Online courses directory (381)

Were the Middle Ages really all that dark? Hardly! How could we call the period that saw the building of Chartres Cathedral with its stunning stained-glass windows, dark? Sure, the Roman empire collapsed, but with the Christianization of Europe came magnificent churches, illuminated bibles, and intricately designed broaches. This period also saw the birth of Islam, the third great monotheistic religion. Introduction. Medieval and Byzantine Art. A New Pictorial Language: The Image in Early Medieval Art. Iconoclasm. Medieval Manuscripts. The Bestiary. Beginner's Guide to Medieval Art. An Introduction to Christianity. Standard Scenes from the Life of Christ in Art. An Introduction to Early Christian Art. Early Christian Art & Architecture after Constantine. Sarcophagus of Junius Bassus. Santa Sabina. Santa Maria Maggiore. The Mausoleum of Galla Placidia, Ravenna. Early Christian. Sutton Hoo Ship Burial. The Lindesfarne Gospels. Medieval and Byzantine Art. San Vitale. Sant'Apollinare in Classe, Ravenna, Italy, c. 533-49. Hagia Sophia. Ivory panel with Archangel. Icon of Saint George (the "Black George"). Icon of the Triumph of Orthodoxy. Byzantine Art. Introduction to Islam. The Five Pillars of Islam. Arts of the Islamic World. Two Royal Figures (Saljuq Period). Coronation Mantle. Ilkhanid Mihrab. Hebrew Astrolabe. Qa'a: The Damascus Room. Carolingian Art: An Introduction. Charlemagne: An Introduction (1 of 2). Charlemagne and the Carolingian Revival (part 2 of 2). Saint Matthew from the Ebbo Gospel. Lindau Gospels Cover. Santa Prassede (Praxedes). Carolingian. Ottonian Art: An Introduction. Bronze doors, Saint Michael's, Hildesheim, commissioned by Bishop Bernward, 1015. Pilgrimage Routes and the Cult of the Relic. Pentecost and Mission to the Apostles Tympanum, V

Exploring a world where both sides aren't equal anymore!. Inequalities Using Multiplication and Division. One-step inequality with multiplication and division example. Constructing and solving one-step inequality. One step inequalities. One-Step inequality involving addition. Inequalities Using Addition and Subtraction. Two-step inequality example. Multi-Step Inequalities. Multi-Step Inequalities 2. Multi-Step Inequalities 3. Multi-step linear inequalities. Interpreting Inequalities. Writing and using inequalities 2. Writing and using inequalities 3. Interpreting and solving linear inequalities. Inequality examples. Compound Inequalities. Compound Inequalities. Compound Inequalities 2. Compound Inequalities 3. Compound Inequalities 4. Compound inequalities. Absolute Value Inequalities. Absolute value inequalities Example 1. Absolute Value Inequalities Example 2. Absolute value inequalities example 3. Writing and using inequalities. Dogs cats and bears in a pet store visual argument. Dogs cats and bears in a pet store analytic argument. Reasoning through inequality expressions. Using expressions to understand relationships. Structure in expressions 1. Inequalities Using Multiplication and Division. One-step inequality with multiplication and division example. Constructing and solving one-step inequality. One step inequalities. One-Step inequality involving addition. Inequalities Using Addition and Subtraction. Two-step inequality example. Multi-Step Inequalities. Multi-Step Inequalities 2. Multi-Step Inequalities 3. Multi-step linear inequalities. Interpreting Inequalities. Writing and using inequalities 2. Writing and using inequalities 3. Interpreting and solving linear inequalities. Inequality examples. Compound Inequalities. Compound Inequalities. Compound Inequalities 2. Compound Inequalities 3. Compound Inequalities 4. Compound inequalities. Absolute Value Inequalities. Absolute value inequalities Example 1. Absolute Value Inequalities Example 2. Absolute value inequalities example 3. Writing and using inequalities. Dogs cats and bears in a pet store visual argument. Dogs cats and bears in a pet store analytic argument. Reasoning through inequality expressions. Using expressions to understand relationships. Structure in expressions 1.

This topic introduces the basic conceptual tools that underpin our journey through Euclidean geometry. These include the ideas of points, lines, line segments, rays, and planes. Euclid as the Father of Geometry. Language and Notation of Basic Geometry. Lines, Line Segments, and Rays. Recognizing rays lines and line segments. Specifying planes in three dimensions. Points, lines, and planes. Language and Notation of the Circle. The Golden Ratio. Identifying Rays. Measuring segments. Measuring segments. Congruent segments. Congruent segments. Segment addition. Segment addition. Algebraic midpoint of a segment exercise. Midpoint of a segment. Euclid as the Father of Geometry. Language and Notation of Basic Geometry. Lines, Line Segments, and Rays. Recognizing rays lines and line segments. Specifying planes in three dimensions. Points, lines, and planes. Language and Notation of the Circle. The Golden Ratio. Identifying Rays. Measuring segments. Measuring segments. Congruent segments. Congruent segments. Segment addition. Segment addition. Algebraic midpoint of a segment exercise. Midpoint of a segment.

This topic continues our journey through the world of Euclid by helping us understand angles and how they can relate to each other. Angle basics. Measuring angles in degrees. Using a protractor. Measuring angles. Measuring angles. Acute right and obtuse angles. Angle types. Vertical, adjacent and linearly paired angles. Exploring angle pairs. Introduction to vertical angles. Vertical angles. Using algebra to find the measures of vertical angles. Vertical angles 2. Proof-Vertical Angles are Equal. Angles Formed by Parallel Lines and Transversals. Identifying Parallel and Perpendicular Lines. Figuring out angles between transversal and parallel lines. Congruent angles. Parallel lines 1. Using algebra to find measures of angles formed from transversal. Parallel lines 2. CA Geometry: Deducing Angle Measures. Proof - Sum of Measures of Angles in a Triangle are 180. Triangle Angle Example 1. Triangle Angle Example 2. Triangle Angle Example 3. Challenging Triangle Angle Problem. Proof - Corresponding Angle Equivalence Implies Parallel Lines. Finding more angles. Angles 1. Angles 2. Sum of Interior Angles of a Polygon. Angles of a polygon. Sum of the exterior angles of convex polygon. Introduction to angles (old). Angles (part 2). Angles (part 3). Angles formed between transversals and parallel lines. Angles of parallel lines 2. The Angle Game. Angle Game (part 2). Acute right and obtuse angles. Complementary and supplementary angles. Complementary and supplementary angles. Example using algebra to find measure of complementary angles. Example using algebra to find measure of supplementary angles. Angle addition postulate. Angle basics. Measuring angles in degrees. Using a protractor. Measuring angles. Measuring angles. Acute right and obtuse angles. Angle types. Vertical, adjacent and linearly paired angles. Exploring angle pairs. Introduction to vertical angles. Vertical angles. Using algebra to find the measures of vertical angles. Vertical angles 2. Proof-Vertical Angles are Equal. Angles Formed by Parallel Lines and Transversals. Identifying Parallel and Perpendicular Lines. Figuring out angles between transversal and parallel lines. Congruent angles. Parallel lines 1. Using algebra to find measures of angles formed from transversal. Parallel lines 2. CA Geometry: Deducing Angle Measures. Proof - Sum of Measures of Angles in a Triangle are 180. Triangle Angle Example 1. Triangle Angle Example 2. Triangle Angle Example 3. Challenging Triangle Angle Problem. Proof - Corresponding Angle Equivalence Implies Parallel Lines. Finding more angles. Angles 1. Angles 2. Sum of Interior Angles of a Polygon. Angles of a polygon. Sum of the exterior angles of convex polygon. Introduction to angles (old). Angles (part 2). Angles (part 3). Angles formed between transversals and parallel lines. Angles of parallel lines 2. The Angle Game. Angle Game (part 2). Acute right and obtuse angles. Complementary and supplementary angles. Complementary and supplementary angles. Example using algebra to find measure of complementary angles. Example using algebra to find measure of supplementary angles. Angle addition postulate.

A detailed look at shapes that are prevalent in science: conic sections. Introduction to Conic Sections. Recognizing conic sections. Radius and center for a circle equation in standard form. Equation of a circle in factored form. Conic Sections: Intro to Circles. Graphing circles. Equation of a circle in non-factored form. Graphing circles 2. Conic Sections: Intro to Ellipses. Equation of an ellipse. Foci of an Ellipse. Parabola Focus and Directrix 1. Focus and Directrix of a Parabola 2. Parabola intuition 1. Parabola intuition 2. Conic Sections: Intro to Hyperbolas. Conic Sections: Hyperbolas 2. Conic Sections: Hyperbolas 3. Equation of a hyperbola. Foci of a Hyperbola. Proof: Hyperbola Foci. Identifying an ellipse from equation. Identifying a hyperbola from an equation. Identifying circles and parabolas from equations. Hyperbola and parabola examples. Tangent Line Hyperbola Relationship (very optional). IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Circle Hyperbola Intersection. Introduction to Conic Sections. Recognizing conic sections. Radius and center for a circle equation in standard form. Equation of a circle in factored form. Conic Sections: Intro to Circles. Graphing circles. Equation of a circle in non-factored form. Graphing circles 2. Conic Sections: Intro to Ellipses. Equation of an ellipse. Foci of an Ellipse. Parabola Focus and Directrix 1. Focus and Directrix of a Parabola 2. Parabola intuition 1. Parabola intuition 2. Conic Sections: Intro to Hyperbolas. Conic Sections: Hyperbolas 2. Conic Sections: Hyperbolas 3. Equation of a hyperbola. Foci of a Hyperbola. Proof: Hyperbola Foci. Identifying an ellipse from equation. Identifying a hyperbola from an equation. Identifying circles and parabolas from equations. Hyperbola and parabola examples. Tangent Line Hyperbola Relationship (very optional). IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Circle Hyperbola Intersection.

Check out the flow of positive charge through the heart that happens every time your heart beats! Learn how the heart is able to keep a regular rate and rhythm throughout your life. Membrane Potentials - Part 1. Membrane Potentials - Part 2. Permeability and Membrane Potentials. Action Potentials in Pacemaker Cells. Action Potentials in Cardiac Myocytes. Reseting Cardiac Concentration Gradients. Electrical System of the Heart. Depolarization Waves Flowing through the Heart. A Race to Keep Pace!. Thinking about Heartbeats. New Perspective on the Heart. Membrane Potentials - Part 1. Membrane Potentials - Part 2. Permeability and Membrane Potentials. Action Potentials in Pacemaker Cells. Action Potentials in Cardiac Myocytes. Reseting Cardiac Concentration Gradients. Electrical System of the Heart. Depolarization Waves Flowing through the Heart. A Race to Keep Pace!. Thinking about Heartbeats. New Perspective on the Heart.

Basic trigonometry. Example: Using soh cah toa. Trigonometry 0.5. Basic trigonometry II. Trigonometry 1. Secant (sec), cosecant (csc) and cotangent (cot) example. Example: Using trig to solve for missing information. Reciprocal trig functions. Trigonometry 1.5. Example: Calculator to evaluate a trig function. Example: Trig to solve the sides and angles of a right triangle. Trigonometry 2. Example: Solving a 30-60-90 triangle. Special right triangles. Using Trig Functions. Using Trig Functions Part II. Introduction to radians. Radian and degree conversion practice. Example: Radian measure and arc length. Example: Converting degrees to radians. Degrees to radians. Example: Converting radians to degrees. Radians to degrees. Radians and degrees. Radians and degrees. Unit circle definition of trig functions. Example: Unit circle definition of sin and cos. Example: Using the unit circle definition of trig functions. Example: Trig function values using unit circle definition. Example: The signs of sine and cosecant. Unit Circle Manipulative. Unit circle. Example: Graph, domain, and range of sine function. Example: Graph of cosine. Example: Intersection of sine and cosine. Example: Amplitude and period. Example: Amplitude and period transformations. Example: Amplitude and period cosine transformations. Example: Figure out the trig function. Graphs of sine and cosine. Graph of the sine function. Graphs of trig functions. Graphing trig functions. More trig graphs. Determining the equation of a trigonometric function. Inverse Trig Functions: Arcsin. Inverse Trig Functions: Arccos. Inverse Trig Functions: Arctan. Example: Calculator to evaluate inverse trig function. Inverse trig functions. Tau versus Pi. Pi Is (still) Wrong.. Basic trigonometry. Example: Using soh cah toa. Trigonometry 0.5. Basic trigonometry II. Trigonometry 1. Secant (sec), cosecant (csc) and cotangent (cot) example. Example: Using trig to solve for missing information. Reciprocal trig functions. Trigonometry 1.5. Example: Calculator to evaluate a trig function. Example: Trig to solve the sides and angles of a right triangle. Trigonometry 2. Example: Solving a 30-60-90 triangle. Special right triangles. Using Trig Functions. Using Trig Functions Part II. Introduction to radians. Radian and degree conversion practice. Example: Radian measure and arc length. Example: Converting degrees to radians. Degrees to radians. Example: Converting radians to degrees. Radians to degrees. Radians and degrees. Radians and degrees. Unit circle definition of trig functions. Example: Unit circle definition of sin and cos. Example: Using the unit circle definition of trig functions. Example: Trig function values using unit circle definition. Example: The signs of sine and cosecant. Unit Circle Manipulative. Unit circle. Example: Graph, domain, and range of sine function. Example: Graph of cosine. Example: Intersection of sine and cosine. Example: Amplitude and period. Example: Amplitude and period transformations. Example: Amplitude and period cosine transformations. Example: Figure out the trig function. Graphs of sine and cosine. Graph of the sine function. Graphs of trig functions. Graphing trig functions. More trig graphs. Determining the equation of a trigonometric function. Inverse Trig Functions: Arcsin. Inverse Trig Functions: Arccos. Inverse Trig Functions: Arctan. Example: Calculator to evaluate inverse trig function. Inverse trig functions. Tau versus Pi. Pi Is (still) Wrong..

You have probably been wondering whether our powers of algebraic problem solving break down if we divide by the variable or we have entire expressions in denominator of a fraction. Well, they don't! In this topic, you'll learn how to interpret and manipulate rational expressions (when you have one algebraic expression divided by another)!. Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Dividing polynomials by binomials 1. Simplifying Rational Expressions 2. Dividing polynomials by binomials 2. Simplifying rational expressions 2. Simplifying Rational Expressions 3. Simplifying Rational Expressions Example 2. Dividing polynomials by binomials 3. Simplifying rational expressions 3. Simplifying rational expressions 4. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Subtracting Rational Expressions. Simplifying First for Subtracting Rational Expressions. Adding and subtracting rational expressions 0.5. Adding and subtracting rational expressions 1. Adding and subtracting rational expressions 1.5. Adding and subtracting rational expressions 2. Adding and subtracting rational expressions 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Multiplying and dividing rational expressions 1. Multiplying and dividing rational expressions 2. Multiplying and dividing rational expressions 3. Multiplying and dividing rational expressions 4. Multiplying and dividing rational expressions 5. Rationalizing Denominators of Expressions. Asymptotes of Rational Functions. Another Rational Function Graph Example. A Third Example of Graphing a Rational Function. Partial Fraction Expansion 1. Partial Fraction Expansion 2. Partial Fraction Expansion 3. Partial fraction expansion. Ex 1 Multi step equation. Solving rational equations 1. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Solving rational equations 2. Extraneous Solutions to Rational Equations. Extraneous solutions. Rational Inequalities. Rational Inequalities 2. Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Dividing polynomials by binomials 1. Simplifying Rational Expressions 2. Dividing polynomials by binomials 2. Simplifying rational expressions 2. Simplifying Rational Expressions 3. Simplifying Rational Expressions Example 2. Dividing polynomials by binomials 3. Simplifying rational expressions 3. Simplifying rational expressions 4. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Subtracting Rational Expressions. Simplifying First for Subtracting Rational Expressions. Adding and subtracting rational expressions 0.5. Adding and subtracting rational expressions 1. Adding and subtracting rational expressions 1.5. Adding and subtracting rational expressions 2. Adding and subtracting rational expressions 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Multiplying and dividing rational expressions 1. Multiplying and dividing rational expressions 2. Multiplying and dividing rational expressions 3. Multiplying and dividing rational expressions 4. Multiplying and dividing rational expressions 5. Rationalizing Denominators of Expressions. Asymptotes of Rational Functions. Another Rational Function Graph Example. A Third Example of Graphing a Rational Function. Partial Fraction Expansion 1. Partial Fraction Expansion 2. Partial Fraction Expansion 3. Partial fraction expansion. Ex 1 Multi step equation. Solving rational equations 1. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Solving rational equations 2. Extraneous Solutions to Rational Equations. Extraneous solutions. Rational Inequalities. Rational Inequalities 2.

Introduction to Ratios (new HD version). Ratios as Fractions in Simplest Form. Simplifying Rates and Ratios. Expressing ratios as fractions. Describing ratios exercise. Describing ratios. Ratio word problem exercise example 1. Ratio word problem exercise example 2. Ratio word problems. Proportion validity example. Solving ratio problems with tables exercise. Solving ratio problems with tables exercise 2. Solving ratio problems with tables exercise 3. Solving ratio problems with tables. Usain Bolt's Average Speed. Finding Unit Rates. Finding Unit Prices. Rate problems 0.5. Multiple rates word problem. Rate problems 2. Converting pounds to ounces. Converting Gallons to quarts pints and cups. Converting Yards into Inches. Performing arithmetic calculations on units of volume. Application problems involving units of weight. Solving application problems involving units of volume. Gas cost for a roadtrip. Squirrel survival. Converting units of length. Unit Conversion Example: Drug Dosage. Unit Conversion with Fractions. Units. Speed translation. Unit conversion within the metric system. Converting within the metric system. Perimeter and Unit Conversion. Applying the Metric System. Conversion between metric units. U.S. Customary and Metric units. Converting Fahrenheit to Celsius. Comparing Celsius and Farenheit temperature scales. Introduction to Ratios (new HD version). Ratios as Fractions in Simplest Form. Simplifying Rates and Ratios. Expressing ratios as fractions. Describing ratios exercise. Describing ratios. Ratio word problem exercise example 1. Ratio word problem exercise example 2. Ratio word problems. Proportion validity example. Solving ratio problems with tables exercise. Solving ratio problems with tables exercise 2. Solving ratio problems with tables exercise 3. Solving ratio problems with tables. Usain Bolt's Average Speed. Finding Unit Rates. Finding Unit Prices. Rate problems 0.5. Multiple rates word problem. Rate problems 2. Converting pounds to ounces. Converting Gallons to quarts pints and cups. Converting Yards into Inches. Performing arithmetic calculations on units of volume. Application problems involving units of weight. Solving application problems involving units of volume. Gas cost for a roadtrip. Squirrel survival. Converting units of length. Unit Conversion Example: Drug Dosage. Unit Conversion with Fractions. Units. Speed translation. Unit conversion within the metric system. Converting within the metric system. Perimeter and Unit Conversion. Applying the Metric System. Conversion between metric units. U.S. Customary and Metric units. Converting Fahrenheit to Celsius. Comparing Celsius and Farenheit temperature scales.

chirality, stereoisomers, assigning absolute configuration using the R,S system, optical activity, diastereomers, meso compounds, fischer projections. Introduction to Chirality. Chiral Examples 1. Chiral Examples 2. Cahn-Ingold-Prelog System for Naming Enantiomers. R,S (Cahn-Ingold-Prelog) Naming System Example 2. chirality centers and stereoisomers. R,S system for determining absolute configuration. R,S system for cyclic compounds. optical activity I: theory. optical activity II: calculations. Stereoisomers, Enantiomers, Diastereomers, Constitutional Isomers and Meso Compounds. diastereomers. meso compounds. fischer projections. Introduction to Chirality. Chiral Examples 1. Chiral Examples 2. Cahn-Ingold-Prelog System for Naming Enantiomers. R,S (Cahn-Ingold-Prelog) Naming System Example 2. chirality centers and stereoisomers. R,S system for determining absolute configuration. R,S system for cyclic compounds. optical activity I: theory. optical activity II: calculations. Stereoisomers, Enantiomers, Diastereomers, Constitutional Isomers and Meso Compounds. diastereomers. meso compounds. fischer projections.

conjugation, conjugated dienes, addition reactions of conjugated dienes, diels-alder reaction, MO theory, color. addition reaction of conjugated dienes I: mechanism. addition reaction of conjugated dienes II: example. addition reaction of conjugated dienes III: control. diels-alder I: mechanism. diels-alder II: endo vs exo. diels-alder III: stereochemistry of dienophile. diels-alder IV: stereochemistry of diene. diels-alder V: regiochemistry. diels-alder VI: more regiochemistry. diels-alder VII: intramolecular. intro to molecular orbital (MO) theory. MO theory for butadiene. MO theory for Diels-Alder. intro to color theory. conjugation and color. color in organic molecules. addition reaction of conjugated dienes I: mechanism. addition reaction of conjugated dienes II: example. addition reaction of conjugated dienes III: control. diels-alder I: mechanism. diels-alder II: endo vs exo. diels-alder III: stereochemistry of dienophile. diels-alder IV: stereochemistry of diene. diels-alder V: regiochemistry. diels-alder VI: more regiochemistry. diels-alder VII: intramolecular. intro to molecular orbital (MO) theory. MO theory for butadiene. MO theory for Diels-Alder. intro to color theory. conjugation and color. color in organic molecules.

Demand Curve as Marginal Benefit Curve. Consumer Surplus Introduction. Total Consumer Surplus as Area. Producer Surplus. Rent Control and Deadweight Loss. Minimum Wage and Price Floors. Taxation and Dead Weight Loss. Percentage Tax on Hamburgers. Taxes and Perfectly Inelastic Demand. Taxes and Perfectly Elastic Demand. Negative Externalities. Taxes for Factoring in Negative Externalities. Positive Externalities. Tragedy of the Commons. Demand Curve as Marginal Benefit Curve. Consumer Surplus Introduction. Total Consumer Surplus as Area. Producer Surplus. Rent Control and Deadweight Loss. Minimum Wage and Price Floors. Taxation and Dead Weight Loss. Percentage Tax on Hamburgers. Taxes and Perfectly Inelastic Demand. Taxes and Perfectly Elastic Demand. Negative Externalities. Taxes for Factoring in Negative Externalities. Positive Externalities. Tragedy of the Commons.

Trigonometry Identity Review/Fun. Trigonometric Identities. Examples using Pythagorean identities to simplify trigonometric expressions. Pythagorean identities. Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b). Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b). Trig identities part 2 (part 4 if you watch the proofs). Trig identies part 3 (part 5 if you watch the proofs). Cosine addition identity example. Double angle formula for cosine example. Addition and subtraction trig identities. Navigation Word Problem. Fun Trig Problem. IIT JEE Trigonometry Problem 1. IIT JEE Trigonometric Maximum. IIT JEE Trigonometric Constraints. Trigonometric System Example. 2003 AIME II Problem 11. 2003 AIME II Problem 14. Trigonometry word problems (part 1). Trigonometry word problems (part 2). Ferris Wheel Trig Problem. Ferris Wheel Trig Problem (part 2). Law of cosines example. Proof of the law of cosines. Law of cosines. Proof: Law of Sines. Trigonometry Identity Review/Fun. Trigonometric Identities. Examples using Pythagorean identities to simplify trigonometric expressions. Pythagorean identities. Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b). Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b). Trig identities part 2 (part 4 if you watch the proofs). Trig identies part 3 (part 5 if you watch the proofs). Cosine addition identity example. Double angle formula for cosine example. Addition and subtraction trig identities. Navigation Word Problem. Fun Trig Problem. IIT JEE Trigonometry Problem 1. IIT JEE Trigonometric Maximum. IIT JEE Trigonometric Constraints. Trigonometric System Example. 2003 AIME II Problem 11. 2003 AIME II Problem 14. Trigonometry word problems (part 1). Trigonometry word problems (part 2). Ferris Wheel Trig Problem. Ferris Wheel Trig Problem (part 2). Law of cosines example. Proof of the law of cosines. Law of cosines. Proof: Law of Sines.

Permutations and combinations. Using combinatorics to solve questions in probability. Permutations. Combinations. Counting 2. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Permutations. Combinations. Permutations and combinations. Example: Probability through counting outcomes. Example: All the ways you can flip a coin. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Generalizing with Binomial Coefficients (bit advanced). Conditional Probability and Combinations. Conditional Probability (Bayes Theorem) Visualized. Birthday Probability Problem. Probability with permutations and combinations. Permutations. Combinations. Counting 2. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Permutations. Combinations. Permutations and combinations. Example: Probability through counting outcomes. Example: All the ways you can flip a coin. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Generalizing with Binomial Coefficients (bit advanced). Conditional Probability and Combinations. Conditional Probability (Bayes Theorem) Visualized. Birthday Probability Problem. Probability with permutations and combinations.

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation. Statistics intro: mean, median and mode. Example: Finding mean, median and mode. Mean median and mode. Exploring Mean and Median Module. Exploring mean and median. Average word problems. Sample mean versus population mean.. Reading Box-and-Whisker Plots. Constructing a box-and-whisker plot. Box-and-Whisker Plots. Creating box and whisker plots. Example: Range and mid-range. Range, Variance and Standard Deviation as Measures of Dispersion. Variance of a population. Sample variance. Review and intuition why we divide by n-1 for the unbiased sample variance. Simulation showing bias in sample variance. Unbiased Estimate of Population Variance. Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance. Simulation providing evidence that (n-1) gives us unbiased estimate. Will it converge towards -1?. Variance. Population standard deviation. Sample standard deviation and bias. Statistics: Standard Deviation. Exploring Standard Deviation 1 Module. Exploring standard deviation 1. Standard deviation. Statistics: Alternate Variance Formulas. Statistics: The Average. Statistics: Variance of a Population. Statistics: Sample Variance. Statistics intro: mean, median and mode. Example: Finding mean, median and mode. Mean median and mode. Exploring Mean and Median Module. Exploring mean and median. Average word problems. Sample mean versus population mean.. Reading Box-and-Whisker Plots. Constructing a box-and-whisker plot. Box-and-Whisker Plots. Creating box and whisker plots. Example: Range and mid-range. Range, Variance and Standard Deviation as Measures of Dispersion. Variance of a population. Sample variance. Review and intuition why we divide by n-1 for the unbiased sample variance. Simulation showing bias in sample variance. Unbiased Estimate of Population Variance. Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance. Simulation providing evidence that (n-1) gives us unbiased estimate. Will it converge towards -1?. Variance. Population standard deviation. Sample standard deviation and bias. Statistics: Standard Deviation. Exploring Standard Deviation 1 Module. Exploring standard deviation 1. Standard deviation. Statistics: Alternate Variance Formulas. Statistics: The Average. Statistics: Variance of a Population. Statistics: Sample Variance.

This tutorial is the meat of much of classical physics. We think about what a force is and how Newton changed the world's (and possibly your) view of how reality works. Newton's First Law of Motion. Newton's First Law of Motion Concepts. Newton's First Law of Motion. Newton's First Law. Newton's Second Law of Motion. Newton's Third Law of Motion. Newton's Third Law of Motion. All of Newton's Laws of Motion. Normal Force and Contact Force. Normal Force in an Elevator. Balanced and Unbalanced Forces. Unbalanced Forces and Motion. Slow Sock on Lubricon VI. Normal Forces on Lubricon VI. Inclined Plane Force Components. Ice Accelerating Down an Incline. Force of Friction Keeping the Block Stationary. Correction to Force of Friction Keeping the Block Stationary. Force of Friction Keeping Velocity Constant. Intuition on Static and Kinetic Friction Comparisons. Static and Kinetic Friction Example. Introduction to Tension. Introduction to Tension (Part 2). Tension in an accelerating system and pie in the face. Newton's First Law of Motion. Newton's First Law of Motion Concepts. Newton's First Law of Motion. Newton's First Law. Newton's Second Law of Motion. Newton's Third Law of Motion. Newton's Third Law of Motion. All of Newton's Laws of Motion. Normal Force and Contact Force. Normal Force in an Elevator. Balanced and Unbalanced Forces. Unbalanced Forces and Motion. Slow Sock on Lubricon VI. Normal Forces on Lubricon VI. Inclined Plane Force Components. Ice Accelerating Down an Incline. Force of Friction Keeping the Block Stationary. Correction to Force of Friction Keeping the Block Stationary. Force of Friction Keeping Velocity Constant. Intuition on Static and Kinetic Friction Comparisons. Static and Kinetic Friction Example. Introduction to Tension. Introduction to Tension (Part 2). Tension in an accelerating system and pie in the face.

Topics covered in a traditional college level introductory macroeconomics course. Introduction to Economics. Circular Flow of Income and Expenditures. Parsing Gross Domestic Product. More on Final and Intermediate GDP Contributions. Investment and Consumption. Income and Expenditure Views of GDP. Components of GDP. Examples of Accounting for GDP. Real GDP and Nominal GDP. GDP Deflator. Example Calculating Real GDP with a Deflator. Introduction to Inflation. Actual CPI-U Basket of Goods. Inflation Data. Moderate Inflation in a Good Economy. Stagflation. Real and Nominal Return. Calculating Real Return in Last Year Dollars. Relation Between Nominal and Real Returns and Inflation. Deflation. Velocity of Money Rather than Quantity Driving Prices. Deflation Despite Increases in Money Supply. Deflationary Spiral. Hyperinflation. Unemployment Rate Primer. Phillips Curve. Interest as Rent for Money. Money Supply and Demand Impacting Interest Rates. The Business Cycle. Aggregate Demand. Shifts in Aggregate Demand. Long-Run Aggregate Supply. Short Run Aggregate Supply. Demand-Pull Inflation under Johnson. Real GDP driving Price. Cost Push Inflation. Monetary and Fiscal Policy. Tax Lever of Fiscal Policy. Breakdown of Gas Prices. Short-Run Oil Prices. Keynesian Economics. Risks of Keynesian Thinking. Overview of Fractional Reserve Banking. Weaknesses of Fractional Reserve Lending. Full Reserve Banking. Money Supply- M0 M1 and M2. Simple Fractional Reserve Accounting part 1. Simple Fractional Reserve Accounting (part 2). MPC and Multiplier. Mathy Version of MPC and Multiplier (optional). Consumption Function Basics. Generalized Linear Consumption Function. Consumption Function with Income Dependent Taxes. Keynesian Cross. Details on Shifting Aggregate Planned Expenditures. Keynesian Cross and the Multiplier. Investment and Real Interest Rates. Connecting the Keynesian Cross to the IS-Curve. Loanable Funds Interpretation of IS Curve. LM part of the IS-LM model. Government Spending and the IS-LM model. Balance of Payments- Current Account. Balance of Payments- Capital Account. Why Current and Capital Accounts Net Out. Accumulating Foreign Currency Reserves. Using Reserves to Stabilize Currency. Speculative Attack on a Currency. Financial Crisis in Thailand Caused by Speculative Attack. Math Mechanics of Thai Banking Crisis.

American Call Options. Basic Shorting. American Put Options. Call Option as Leverage. Put vs. Short and Leverage. Call Payoff Diagram. Put Payoff Diagram. Put as Insurance. Put-Call Parity. Long Straddle. Put Writer Payoff Diagrams. Call Writer Payoff Diagram. Arbitrage Basics. Put-Call Parity Arbitrage I. Put-Call Parity Arbitrage II. Put-Call Parity Clarification. Actual Option Quotes. Option Expiration and Price. Forward Contract Introduction. Futures Introduction. Motivation for the Futures Exchange. Futures Margin Mechanics. Verifying Hedge with Futures Margin Mechanics. Futures and Forward Curves. Contango from Trader Perspective. Severe Contango Generally Bearish. Backwardation Bullish or Bearish. Futures Curves II. Contango. Backwardation. Contango and Backwardation Review. Upper Bound on Forward Settlement Price. Lower Bound on Forward Settlement Price. Arbitraging Futures Contract. Arbitraging Futures Contracts II. Futures Fair Value in the Pre-Market. Interpreting Futures Fair Value in the PreMarket. Mortgage Back Security Overview. Mortgage-Backed Securities I. Mortgage-backed securities II. Mortgage-backed securities III. Collateralized Debt Obligation Overview. Collateralized Debt Obligation (CDO). Credit Default Swaps (CDS) Intro. Credit Default Swaps. Credit Default Swaps 2. Use Cases for Credit Default Swaps. Financial Weapons of Mass Destruction. Interest Rate Swap 1. Interest Rate Swap 2. Introduction to the Black Scholes Formula. Implied volatility. American Call Options. Basic Shorting. American Put Options. Call Option as Leverage. Put vs. Short and Leverage. Call Payoff Diagram. Put Payoff Diagram. Put as Insurance. Put-Call Parity. Long Straddle. Put Writer Payoff Diagrams. Call Writer Payoff Diagram. Arbitrage Basics. Put-Call Parity Arbitrage I. Put-Call Parity Arbitrage II. Put-Call Parity Clarification. Actual Option Quotes. Option Expiration and Price. Forward Contract Introduction. Futures Introduction. Motivation for the Futures Exchange. Futures Margin Mechanics. Verifying Hedge with Futures Margin Mechanics. Futures and Forward Curves. Contango from Trader Perspective. Severe Contango Generally Bearish. Backwardation Bullish or Bearish. Futures Curves II. Contango. Backwardation. Contango and Backwardation Review. Upper Bound on Forward Settlement Price. Lower Bound on Forward Settlement Price. Arbitraging Futures Contract. Arbitraging Futures Contracts II. Futures Fair Value in the Pre-Market. Interpreting Futures Fair Value in the PreMarket. Mortgage Back Security Overview. Mortgage-Backed Securities I. Mortgage-backed securities II. Mortgage-backed securities III. Collateralized Debt Obligation Overview. Collateralized Debt Obligation (CDO). Credit Default Swaps (CDS) Intro. Credit Default Swaps. Credit Default Swaps 2. Use Cases for Credit Default Swaps. Financial Weapons of Mass Destruction. Interest Rate Swap 1. Interest Rate Swap 2. Introduction to the Black Scholes Formula. Implied volatility.

How do you decide what to produce or trade? How can you maximize happiness in a world of scarcity. What are you giving up when you choose something (i.e., opportunity cost)?. Production Possibilities Frontier. Opportunity Cost. Increasing Opportunity Cost. Allocative Efficiency and Marginal Benefit. Economic Growth through Investment. Comparative Advantage Specialization and Gains from Trade. Comparative Advantage and Absolute Advantage. Marginal Utility. Equalizing Marginal Utility per Dollar Spent. Deriving Demand Curve from Tweaking Marginal Utility per Dollar. Budget Line. Indifference Curves and Marginal Rate of Substitution. Optimal Point on Budget Line. Types of Indifference Curves. Production Possibilities Frontier. Opportunity Cost. Increasing Opportunity Cost. Allocative Efficiency and Marginal Benefit. Economic Growth through Investment. Comparative Advantage Specialization and Gains from Trade. Comparative Advantage and Absolute Advantage. Marginal Utility. Equalizing Marginal Utility per Dollar Spent. Deriving Demand Curve from Tweaking Marginal Utility per Dollar. Budget Line. Indifference Curves and Marginal Rate of Substitution. Optimal Point on Budget Line. Types of Indifference Curves.

nomenclature and reactions of amines. Amine Naming Introduction. Amine Naming 2. Amine as Nucleophile in Sn2 Reaction. Amine in Sn2 part 2. Sn1 Amine Reaction. Amine Naming Introduction. Amine Naming 2. Amine as Nucleophile in Sn2 Reaction. Amine in Sn2 part 2. Sn1 Amine Reaction.