Lecture 2: THE LANGUAGE OF MATHEMATICS
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.]
Lecture 3: THE POWERS THAT BE: EXPONENTS
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.]
Lecture 4 Part 1: POLYNOMIAL EXPRESSIONS
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.]
Lecture 4 Part 2: POLYNOMIAL EXPRESSION
Dividing Polynomials: Rational Expressions [24 min.]
The Art of Simplification [14 min.]
Solving Some Polynomial & Rational Equations [46 min.]
Lecture
7: GRAPHS
Graphs of Equations [25 min.]
Intercepts: Crossing the Axes [12 min.]
Symmetry of Graphs [14 min.]
Lines: Defining "Slope" [34 min.]
Lecture
10: FUNCTIONS AND THEIR GRAPHS
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.]
Lecture
11: FUNCTIONS AND THEIR GRAPHS
A Library of Important Functions [20 min.]
Piecewise Defined Functions [19 min.]
Some Exercises Explained [11 min.]
Lecture 12: FUNCTIONS AND THEIR GRAPHS
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.]
Lecture 13: FUNCTIONS AND THEIR
GRAPHS
The Algebra of Functions [16 min.]
A New Operation Unique To Functions: Composition
[24 min.]
Lecture
16: EQUATIONS IN 1 VARIABLE 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.]
Lecture
17: EQUATIONS IN 1 VARIABLE Some Linear
& Quadratic Equation Exercises Explained [24 min.]
Lecture
18: EQUATIONS IN 1 VARIABLESetting Up Equations:
More Mathematical Models [65 min.]
Lecture
19: EQUATIONS IN 1 VARIABLE Solving
"Radical" Equations [14 min.]
Solving Equations "Quadratic in Form" [15 min.]
Solving Factorable Equations [7 min.]
Lecture
20: INEQUALITIES IN 1 VARIABLE
Properties of Inequalities [20 min.]
Solving Inequalities In General [17 min.]
Solving Linear Inequalities [19 min.]
Lecture
21: INEQUALITIES IN 1 VARIABLE
Solving Quadratic Inequalities [17 min.]
Solving Higher-Degree Polynomial Inequalities [14 min.]
Solving Rational Inequalities [27 min.]
Lecture 24: POLYNOMIAL FUNCTIONS
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.]
Lecture
25: LOCATING THE ZEROS OF A POLYNOMIAL FUNCTION
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.]
Lecture
26: LOCATING THE ZEROS OF A POLYNOMIAL FUNCTION
Strategy & Tools: A Practical Checklist [14 min.]
Some Polynomial Exercises Explained [22 min.]
Lecture 29: LOGARITHMIC FUNCTIONS
Inverse Functions [23 min.]
Logarithmic Functions & Their Graphs [24 min.]
The Natural Logarithmic Function [4 min.]
Lecture 30: LOGARITHMIC FUNCTIONS
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.]
Lecture
33: SYSTEMS OF LINEAR EQUATIONS
Some Exercises Explained [31 min.]
An Application: Writing Proper Rational Functions As Sums of
Simpler Proper Rational Functions (Partial Fractions) [43 min.]
Lecture
36: SEQUENCES
Arithmetic Sequences: Adding Your Way to Infinity
[18 min.]
Geometric Sequences: Multiplying Your Way to
Infinity [30 min.]
Lecture 37: SERIES & INDUCTION
Geometric Series & Their (Infinite) Sums [26
min.]
The Principle of Mathematical Induction [30 min.]
FOR UNIT 2 [17 min.]
FOR UNIT 4 [21 min.]
FOR UNIT 7 [19 min.]
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