Online courses directory (381)

We explore creating and moving between various coordinate systems. Orthogonal Complements. dim(V) + dim(orthogonal complement of V)=n. Representing vectors in Rn using subspace members. Orthogonal Complement of the Orthogonal Complement. Orthogonal Complement of the Nullspace. Unique rowspace solution to Ax=b. Rowspace Solution to Ax=b example. Projections onto Subspaces. Visualizing a projection onto a plane. A Projection onto a Subspace is a Linear Transforma. Subspace Projection Matrix Example. Another Example of a Projection Matrix. Projection is closest vector in subspace. Least Squares Approximation. Least Squares Examples. Another Least Squares Example. Coordinates with Respect to a Basis. Change of Basis Matrix. Invertible Change of Basis Matrix. Transformation Matrix with Respect to a Basis. Alternate Basis Transformation Matrix Example. Alternate Basis Transformation Matrix Example Part 2. Changing coordinate systems to help find a transformation matrix. Introduction to Orthonormal Bases. Coordinates with respect to orthonormal bases. Projections onto subspaces with orthonormal bases. Finding projection onto subspace with orthonormal basis example. Example using orthogonal change-of-basis matrix to find transformation matrix. Orthogonal matrices preserve angles and lengths. The Gram-Schmidt Process. Gram-Schmidt Process Example. Gram-Schmidt example with 3 basis vectors. Introduction to Eigenvalues and Eigenvectors. Proof of formula for determining Eigenvalues. Example solving for the eigenvalues of a 2x2 matrix. Finding Eigenvectors and Eigenspaces example. Eigenvalues of a 3x3 matrix. Eigenvectors and Eigenspaces for a 3x3 matrix. Showing that an eigenbasis makes for good coordinate systems. Orthogonal Complements. dim(V) + dim(orthogonal complement of V)=n. Representing vectors in Rn using subspace members. Orthogonal Complement of the Orthogonal Complement. Orthogonal Complement of the Nullspace. Unique rowspace solution to Ax=b. Rowspace Solution to Ax=b example. Projections onto Subspaces. Visualizing a projection onto a plane. A Projection onto a Subspace is a Linear Transforma. Subspace Projection Matrix Example. Another Example of a Projection Matrix. Projection is closest vector in subspace. Least Squares Approximation. Least Squares Examples. Another Least Squares Example. Coordinates with Respect to a Basis. Change of Basis Matrix. Invertible Change of Basis Matrix. Transformation Matrix with Respect to a Basis. Alternate Basis Transformation Matrix Example. Alternate Basis Transformation Matrix Example Part 2. Changing coordinate systems to help find a transformation matrix. Introduction to Orthonormal Bases. Coordinates with respect to orthonormal bases. Projections onto subspaces with orthonormal bases. Finding projection onto subspace with orthonormal basis example. Example using orthogonal change-of-basis matrix to find transformation matrix. Orthogonal matrices preserve angles and lengths. The Gram-Schmidt Process. Gram-Schmidt Process Example. Gram-Schmidt example with 3 basis vectors. Introduction to Eigenvalues and Eigenvectors. Proof of formula for determining Eigenvalues. Example solving for the eigenvalues of a 2x2 matrix. Finding Eigenvectors and Eigenspaces example. Eigenvalues of a 3x3 matrix. Eigenvectors and Eigenspaces for a 3x3 matrix. Showing that an eigenbasis makes for good coordinate systems.

The core ideas in microeconomics. Supply, demand and equilibrium. Introduction to Economics. Law of Demand. Change in Expected Future Prices and Demand. Price of Related Products and Demand. Changes in Income, Population, or Preferences. Normal and Inferior Goods. Inferior Goods Clarification. Law of Supply. Factors Affecting Supply. Long Term Supply Curve. Market Equilibrium. Changes in Market Equilibrium. Breakdown of Gas Prices. Short-Run Oil Prices. Introduction to Economics. Law of Demand. Change in Expected Future Prices and Demand. Price of Related Products and Demand. Changes in Income, Population, or Preferences. Normal and Inferior Goods. Inferior Goods Clarification. Law of Supply. Factors Affecting Supply. Long Term Supply Curve. Market Equilibrium. Changes in Market Equilibrium. Breakdown of Gas Prices. Short-Run Oil Prices.

Price elasticity of demand and supply. How sensitive are things to change in price. Price Elasticity of Demand. More on Elasticity of Demand. Perfect Inelasticity and Perfect Elasticity of Demand. Constant Unit Elasticity. Total Revenue and Elasticity. More on Total Revenue and Elasticity. Cross Elasticity of Demand. Elasticity of Supply. Elasticity and Strange Percent Changes. Price Elasticity of Demand. More on Elasticity of Demand. Perfect Inelasticity and Perfect Elasticity of Demand. Constant Unit Elasticity. Total Revenue and Elasticity. More on Total Revenue and Elasticity. Cross Elasticity of Demand. Elasticity of Supply. Elasticity and Strange Percent Changes.

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.

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.

Economic profit vs. accounting profit. Average total cost (ATC) and marginal cost (MC). Marginal product of labor (MPL). Price discrimination. Economic Profit vs Accounting Profit. Depreciation and Opportunity Cost of Capital. Marginal Cost and Average Total Cost. Marginal Revenue and Marginal Cost. Marginal Revenue Below Average Total Cost. Long Term Supply Curve and Economic Profit. Fixed, Variable, and Marginal Cost.. Visualizing Average Costs and Marginal Costs as Slope. A Firm's Marginal Product Revenue Curve. How Many People to Hire Given the MPR curve. Adding Demand Curves. First Degree Price Discrimination. Economic Profit vs Accounting Profit. Depreciation and Opportunity Cost of Capital. Marginal Cost and Average Total Cost. Marginal Revenue and Marginal Cost. Marginal Revenue Below Average Total Cost. Long Term Supply Curve and Economic Profit. Fixed, Variable, and Marginal Cost.. Visualizing Average Costs and Marginal Costs as Slope. A Firm's Marginal Product Revenue Curve. How Many People to Hire Given the MPR curve. Adding Demand Curves. First Degree Price Discrimination.

Perfect Competition. Monopoly Basics. Monopolist Optimizing Price (part 1)- Total Revenue.. Monopolist Optimizing Price (part 2)- Marginal Revenue. Monopolist Optimizing Price (part 3)- Dead Weight Loss.avi. Optional Calculus Proof to Show that MR has Twice Slope of Demand. Review of Revenue and Cost Graphs for a Monopoly. Oligopolies and Monopolistic Competition. Monopolistic Competition and Economic Profit. Oligopolies, Duopolies, Collusion, and Cartels. Perfect Competition. Monopoly Basics. Monopolist Optimizing Price (part 1)- Total Revenue.. Monopolist Optimizing Price (part 2)- Marginal Revenue. Monopolist Optimizing Price (part 3)- Dead Weight Loss.avi. Optional Calculus Proof to Show that MR has Twice Slope of Demand. Review of Revenue and Cost Graphs for a Monopoly. Oligopolies and Monopolistic Competition. Monopolistic Competition and Economic Profit. Oligopolies, Duopolies, Collusion, and Cartels.

Prisoners' Dilemma and Nash Equilibrium. More on Nash Equilibrium. Why Parties to Cartels Cheat. Game Theory of Cheating Firms. Prisoners' Dilemma and Nash Equilibrium. More on Nash Equilibrium. Why Parties to Cartels Cheat. Game Theory of Cheating Firms.

A review of hybrid orbitals, dot structures, electronegativity, and polarity. sp3 Hybridized Orbitals and Sigma Bonds. Pi bonds and sp2 Hybridized Orbitals. dot structures I: single bonds. dot structures II: multiple bonds. sp3 hybrid orbitals. tetrahedral bond angle proof. sp2 hybrid orbitals. sp hybrid orbitals. more hybridization. electronegativity. electronegativity and intermolecular forces. sp3 Hybridized Orbitals and Sigma Bonds. Pi bonds and sp2 Hybridized Orbitals. dot structures I: single bonds. dot structures II: multiple bonds. sp3 hybrid orbitals. tetrahedral bond angle proof. sp2 hybrid orbitals. sp hybrid orbitals. more hybridization. electronegativity. electronegativity and intermolecular forces.

bond-line structures, functional groups, formal charges, resonance structures, oxidation and reduction, acid/base chemistry. bond-line structures. 3-D bond-line structures. structural (constitutional) isomers. functional groups I. functional groups II. formal charge I. formal charge II. resonance structures I. resonance structures II. resonance structures III. oxidation states I. oxidation states II. Acid/Base Definitions. Ka and pKa Derivation. Stabilization of Conjugate Base I. Stabilization of Conjugate Base II. Stabilization of Conjugate Base III. Stabilization of Conjugate Base IV. bond-line structures. 3-D bond-line structures. structural (constitutional) isomers. functional groups I. functional groups II. formal charge I. formal charge II. resonance structures I. resonance structures II. resonance structures III. oxidation states I. oxidation states II. Acid/Base Definitions. Ka and pKa Derivation. Stabilization of Conjugate Base I. Stabilization of Conjugate Base II. Stabilization of Conjugate Base III. Stabilization of Conjugate Base IV.

naming alkanes and cycloalkanes, conformations of alkanes and cycloalkanes, and free radical reactions. Representing Structures of Organic Molecules. Naming Simple Alkanes. Naming Alkanes with Alkyl Groups. Correction - 2-Propylheptane should never be the name!. Common and Systematic Naming-Iso, Sec and Tert Prefixes. Organic Chemistry Naming Examples 1. Organic Chemistry Naming Examples 2. Organic Chemistry Naming Examples 3. Organic Chemistry Naming Examples 4. Organic Chemistry Naming Examples 5. Newman Projections. Newman Projections 2. Chair and Boat Shapes for Cyclohexane. Double Newman Diagram for Methcyclohexane. alkane and cycloalkane nomenclature I. alkane and cycloalkane nomenclature II. alkane and cycloalkane nomenclature III. bicyclic compounds. naming cubane. conformations of ethane and propane. conformations of butane. conformations of cyclohexane I: chair and boat. conformations of cyclohexane II: monosubstituted. conformations of cyclohexane III: disubstituted. conformations of cyclohexane IV: trisubstituted. Free Radical Reactions. Representing Structures of Organic Molecules. Naming Simple Alkanes. Naming Alkanes with Alkyl Groups. Correction - 2-Propylheptane should never be the name!. Common and Systematic Naming-Iso, Sec and Tert Prefixes. Organic Chemistry Naming Examples 1. Organic Chemistry Naming Examples 2. Organic Chemistry Naming Examples 3. Organic Chemistry Naming Examples 4. Organic Chemistry Naming Examples 5. Newman Projections. Newman Projections 2. Chair and Boat Shapes for Cyclohexane. Double Newman Diagram for Methcyclohexane. alkane and cycloalkane nomenclature I. alkane and cycloalkane nomenclature II. alkane and cycloalkane nomenclature III. bicyclic compounds. naming cubane. conformations of ethane and propane. conformations of butane. conformations of cyclohexane I: chair and boat. conformations of cyclohexane II: monosubstituted. conformations of cyclohexane III: disubstituted. conformations of cyclohexane IV: trisubstituted. Free Radical Reactions.

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.

SN1, SN2, E1, E2, nucleophiles, nucleophilicity, basicity. Naming Alkyl Halides. Sn2 Reactions. Sn1 Reactions. Steric hindrance. Sn2 Stereochemistry. Solvent Effects on Sn1 and Sn2 Reactions. Nucleophilicity (Nucleophile Strength). Nucleophilicity vs. Basicity. E2 Reactions. E1 Reactions. Zaitsev's Rule. Comparing E2 E1 Sn2 Sn1 Reactions. E2 E1 Sn2 Sn1 Reactions Example 2. E2 E1 Sn2 Sn1 Reactions Example 3. nucleophile/electrophile and The Schwartz Rules. alkyl halide nomenclature. SN1 reaction: mechanism. SN1 reaction: stereochemistry. SN2 mechanism and stereochemistry. SN1 vs SN2: solvent effects. SN1 vs SN2: summary. E1 Elimination: mechanism. E1 Elimination: regioselectivity and stereoselectivity. carbocations and rearrangements. E1 Elimination: carbocation rearrangements. E2 Elimination: mechanism. E2 Elimination: regioselectivity. E2 Elimination: stereoselectivity. E2 Elimination: stereospecificity. E2 Elimination: substituted cyclohexanes. nucleophilicity and basicity. SN1 SN2 E1 E2 reactions: primary and tertiary alkyl halides. SN1 SN2 E1 E2 reactions: secondary alkyl halides. Naming Alkyl Halides. Sn2 Reactions. Sn1 Reactions. Steric hindrance. Sn2 Stereochemistry. Solvent Effects on Sn1 and Sn2 Reactions. Nucleophilicity (Nucleophile Strength). Nucleophilicity vs. Basicity. E2 Reactions. E1 Reactions. Zaitsev's Rule. Comparing E2 E1 Sn2 Sn1 Reactions. E2 E1 Sn2 Sn1 Reactions Example 2. E2 E1 Sn2 Sn1 Reactions Example 3. nucleophile/electrophile and The Schwartz Rules. alkyl halide nomenclature. SN1 reaction: mechanism. SN1 reaction: stereochemistry. SN2 mechanism and stereochemistry. SN1 vs SN2: solvent effects. SN1 vs SN2: summary. E1 Elimination: mechanism. E1 Elimination: regioselectivity and stereoselectivity. carbocations and rearrangements. E1 Elimination: carbocation rearrangements. E2 Elimination: mechanism. E2 Elimination: regioselectivity. E2 Elimination: stereoselectivity. E2 Elimination: stereospecificity. E2 Elimination: substituted cyclohexanes. nucleophilicity and basicity. SN1 SN2 E1 E2 reactions: primary and tertiary alkyl halides. SN1 SN2 E1 E2 reactions: secondary alkyl halides.

naming alkenes and alkynes, reactions of alkenes and alkynes, synthesis. Naming Alkenes Examples. Cis-Trans and E-Z Naming Scheme for Alkenes. Entgegen-Zusammen Naming Scheme for Alkenes Examples. Introduction to Reaction Mechanisms. Markovnikov's Rule and Carbocations. Addition of Water (Acid-Catalyzed) Mechanism. Polymerization of Alkenes with Acid. Alkene intro and stability. Alkene nomenclature. cis/trans and the E/Z system. hydrogenation. hydrohalogenation. hydration. halogenation. halohydrin formation. hydroboration-oxidation. epoxide formation and anti dihydroxylation. syn dihydroxylation. Ozonolysis. alkyne nomenclature. alkyne acidity and alkylation. preparation of alkynes. reduction of alkynes. hydrohalogenation of alkynes. hydration of alkynes. hydroboration-oxidation of alkynes. halogenation and ozonolysis of alkynes. synthesis using alkynes. Naming Alkenes Examples. Cis-Trans and E-Z Naming Scheme for Alkenes. Entgegen-Zusammen Naming Scheme for Alkenes Examples. Introduction to Reaction Mechanisms. Markovnikov's Rule and Carbocations. Addition of Water (Acid-Catalyzed) Mechanism. Polymerization of Alkenes with Acid. Alkene intro and stability. Alkene nomenclature. cis/trans and the E/Z system. hydrogenation. hydrohalogenation. hydration. halogenation. halohydrin formation. hydroboration-oxidation. epoxide formation and anti dihydroxylation. syn dihydroxylation. Ozonolysis. alkyne nomenclature. alkyne acidity and alkylation. preparation of alkynes. reduction of alkynes. hydrohalogenation of alkynes. hydration of alkynes. hydroboration-oxidation of alkynes. halogenation and ozonolysis of alkynes. synthesis using alkynes.

alcohols, ethers, epoxides, thiols, sulfides. Alcohols. Alcohol Properties. alcohol nomenclature. physical properties of alcohols and preparation of alkoxides. preparation of alcohols using NaBH4. preparation of alcohols using LiAlH4. synthesis of alcohols using grignard reagents I. synthesis of alcohols using grignard reagents II. oxidation of alcohols I: mechanism and oxidation states. oxidation of alcohols II: examples. biological redox reactions. formation of nitrate esters. preparation of alkyl halides from alcohols. Ether Naming and Introduction. Ether nomenclature. Properties of ethers and crown ethers. williamson ether synthesis. acidic cleavage of ethers. Cyclic ethers and epoxide naming. nomenclature and preparation of epoxides. preparation of epoxides: stereochemistry. Ring-opening Sn2 reaction of expoxides. Sn1 and Sn2 epoxide opening discussion. ring-opening reactions of epoxides: strong nucleophiles. ring opening reactions of epoxides: acid-catalyzed. preparation of sulfides. Alcohols. Alcohol Properties. alcohol nomenclature. physical properties of alcohols and preparation of alkoxides. preparation of alcohols using NaBH4. preparation of alcohols using LiAlH4. synthesis of alcohols using grignard reagents I. synthesis of alcohols using grignard reagents II. oxidation of alcohols I: mechanism and oxidation states. oxidation of alcohols II: examples. biological redox reactions. formation of nitrate esters. preparation of alkyl halides from alcohols. Ether Naming and Introduction. Ether nomenclature. Properties of ethers and crown ethers. williamson ether synthesis. acidic cleavage of ethers. Cyclic ethers and epoxide naming. nomenclature and preparation of epoxides. preparation of epoxides: stereochemistry. Ring-opening Sn2 reaction of expoxides. Sn1 and Sn2 epoxide opening discussion. ring-opening reactions of epoxides: strong nucleophiles. ring opening reactions of epoxides: acid-catalyzed. preparation of sulfides.

Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions. Factoring quadratic expressions. Examples: Factoring simple quadratics. Factoring polynomials 1. Example 1: Solving a quadratic equation by factoring. Example 2: Solving a quadratic equation by factoring. Solving quadratics by factoring. Example 1: Factoring trinomials with a common factor. Factoring polynomials 2. Solving quadratics by factoring 2. Factoring Special Products. Example 1: Factoring difference of squares. Factoring difference of squares 1. Example 2: Factoring difference of squares. Factoring difference of squares 2. Factoring to produce difference of squares. Factoring difference of squares 3. Example 5: Factoring by grouping. Example 6: Factoring by grouping. Factoring polynomials by grouping. Solving Quadratic Equations by Square Roots. Solving quadratics by taking the square root. Solving Quadratic Equations by Completing the Square. Completing the square 1. Completing the square 2. How to use the Quadratic Formula. Proof of Quadratic Formula. Quadratic formula. Example: Complex roots for a quadratic. Discriminant of Quadratic Equations. Discriminant for Types of Solutions for a Quadratic. Solutions to quadratic equations. Quadratic Inequalities. Quadratic Inequalities (Visual Explanation). Terms coefficients and exponents in a polynomial. Addition and Subtraction of Polynomials. Adding and subtracting polynomials. Multiplying Polynomials. Multiplying Polynomials 3. Multiplying polynomials. Polynomial Division. Dividing polynomials 1. Dividing polynomials with remainders. Synthetic Division. Synthetic Division Example 2. Why Synthetic Division Works. Factoring Sum of Cubes. Difference of Cubes Factoring. Binomial Theorem (part 1). Binomial Theorem (part 2). Binomial Theorem (part 3). Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Simplifying Rational Expressions 2. Simplifying Rational Expressions 3. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Subtracting Rational Expressions. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Extraneous Solutions to Rational Equations. Rational Inequalities. Rational Inequalities 2. 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. Factoring quadratic expressions. Examples: Factoring simple quadratics. Factoring polynomials 1. Example 1: Solving a quadratic equation by factoring. Example 2: Solving a quadratic equation by factoring. Solving quadratics by factoring. Example 1: Factoring trinomials with a common factor. Factoring polynomials 2. Solving quadratics by factoring 2. Factoring Special Products. Example 1: Factoring difference of squares. Factoring difference of squares 1. Example 2: Factoring difference of squares. Factoring difference of squares 2. Factoring to produce difference of squares. Factoring difference of squares 3. Example 5: Factoring by grouping. Example 6: Factoring by grouping. Factoring polynomials by grouping. Solving Quadratic Equations by Square Roots. Solving quadratics by taking the square root. Solving Quadratic Equations by Completing the Square. Completing the square 1. Completing the square 2. How to use the Quadratic Formula. Proof of Quadratic Formula. Quadratic formula. Example: Complex roots for a quadratic. Discriminant of Quadratic Equations. Discriminant for Types of Solutions for a Quadratic. Solutions to quadratic equations. Quadratic Inequalities. Quadratic Inequalities (Visual Explanation). Terms coefficients and exponents in a polynomial. Addition and Subtraction of Polynomials. Adding and subtracting polynomials. Multiplying Polynomials. Multiplying Polynomials 3. Multiplying polynomials. Polynomial Division. Dividing polynomials 1. Dividing polynomials with remainders. Synthetic Division. Synthetic Division Example 2. Why Synthetic Division Works. Factoring Sum of Cubes. Difference of Cubes Factoring. Binomial Theorem (part 1). Binomial Theorem (part 2). Binomial Theorem (part 3). Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Simplifying Rational Expressions 2. Simplifying Rational Expressions 3. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Subtracting Rational Expressions. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Extraneous Solutions to Rational Equations. Rational Inequalities. Rational Inequalities 2. 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.

An look at exponential and logarithmic functions including many of their properties and graphs. Exponential Growth Functions. Ex: Graphing exponential functions. Subtracting Rational Expressions. Word Problem Solving- Exponential Growth and Decay. Exponential Growth. Graphing Logarithmic Functions. Logarithmic Scale. Vi and Sal Explore How We Think About Scale. Vi and Sal Talk About the Mysteries of Benford's Law. Benford's Law Explanation (Sequel to Mysteries of Benford's Law). Solving Logarithmic Equations. Solving Logarithmic Equations. Introduction to interest. Interest (part 2). Introduction to compound interest and e. Compound Interest and e (part 2). Compound Interest and e (part 3). Compound Interest and e (part 4). Exponential Growth Functions. Ex: Graphing exponential functions. Subtracting Rational Expressions. Word Problem Solving- Exponential Growth and Decay. Exponential Growth. Graphing Logarithmic Functions. Logarithmic Scale. Vi and Sal Explore How We Think About Scale. Vi and Sal Talk About the Mysteries of Benford's Law. Benford's Law Explanation (Sequel to Mysteries of Benford's Law). Solving Logarithmic Equations. Solving Logarithmic Equations. Introduction to interest. Interest (part 2). Introduction to compound interest and e. Compound Interest and e (part 2). Compound Interest and e (part 3). Compound Interest and e (part 4).

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.

What happens when we have many variables but also many constraints. Trolls, Tolls, and Systems of Equations. Solving the Troll Riddle Visually. Solving Systems Graphically. Graphing systems of equations. King's Cupcakes: Solving Systems by Elimination. Simple Elimination Practice. Systems of equations with simple elimination. How many bags of potato chips do people eat?. Systems with Elimination Practice. Systems of equations with elimination. Talking bird solves systems with substitution. Practice using substitution for systems. Systems of equations with substitution. Systems of equations. Systems of equations word problems. Inconsistent systems of equations. Infinite solutions to systems. Consistent and Inconsistent Systems. Independent and Dependent Systems. Practice thinking about number of solutions to systems. Solutions to systems of equations. Visualizing the solution set for a system of inequalities. Graphing systems of inequalities. Graphing systems of inequalities 2. Graphing systems of inequalities. Graphing and solving systems of inequalities. Systems of Three Variables. Systems of Three Variables 2. Solutions to Three Variable System. Solutions to Three Variable System 2. Three Equation Application Problem. Non-Linear Systems of Equations 1. Non-Linear Systems of Equations 2. Non-Linear Systems of Equations 3. Systems of nonlinear equations 1. Systems of nonlinear equations 2. Systems of nonlinear equations 3. Systems of nonlinear equations. Trolls, Tolls, and Systems of Equations. Solving the Troll Riddle Visually. Solving Systems Graphically. Graphing systems of equations. King's Cupcakes: Solving Systems by Elimination. Simple Elimination Practice. Systems of equations with simple elimination. How many bags of potato chips do people eat?. Systems with Elimination Practice. Systems of equations with elimination. Talking bird solves systems with substitution. Practice using substitution for systems. Systems of equations with substitution. Systems of equations. Systems of equations word problems. Inconsistent systems of equations. Infinite solutions to systems. Consistent and Inconsistent Systems. Independent and Dependent Systems. Practice thinking about number of solutions to systems. Solutions to systems of equations. Visualizing the solution set for a system of inequalities. Graphing systems of inequalities. Graphing systems of inequalities 2. Graphing systems of inequalities. Graphing and solving systems of inequalities. Systems of Three Variables. Systems of Three Variables 2. Solutions to Three Variable System. Solutions to Three Variable System 2. Three Equation Application Problem. Non-Linear Systems of Equations 1. Non-Linear Systems of Equations 2. Non-Linear Systems of Equations 3. Systems of nonlinear equations 1. Systems of nonlinear equations 2. Systems of nonlinear equations 3. Systems of nonlinear equations.

An assortment of concepts in math that help us deal with sequences and proofs. Proof by Induction. Alternate Proof to Induction for Integer Sum. Explicit and recursive definitions of sequences. Arithmetic sequences. Finding the 100th Term in a Sequence. Arithmetic sequences 1. Equations of Sequence Patterns. Arithmetic sequences 2. Geometric sequences introduction. Geometric sequences. Geometric sequences 1. Geometric sequences 2. Converting an explicit function to a recursive function. Recursive and explicit functions. Sum of arithmetic sequence (arithmetic series). Formula for arithmetic series. Arithmetic series. Difference between inductive and deductive reasoning. Deductive Reasoning 2. Deductive Reasoning 3. Inductive Reasoning 1. Inductive Reasoning 2. Inductive Reasoning 3. Inductive Patterns. Convergent and divergent sequences. Definition of limit of a sequence and sequence convergence. Proving a sequence converges. Series as sum of sequence. Formula for finite geometric series. 2003 AIME II Problem 8. Advanced: Geometric series sum to figure out mortgage payments. Series Sum Example. Proof by Induction. Alternate Proof to Induction for Integer Sum. Explicit and recursive definitions of sequences. Arithmetic sequences. Finding the 100th Term in a Sequence. Arithmetic sequences 1. Equations of Sequence Patterns. Arithmetic sequences 2. Geometric sequences introduction. Geometric sequences. Geometric sequences 1. Geometric sequences 2. Converting an explicit function to a recursive function. Recursive and explicit functions. Sum of arithmetic sequence (arithmetic series). Formula for arithmetic series. Arithmetic series. Difference between inductive and deductive reasoning. Deductive Reasoning 2. Deductive Reasoning 3. Inductive Reasoning 1. Inductive Reasoning 2. Inductive Reasoning 3. Inductive Patterns. Convergent and divergent sequences. Definition of limit of a sequence and sequence convergence. Proving a sequence converges. Series as sum of sequence. Formula for finite geometric series. 2003 AIME II Problem 8. Advanced: Geometric series sum to figure out mortgage payments. Series Sum Example.