Math 110 - College Algebra
This is a collection of video lectures for Math 110: College Algebra from UMKC (University of Missouri-Kansas city). Taught by Professor Richard Delaware, this course emphasizes the concepts of college algebra,
covering a variety of topics on algebra: numbers, graphs, equations and inequalities, functions, polynomials, exponential and logarithmic functions, systems of linear equations, binomial theorem, and sequences.
More details of the videos are found:
Listing of the videos and their contents
Unit 0 - Basics: Remembrance of Things Past
Lecture 01 - Numbers
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 02 - Language of Mathematics
Learning to Read Mathematics. Some Symbols of Algebra. Nouns, Pronouns, & The Main Verb of Algebra. Theorems, Corollaries, Lemmas, and All That
Lecture 03 - The Powers That be: Exponents
Integer Exponents. Operations with Integer Exponents. Square Roots: A Pair Of Equal Factors. Nth Roots & Rational Exponents. Operations with Rational Exponents
Lecture 4a - Polynomial Expressions
What is a Polynomial? Adding & Subtracting Polynomials. Multiplying Polynomials. A Common Error. Handy Polynomial Products. Un-Multiplying (Factoring) Polynomials. Completing A Perfect Square
Lecture 4b - Polynomial Expressions (cont.)
Dividing Polynomials: Rational Expressions. The Art of Simplification. Solving Some Polynomial & Rational Equations
Lecture 05 - More Numbers and a Little Geometry
Beyond Real Numbers: Complex Numbers. Some Area Formulas. The Pythagorean Theorem & A Visual Proof
Unit 1 - Graphs
Lecture 06 - Graphs
Rectangular Coordinates: Geometry Meets Algebra. Distance Between Points. Midpoint of a Line Segment. Your Graphing Device
Lecture 07 - Graphs (cont.)
Graphs of Equations. Intercepts: Crossing the Axes. Symmetry of Graphs. Lines: Defining "Slope"
Lecture 08 - Graphs (cont.)
Lines & Their Equations. Parallel & Perpendicular Lines. Circles & Their Equations. Some Exercises Explained
Unit 2 - Functions and Their Graphs
Lecture 09 - Functions and Their Graphs
Function: The Central Idea of Mathematics. The Language & Notation of Functions. More On Domains. Function Notation Practice
Lecture 10 - Functions and Their Graphs (cont.)
Visualizing Functions: Graphs of (x, f(x)) Pairs. Increasing & Decreasing Functions. Local Maximums & Local Minimums. Even & Odd Functions
Lecture 11 - Functions and Their Graphs (cont.)
A Library of Important Functions. Piecewise Defined Functions. Some Exercises Explained
Lecture 12 - Functions and Their Graphs (cont.)
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 13 - Functions and Their Graphs (cont.)
The Algebra of Functions. A New Operation Unique To Functions: Composition
Lecture 14 - Functions and Their Graphs (cont.)
Mathematical Models of Real World Problems: Constructing Functions
Unit 3 - Equations and Inequalities
Lecture 15 - Equations in One Variable
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 16 - Equations in One Variable (cont.)
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 17 - Equations in One Variable (cont.)
Some Linear & Quadratic Equation Exercises Explained
Lecture 18 - Equations in One Variable (cont.)
Setting Up Equations: More Mathematical Models
Lecture 19 - Equations in One Variable (cont.)
Solving "Radical" Equations. Solving Equations "Quadratic in Form". Solving Factorable Equations
Lecture 20 - Inequalities in One Variable
Properties of Inequalities. Solving Inequalities In General. Solving Linear Inequalities
Lecture 21 - Inequalities in One Variable (cont.)
Solving Quadratic Inequalities. Solving Higher-Degree Polynomial Inequalities. Solving Rational Inequalities
Lecture 22 - Inequalities in One Variable (cont.)
When Absolute Value Appears: Equations. When Absolute Value Appears: Inequalities. More Exercises Explained
Unit 4 - Polynomial and Rational Functions
Lecture 23 - Polynomial and Rational Functions
Degree 2: Quadratic Functions. Graphing Quadratic Functions. Quadratic Functions As Mathematical Models
Lecture 24 - Polynomial and Rational Functions (cont.)
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
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 (cont.)
Strategy & Tools: A Practical Checklist. Some Polynomial Exercises Explained
Lecture 27 - Rational Functions
General Rational Functions. What Is An Asymptote? Finding Asymptotes of Rational Functions. Graphing Rational Functions
Unit 5 - Exponential and Logarithmic Functions
Lecture 28 - Exponential Functions
One-To-One Functions. Exponential Functions & Their Graphs. The Natural Exponential Function
Lecture 29 - Logarithmic Functions
Inverse Functions. Logarithmic Functions & Their Graphs. The Natural Logarithmic Function
Lecture 30 - Logarithmic Functions (cont.)
Properties of Logarithms. All Logarithms are Natural (or Common)! Solving Logarithmic Equations. Logarithmic Models: Sound (Loudness) & Fury (Earthquakes)
Lecture 31 - Exponential Functions (cont.)
Solving Exponential Equations. Exponential Models: Compounded Interest, and Growth & Decay
Unit 6 - Systems of Equations
Lecture 32 - Systems of Linear Equations
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 (cont.)
Some Exercises Explained. An Application: Writing Proper Rational Functions As Sums of Simpler Proper Rational Functions (Partial Fractions)
Lecture 34 - Systems of Non-Linear Equations
Solving (Mostly Graphically) a System of 2 Non-Linear Equations in 2 Variables
Unit 7 - Some Discrete Topics
Lecture 35 - Sequences
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 (cont.)
Arithmetic Sequences: Adding Your Way to Infinity. Geometric Sequences: Multiplying Your Way to Infinity
Lecture 37 - Series & Induction
Geometric Series & Their (Infinite) Sums. The Principle of Mathematical Induction
Lecture 38 - Binomial Theorem
The "Binomial Coefficient" Symbol. Pascal's Triangle. The Binomial Theorem: How to Expand (x+a)^n
The X-Y Files: The Proof is in Here
Lecture 39 - The X-Y Files
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! Algebra For Science: Variation. How Can You Find Rational Zeros (if any) of a Polynomial Function?