between Points

- Midpoint of a Line Segment

- Your Graphing Device
Lecture 8
Graphs (Part II)
Play Video		 Graphs (Part II)

In this video lecture, Prof. Richard Delaware gives an overview of equations of lines, parallel and perpendicular lines and graphing a circle.Topics covered are:



- Graphs of Equations

- Intercepts: Crossing the Axes

- Symmetry of Graphs

- Lines: Defining "Slope"
Lecture 9
Graphs (Part III)
Play Video		 Graphs (Part III)

In this video lecture, Prof. Richard Delaware gives an overview of equations of lines, parallel and perpendicular lines and graphing a circle. Topics covered are:



- Lines & Their Equations

- Parallel & Perpendicular Lines

- Circles & Their Equations

- Some Exercises Explained
III. Unit 2 - Functions and their Graphs
Lecture 10
Functions and Their Graphs (Part I)
Play Video		 Functions and Their Graphs (Part I)

In this video lecture, Prof. Richard Delaware discusses more about functions, finding local maximums and minimums, etc.Topics discussed include:



- Function: The Central Idea of Mathematics

- The Language & Notation of Functions

- More On Domains

- Function Notation Practice
Lecture 11
Functions and Their Graphs (Part II)
Play Video		 Functions and Their Graphs (Part II)

In this video lecture, Prof. Richard Delaware explains a lot of exercises related to functions.Topics covered are:



- Visualizing Functions: Graphs of (x, f(x)) Pairs

- Increasing & Decreasing Functions

- Local Maximums & Local Minimums

- Even & Odd Functions
Lecture 12
Functions and Their Graphs (Part III)
Play Video		 Functions and Their Graphs (Part III)

In this video lecture, Prof. Richard Delaware teaches more about graphing techniques like shifts, stretches and compressions.Topics covered are:



- A Library of Important Functions

- Piecewise Defined Functions

- Some Exercises Explained
Lecture 13
Functions and Their Graphs (Part IV)
Play Video		 Functions and Their Graphs (Part IV)

In this video lecture, Prof. Richard Delaware teaches more about the algebra of functions. Topics covered are:



- Graphing Techniques: Vertical & Horizontal Shifts

- Graphing Techniques: Compressions & Stretches

- Graphing Techniques: Reflections Across the Axes

- Putting It All Together: Moving The Graphs of Functions Around The Plane
Lecture 14
Functions and Their Graphs (Part V)
Play Video		 Functions and Their Graphs (Part V)

In this video lecture, Prof. Richard Delaware teaches how to construct functions. Topics covered are:



- The Algebra of Functions

- A New Operation Unique To Functions: Composition
Lecture 15
Functions and Their Graphs (Part VI)
Play Video		 Functions and Their Graphs (Part VI)

In this video lecture, Prof. Richard Delaware discusses equations, linear and non-linear equations and solving them algebraically and graphically. Topics covered are:



- Mathematical Models of Real World Problems: Constructing Functions
IV. Unit 3 - Equations & Inequalities
Lecture 16
Equations in One Variable (Part I)
Play Video		 Equations in One Variable (Part I)

In this video lecture, Prof. Richard Delaware teaches how to solve Quadratic Equations.



Topics covered are:

- Solving Equations (Approximately) with a Graphing Device & The Intermediate Value Theorem

- Solving Linear Equations: The "Linear Formula" or, Graphing

- Solving Non-Linear Equations That Lead To Linear Equations
Lecture 17
Equations in One Variable (Part II)
Play Video		 Equations in One Variable (Part II)

In this video lecture, Prof. Richard Delaware gives some more examples on equations and explains them.



Topics covered are:

- Solving Quadratic Equations: Factoring, or, Graphing

- A Complex Reminder & The Principal Square Root of a Negative Number

- Solving Quadratic Equations: The "Quadratic Formula" & The Discriminant or, Graphing
Lecture 18
Equations in One Variable (Part III)
Play Video		 Equations in One Variable (Part III)

In this video lecture, Prof. Richard Delaware gives some more mathematical models.



Topics covered are:

- Some Linear & Quadratic Equation Exercises Explained
Lecture 19
Equations in One Variable (Part IV)
Play Video		 Equations in One Variable (Part IV)

In this video lecture, Prof. Richard Delaware teaches about radical equations and solving factorable equations.



Topics covered are:

- Setting Up Equations: More Mathematical Models
Lecture 20
Equations in One Variable (Part V)
Play Video		 Equations in One Variable (Part V)

Topics covered are:

- Solving "Radical" Equations

- Solving Equations "Quadratic in Form"

- Solving Factorable Equations
Lecture 21
Inequalities in One Variable (Part I)
Play Video		 Inequalities in One Variable (Part I)

In this video lecture, Prof. Richard Delaware teaches about Quadratic Inequalities, Rational Inequalities and Higher Degree Inequalities.



Topics covered are:

- Properties of Inequalities

- Solving Inequalities In General

- Solving Linear Inequalities
Lecture 22
Inequalities in One Variable (Part II)
Play Video		 Inequalities in One Variable (Part II)

In this video lecture, Prof. Richard Delaware teaches about what happens when absolute value appears in equations and inequalities.



Topics covered:

- Solving Quadratic Inequalities

- Solving Higher-Degree Polynomial Inequalities

- Solving Rational Inequalities

- When Absolute Value Appears: Equations

- When Absolute Value Appears: Inequalities

- More Exercises Explained
V. Unit 4 - Polynomial & Rational Functions
Lecture 23
Polynomial Functions (Part I)
Play Video		 Polynomial Functions (Part I)

In this video lecture, Prof. Richard Delaware teaches about quadratic functions and graphing them.



Topics covered are:

- Degree 2: Quadratic Functions

- Graphing Quadratic Functions

- Quadratic Functions As Mathematical Models
Lecture 24
Polynomial Functions (Part II)
Play Video		 Polynomial Functions (Part II)

In this video lecture, Prof. Richard Delaware teaches about general polynomial functions, power functions and their graphs.



Topics covered:

- Degree "n": General Polynomial Functions

- Special Case: Power Functions & Their Graphs

- Graphing General Polynomial Functions: Zeros, Multiplicity, Turning Points & End Behavior
Lecture 25
Locating the Zeros of a Polynomial Function (Part I)
Play Video		 Locating the Zeros of a Polynomial Function (Part I)

In this video lecture, Prof. Richard Delaware teaches how to find zeroes of a polynomial function and how to check whether they are positive or negative.



Topics covered:

- How Many Zeros Are There?

- How Many Zeros Are Real?

- How Many Real Zeros Are Positive? Negative?

- Where (On What Interval) Are All Real Zeros?

- How Can You Guess The Location of Real Zeros?

- How Can You Reduce The Number of Real Zeros?
Lecture 26
Locating the Zeros of a Polynomial Function (Part II)
Play Video		 Locating the Zeros of a Polynomial Function (Part II)

In this video lecture, Prof. Richard Delaware teaches how to locate the zeroes of a polynomial function.



Topics covered:

- Strategy & Tools: A Practical Checklist

- Some Polynomial Exercises Explained
Lecture 27
Rational Functions
Play Video		 Rational Functions

In this video lecture, Prof. Richard Delaware teaches about asymptotes and finding the asymptotes of rational functions.



Topics covered:

- General Rational Functions

- What Is An Asymptote?

- Finding Asymptotes of Rational Functions

- Graphing Rational Functions
VI. Unit 5 - Exponential & Logarithmic Functions
Lecture 28
Exponential Functions (Part I)
Play Video		 Exponential Functions (Part I)

In this video lecture, Prof. Richard Delaware gives an overview of one-one functions, exponential functions and their graphs.



Topics covered:

- One-To-One Functions

- Exponential Functions & Their Graphs

- The Natural Exponential Function
Lecture 29
Logarithmic Functions (Part I)
Play Video		 Logarithmic Functions (Part I)

In this video lecture, Prof. Richard Delaware teaches about inverse functions, logarithmic functions and their graphs.



Topics covered:

- Inverse Functions

- Logarithmic Functions & Their Graphs

- The Natural Logarithmic Function
Lecture 30
Logarithmic Functions (Part II)
Play Video		 Logarithmic Functions (Part II)

In this video lecture, Prof. Richard Delaware teaches about the properties of logarithmic functions and solving logarithmic functions.



Topics covered:

- Properties of Logarithms

- All Logarithms are Natural (or Common)!

- Solving Logarithmic Equations

- Logarithmic Models: Sound (Loudness) & Fury (Earthquakes)
Lecture 31
Exponential Functions (Part II)
Play Video		 Exponential Functions (Part II)

In this video lecture, Prof. Richard Delaware continues his lecture about solving exponential functions and more about exponential models.



Topics covered:

- Solving Exponential Equations

- Exponential Models: Compounded Interest, and Growth & Decay
VII. Unit 6 - Systems of Equations
Lecture 32
Systems of Linear Equations (Part I)
Play Video		 Systems of Linear Equations (Part I)

In this video lecture, Prof. Richard Delaware teaches about systems of linear equations, solving them by substitution and elimination.



Topics covered:

- Systems of Linear Equations in General

- Solving A System of 2 (or 3) Linear Equations in 2 (or 3) Variables: Substitution

- Solving A System of 2 (or 3) Linear Equations in 2 (or 3) Variables: Elimination
Lecture 33
Systems of Linear Equations (Part II)
Play Video		 Systems of Linear Equations (Part II)

In this video lecture, Prof. Richard Delaware explains some more exercises.



Topics covered:

- Some Exercises Explained

- An Application: Writing Proper Rational Functions As Sums of Simpler Proper Rational Functions (Partial Fractions)
Lecture 34
System of Non-Linear Equations
Play Video		 System of Non-Linear Equations

In this video lecture, Prof. Richard Delaware teaches solving a system of two non linear equations in two variables.



Topics covered:

- Solving (Mostly Graphically) a System of 2 Non-Linear Equations in 2 Variables
VIII. Unit 7 - Some Discrete Topics
Lecture 35
Sequences (Part I)
Play Video		 Sequences (Part I)

In this video lecture, Prof. Richard Delaware teaches about infinite sequences and how to solve them.



Topics covered:

- Infinite Sequences: Functions With Domain N

- The Factorial Symbol: !

- Adding The First n Terms of a Sequence: nth Partial Sums & Summation Notation
Lecture 36
Sequences (Part II)
Play Video		 Sequences (Part II)

In this video lecture, Prof. Richard Delaware looks into Arithmetic Sequences and Geometric Sequences.



Topics covered:

- Arithmetic Sequences: Adding Your Way to Infinity

- Geometric Sequences: Multiplying Your Way to Infinity
Lecture 37
Series & Induction
Play Video		 Series & Induction

In this video lecture, Prof. Richard Delaware teaches about Geometric Series and their infinite sums and principals of Mathematical Induction.



Topics covered:

- Geometric Series & Their (Infinite) Sums

- The Principle of Mathematical Induction
Lecture 38
The Binominal Theorem
Play Video		 The Binominal Theorem

In this video lecture, Prof. Richard Delaware teaches about the Binomial coefficient and the Binomail Theorem.



Topics covered:

- The "Binomial Coefficient" Symbol

- Pascal's Triangle

- The Binomial Theorem: How to Expand (x+a)n
IX. The X-Y Files: The Proof is in Here
Lecture 39
The X-Y Files: The Proof is in Here
Play Video		 The X-Y Files: The Proof is in Here

For Unit 0

- A Proof That Ö2 Is Irrational

- A Proof That There Are The Same Number of Rational Numbers as Natural



Numbers

- A Proof That There Are More Real Numbers Than Natural Numbers



For Unit 2

- Algebra For Science: Variation



For Unit 4

- How Can You Find Rational Zeros (if any) of a Polynomial Function?



For Unit 7

- A Proof That "e" Is Irrational