Online courses directory (19947)

Introduction to programming and computer science. Introduction to Programs Data Types and Variables. Binary Numbers. Python Lists. For Loops in Python. While Loops in Python. Fun with Strings. Writing a Simple Factorial Program. (Python 2). Stepping Through the Factorial Program. Flowchart for the Factorial Program. Python 3 Not Backwards Compatible with Python 2. Defining a Factorial Function. Diagramming What Happens with a Function Call. Recursive Factorial Function. Comparing Iterative and Recursive Factorial Functions. Exercise - Write a Fibonacci Function. Iterative Fibonacci Function Example. Stepping Through Iterative Fibonacci Function. Recursive Fibonacci Example. Stepping Through Recursive Fibonacci Function. Exercise - Write a Sorting Function. Insertion Sort Algorithm. Insertion Sort in Python. Stepping Through Insertion Sort Function. Simpler Insertion Sort Function. Introduction to Programs Data Types and Variables. Binary Numbers. Python Lists. For Loops in Python. While Loops in Python. Fun with Strings. Writing a Simple Factorial Program. (Python 2). Stepping Through the Factorial Program. Flowchart for the Factorial Program. Python 3 Not Backwards Compatible with Python 2. Defining a Factorial Function. Diagramming What Happens with a Function Call. Recursive Factorial Function. Comparing Iterative and Recursive Factorial Functions. Exercise - Write a Fibonacci Function. Iterative Fibonacci Function Example. Stepping Through Iterative Fibonacci Function. Recursive Fibonacci Example. Stepping Through Recursive Fibonacci Function. Exercise - Write a Sorting Function. Insertion Sort Algorithm. Insertion Sort in Python. Stepping Through Insertion Sort Function. Simpler Insertion Sort Function.

Videos attempting to grasp a little bit about our Universe (many of the topics associated with "Big History"). Scale of Earth and Sun. Scale of Solar System. Scale of Distance to Closest Stars. Scale of the Galaxy. Intergalactic Scale. Hubble Image of Galaxies. Big Bang Introduction. Radius of Observable Universe. (Correction) Radius of Observable Universe. Red Shift. Cosmic Background Radiation. Cosmic Background Radiation 2. Cosmological Time Scale 1. Cosmological Time Scale 2. Four Fundamental Forces. Birth of Stars. Becoming a Red Giant. White and Black Dwarfs. A Universe Smaller than the Observable. Star Field and Nebula Images. Parallax in Observing Stars. Stellar Parallax. Stellar Distance Using Parallax. Stellar Parallax Clarification. Parsec Definition. Hubble's Law. Lifecycle of Massive Stars. Supernova (Supernovae). Supernova clarification. Black Holes. Cepheid Variables 1. Why Cepheids Pulsate. Why Gravity Gets So Strong Near Dense Objects. Supermassive Black Holes. Quasars. Quasar Correction. Galactic Collisions. Earth Formation. Beginnings of Life. Ozone Layer and Eukaryotes Show Up in the Proterozoic Eon. Biodiversity Flourishes in Phanerozoic Eon. First living things on land clarification. Plate Tectonics-- Difference between crust and lithosphere. Structure of the Earth. Plate Tectonics -- Evidence of plate movement. Plate Tectonics -- Geological Features of Divergent Plate Boundaries. Plate Tectonics-- Geological features of Convergent Plate Boundaries. Plates Moving Due to Convection in Mantle. Hawaiian Islands Formation. Compositional and Mechanical Layers of the Earth. Seismic Waves. Why S-Waves Only Travel in Solids. Refraction of Seismic Waves. The Mohorovicic Seismic Discontinuity. How we know about the Earth's core. Pangaea. Scale of the Large. Scale of the Small. Detectable Civilizations in our Galaxy 1. Detectable Civilizations in our Galaxy 2. Detectable Civilizations in our Galaxy 3. Detectable Civilizations in our Galaxy 4. Detectable Civilizations in our Galaxy 5. Human Evolution Overview. Understanding Calendar Notation. Correction Calendar Notation. Development of Agriculture and Writing. Introduction to Light. Seasons Aren't Dictated by Closeness to Sun. How Earth's Tilt Causes Seasons. Milankovitch Cycles Precession and Obliquity. Are Southern Hemisphere Seasons More Severe?. Precession Causing Perihelion to Happen Later. What Causes Precession and Other Orbital Changes. Apsidal Precession (Perihelion Precession) and Milankovitch Cycles. Firestick Farming. Carbon 14 Dating 1. Carbon 14 Dating 2. Potassium-Argon (K-Ar) Dating. K-Ar Dating Calculation. Chronometric Revolution. Collective Learning. Land Productivity Limiting Human Population. Energy Inputs for Tilling a Hectare of Land. Random Predictions for 2060.

Discussions of economic topics and how they relate to current events. Economics of a Cupcake Factory. Cupcake Economics 2. Cupcake Economics 3. Inflation, Deflation & Capacity Utilization. Inflation, Deflation & Capacity Utilization 2. Inflation & Deflation 3: Obama Stimulus Plan. Unemployment. CPI Index. Simple Analysis of Cost per Job Saved from Stimulus. Unemployment Rate Primer. Floating Exchange Resolving Trade Imbalance. China Pegs to Dollar to Keep Trade Imbalance. China buys US Bonds. Review of China US currency situation. Data on Chinese M1 Increase in 2010. Data on Chinese Foreign Assets Increase in 2010. Data on Chinese US Balance of Payments. Chinese inflation. Floating Exchange Effect on China. Floating Exchange Effect on US.

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus playlist before starting here. What is a differential equation. Separable Differential Equations. Separable differential equations 2. Exact Equations Intuition 1 (proofy). Exact Equations Intuition 2 (proofy). Exact Equations Example 1. Exact Equations Example 2. Exact Equations Example 3. Integrating factors 1. Integrating factors 2. First order homegenous equations. First order homogeneous equations 2. 2nd Order Linear Homogeneous Differential Equations 1. 2nd Order Linear Homogeneous Differential Equations 2. 2nd Order Linear Homogeneous Differential Equations 3. 2nd Order Linear Homogeneous Differential Equations 4. Complex roots of the characteristic equations 1. Complex roots of the characteristic equations 2. Complex roots of the characteristic equations 3. Repeated roots of the characteristic equation. Repeated roots of the characteristic equations part 2. Undetermined Coefficients 1. Undetermined Coefficients 2. Undetermined Coefficients 3. Undetermined Coefficients 4. Laplace Transform 1. Laplace Transform 2. Laplace Transform 3 (L{sin(at)}). Laplace Transform 4. Laplace Transform 5. Laplace Transform 6. Laplace Transform to solve an equation. Laplace Transform solves an equation 2. More Laplace Transform tools. Using the Laplace Transform to solve a nonhomogeneous eq. Laplace Transform of : L{t}. Laplace Transform of t^n: L{t^n}. Laplace Transform of the Unit Step Function. Inverse Laplace Examples. Laplace/Step Function Differential Equation. Dirac Delta Function. Laplace Transform of the Dirac Delta Function. Introduction to the Convolution. The Convolution and the Laplace Transform. Using the Convolution Theorem to Solve an Initial Value Prob.

LeBron James asks questions about math and science, and we answer!. LeBron Asks: What muscles do we use when shooting a basket?. LeBron Asks: How does shooting a basketball illustrate Newton's 3rd Law?. LeBron Asks: If Earth's history were a basketball game, when did humans appear?. LeBron Asks: Why does sweating cool you down?. LeBron Asks: Why does humidity make it feel hotter?. LeBron Asks: What are the chances of making 10 free throws in a row?. LeBron Asks: What are the chances of three free throws versus one three pointer?. Monte Carlo Simulation to Answer LeBron's Question. LeBron Asks: What muscles do we use when shooting a basket?. LeBron Asks: How does shooting a basketball illustrate Newton's 3rd Law?. LeBron Asks: If Earth's history were a basketball game, when did humans appear?. LeBron Asks: Why does sweating cool you down?. LeBron Asks: Why does humidity make it feel hotter?. LeBron Asks: What are the chances of making 10 free throws in a row?. LeBron Asks: What are the chances of three free throws versus one three pointer?. Monte Carlo Simulation to Answer LeBron's Question.

Khan Academy is collaborating with MIT to develop videos on science and engineering projects. Through the MIT+K12 initiative, MIT students have created videos on hands-on projects, simulations and historic experiments. Enjoy!. Bridge Design and Destruction! (part 1). 2D Equilibrium -- Balancing Games. Shifts in Equilibrium. The Marangoni Effect: How to make a soap propelled boat!. Earth's Tilt 1: The Reason for the Seasons. Earth's Tilt 2: Land of the Midnight Sun. Homeostasis. A Crash Course on Indoor Flying Robots. The Invention of the Battery. The Forces on an Airplane. Flocculation: Making Clean Water. A Voyage to Mars: Bone Loss in Space. Bouncing Droplets: Superhydrophobic and Superhydrophilic Surfaces. Bread Mold Kills Bacteria.

Videos on finance and macroeconomics. Introduction to interest. Interest (part 2). Introduction to Present Value. Present Value 2. Present Value 3. Present Value 4 (and discounted cash flow). Introduction to Balance Sheets. More on balance sheets and equity. Home equity loans. Renting vs. Buying a home. Renting vs. buying a home (part 2). Renting vs. Buying (detailed analysis). The housing price conundrum. Housing price conundrum (part 2). Housing Price Conundrum (part 3). Housing Conundrum (part 4). What it means to buy a company's stock. Bonds vs. Stocks. Shorting Stock. Shorting Stock 2. Is short selling bad?. Chapter 7:Bankruptcy Liquidation. Chapter 11: Bankruptcy Restructuring. Return on capital. Credit Default Swaps (CDS) Intro. Mortgage Back Security Overview. Collateralized Debt Obligation Overview. Mortgage-Backed Securities I. Mortgage-backed securities II. Mortgage-backed securities III. Collateralized Debt Obligation (CDO). Introduction to the yield curve. Introduction to compound interest and e. Compound Interest and e (part 2). Compound Interest and e (part 3). Compound Interest and e (part 4). Bailout 1: Liquidity vs. Solvency. Bailout 2: Book Value. Bailout 3: Book value vs. market value. Bailout 4: Mark-to-model vs. mark-to-market. Bailout 5: Paying off the debt. Bailout 6: Getting an equity infusion. Bailout 7: Bank goes into bankruptcy. Bailout 8: Systemic Risk. Bailout 9: Paulson's Plan. Bailout 10: Moral Hazard. Credit Default Swaps. Credit Default Swaps 2. Investment vs. Consumption 1. Investment vs. Consumption 2. Bailout 11: Why these CDOs could be worth nothing. Bailout 12: Lone Star Transaction. Bailout 13: Does the bailout have a chance of working?. Wealth Destruction 1. Wealth Destruction 2. Bailout 14: Possible Solution. Bailout 15: More on the solution. Banking 1. Banking 2: A bank's income statement. Banking 3: Fractional Reserve Banking. Banking 4: Multiplier effect and the money supply. Personal Bankruptcy: Chapters 7 and 13. Introduction to Compound Interest. The Rule of 72 for Compound Interest. Annual Percentage Rate (APR) and Effective APR. Introduction to Bonds. Relationship between bond prices and interest rates. Introduction to Mortgage Loans. Traditional IRAs. Roth IRAs. 401(k)s. Payday Loans. Institutional Roles in Issuing and Processing Credit Cards. Ponzi Schemes. Currency Exchange Introduction. Currency Effect on Trade. Currency Effect on Trade Review. Pegging the Yuan. Chinese Central Bank Buying Treasuries. American-Chinese Debt Loop. Debt Loops Rationale and Effects. American Call Options. Basic Shorting. American Put Options. Call Option as Leverage. Put vs. Short and Leverage. Call Payoff Diagram. Put Payoff Diagram. Long Straddle. Put as Insurance. Put-Call Parity. 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. Cash Accounting. Accrual Basis of Accounting. Comparing Accrual and Cash Accounting. Balance Sheet and Income Statement Relationship. Basic Cash Flow Statement. Doing the example with Accounts Payable growing. Expensing a Truck leads to inconsistent performance. Depreciating the truck. Depreciation in Cash Flow. Amortization and Depreciation. Basic Capital Structure Differences. Market Capitalization. Market Value of Assets. LIBOR. Fair Value Accounting. Tax Deductions Introduction. Alternative Minimum Tax. Term Life Insurance and Death Probability. Back of Envelope Office Space Conundrum. Corporations and Limited Liability. Is Limited Liability or Double Taxation Fair. Open-Ended Mutual Fund (Part 1). Open-End Mutual Fund Redemptions. Closed-End Mutual Funds. Exchange Traded Funds (ETFs). Hedge Funds Intro. Hedge Fund Structure and Fees. Are Hedge Funds Bad?. Hedge Funds, Venture Capital, and Private Equity. Treasury Bond Prices and Yields. Annual Interest Varying with Debt Maturity. The Yield Curve. Fed Open Market Operations. Quantitative Easing. More on Quantitative Easing (and Credit Easing). Hedge Fund Strategies - Long Short 1. Hedge Fund Strategies - Long Short 2. Hedge Fund Strategies - Merger Arbitrage 1. Stock Dilution. Acquisitions with Shares. Price Behavior After Announced Acquisition. Simple Merger Arb with Share Acquisition. Basic Leveraged Buyout (LBO). Corporate Debt versus Traditional Mortgages. AMT Overview. Open market operations and Quantitative Easing Overview. Another Quantitative Easing Video. US and Japanese Quantitative Easing. Term and Whole Life Insurance Policies 2. Term and Whole Life Insurance Policies. Estate Tax Introduction. Human Capital. Risk and Reward Introduction. Futures Fair Value in the Pre-Market. What is Inflation. 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. Use Cases for Credit Default Swaps. Financial Weapons of Mass Destruction. Deflation. Velocity of Money Rather than Quantity Driving Prices. Deflation Despite Increases in Money Supply. Deflationary Spiral. Hyperinflation. Estate Tax Basics. Term and Whole Life. Open-Ended Mutual Funds. Unemployment Rate Primer (v2). Time Value of Money. Mortgage Interest Rates. Inflation Overview. Basics of US Income Tax Rate Schedule. Carry Trade Basics. Interpreting Futures Fair Value in the PreMarket. Interest Rate Swap 1. Interest Rate Swap 2. Transfer Pricing and Tax Havens.

SugarCRM es una implementación de CRM, en este curso aprenderás a manejar lo básico. Gratis por tiempo limitado.

Questions from previous IIT JEEs. IIT JEE Trigonometry Problem 1. IIT JEE Perpendicular Planes (Part 1). IIT JEE Perpendicular Plane (part 2). IIT JEE Complex Root Probability (part 1). IIT JEE Complex Root Probability (part 2). IIT JEE Position Vectors. IIT JEE Integral Limit. IIT JEE Algebraic Manipulation. IIT JEE Function Maxima. IIT JEE Diameter Slope. IIT JEE Hairy Trig and Algebra (part 1). IIT JEE Hairy Trig and Algebra (Part 2). IIT JEE Hairy Trig and Algebra (Part 3). IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). IIT JEE Differentiability and Boundedness. IIT JEE Integral with Binomial Expansion. IIT JEE Symmetric and Skew-Symmetric Matrices. IIT JEE Trace and Determinant. IIT JEE Divisible Determinants. IIT JEE Circle Hyperbola Intersection. 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 Trigonometric Constraints. IIT JEE Trigonometric Maximum. Vector Triple Product Expansion (very optional). IIT JEE Lagrange's Formula. Tangent Line Hyperbola Relationship (very optional). 2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity. Normal vector from plane equation. Point distance to plane. Distance Between Planes. Complex Determinant Example. Series Sum Example. Trigonometric System Example. Simple Differential Equation Example. IIT JEE Trigonometry Problem 1. IIT JEE Perpendicular Planes (Part 1). IIT JEE Perpendicular Plane (part 2). IIT JEE Complex Root Probability (part 1). IIT JEE Complex Root Probability (part 2). IIT JEE Position Vectors. IIT JEE Integral Limit. IIT JEE Algebraic Manipulation. IIT JEE Function Maxima. IIT JEE Diameter Slope. IIT JEE Hairy Trig and Algebra (part 1). IIT JEE Hairy Trig and Algebra (Part 2). IIT JEE Hairy Trig and Algebra (Part 3). IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). IIT JEE Differentiability and Boundedness. IIT JEE Integral with Binomial Expansion. IIT JEE Symmetric and Skew-Symmetric Matrices. IIT JEE Trace and Determinant. IIT JEE Divisible Determinants. IIT JEE Circle Hyperbola Intersection. 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 Trigonometric Constraints. IIT JEE Trigonometric Maximum. Vector Triple Product Expansion (very optional). IIT JEE Lagrange's Formula. Tangent Line Hyperbola Relationship (very optional). 2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity. Normal vector from plane equation. Point distance to plane. Distance Between Planes. Complex Determinant Example. Series Sum Example. Trigonometric System Example. Simple Differential Equation Example.

Topics covered in a traditional college level introductory macroeconomics course. 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.

Build professional quality online courses with ease.

Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra. Introduction to matrices. Matrix multiplication (part 1). Matrix multiplication (part 2). Idea Behind Inverting a 2x2 Matrix. Inverting matrices (part 2). Inverting Matrices (part 3). Matrices to solve a system of equations. Matrices to solve a vector combination problem. Singular Matrices. 3-variable linear equations (part 1). Solving 3 Equations with 3 Unknowns. Introduction to Vectors. Vector Examples. Parametric Representations of Lines. Linear Combinations and Span. Introduction to Linear Independence. More on linear independence. Span and Linear Independence Example. Linear Subspaces. Basis of a Subspace. Vector Dot Product and Vector Length. Proving Vector Dot Product Properties. Proof of the Cauchy-Schwarz Inequality. Vector Triangle Inequality. Defining the angle between vectors. Defining a plane in R3 with a point and normal vector. Cross Product Introduction. Proof: Relationship between cross product and sin of angle. Dot and Cross Product Comparison/Intuition. Matrices: Reduced Row Echelon Form 1. Matrices: Reduced Row Echelon Form 2. Matrices: Reduced Row Echelon Form 3. Matrix Vector Products. Introduction to the Null Space of a Matrix. Null Space 2: Calculating the null space of a matrix. Null Space 3: Relation to Linear Independence. Column Space of a Matrix. Null Space and Column Space Basis. Visualizing a Column Space as a Plane in R3. Proof: Any subspace basis has same number of elements. Dimension of the Null Space or Nullity. Dimension of the Column Space or Rank. Showing relation between basis cols and pivot cols. Showing that the candidate basis does span C(A). A more formal understanding of functions. Vector Transformations. Linear Transformations. Matrix Vector Products as Linear Transformations. Linear Transformations as Matrix Vector Products. Image of a subset under a transformation. im(T): Image of a Transformation. Preimage of a set. Preimage and Kernel Example. Sums and Scalar Multiples of Linear Transformations. More on Matrix Addition and Scalar Multiplication. Linear Transformation Examples: Scaling and Reflections. Linear Transformation Examples: Rotations in R2. Rotation in R3 around the X-axis. Unit Vectors. Introduction to Projections. Expressing a Projection on to a line as a Matrix Vector prod. Compositions of Linear Transformations 1. Compositions of Linear Transformations 2. Matrix Product Examples. Matrix Product Associativity. Distributive Property of Matrix Products. Introduction to the inverse of a function. Proof: Invertibility implies a unique solution to f(x)=y. Surjective (onto) and Injective (one-to-one) functions. Relating invertibility to being onto and one-to-one. Determining whether a transformation is onto. Exploring the solution set of Ax=b. Matrix condition for one-to-one trans. Simplifying conditions for invertibility. Showing that Inverses are Linear. Deriving a method for determining inverses. Example of Finding Matrix Inverse. Formula for 2x2 inverse. 3x3 Determinant. nxn Determinant. Determinants along other rows/cols. Rule of Sarrus of Determinants. Determinant when row multiplied by scalar. (correction) scalar multiplication of row. Determinant when row is added. Duplicate Row Determinant. Determinant after row operations. Upper Triangular Determinant. Simpler 4x4 determinant. Determinant and area of a parallelogram. Determinant as Scaling Factor. Transpose of a Matrix. Determinant of Transpose. Transpose of a Matrix Product. Transposes of sums and inverses. Transpose of a Vector. Rowspace and Left Nullspace. Visualizations of Left Nullspace and Rowspace. Orthogonal Complements. Rank(A) = Rank(transpose of A). 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. Showing that A-transpose x A is invertible. 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. Vector Triple Product Expansion (very optional). Normal vector from plane equation. Point distance to plane. Distance Between Planes.

Topics covered in a traditional college level introductory microeconomics course. 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. Law of 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. Market Equilibrium. Changes in Market Equilibrium. 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. Marginal Utility. Equalizing Marginal Utility per Dollar Spent. Deriving Demand Curve from Tweaking Marginal Utility per Dollar. Budget Line. Optimal Point on Budget Line. Types of Indifference Curves. Economic Profit vs Accounting Profit. Depreciation and Opportunity Cost of Capital. Fixed, Variable, and Marginal Cost.. Visualizing Average Costs and Marginal Costs as Slope. Marginal Cost and Average Total Cost. Marginal Revenue and Marginal Cost. Marginal Revenue Below Average Total Cost. Long Term Supply Curve and Economic Profit. Perfect Competition. Monopoly Basics. Review of Revenue and Cost Graphs for a Monopoly. 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. 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. Negative Externalities. Taxes for Factoring in Negative Externalities. Positive Externalities. Tragedy of the Commons. First Degree Price Discrimination. A Firm's Marginal Product Revenue Curve. How Many People to Hire Given the MPR curve. Adding Demand Curves.

Topics covered in college organic chemistry course. Basic understanding of basic high school or college chemistry assumed. 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. Naming Alkenes Examples. Naming Alkyl Halides. sp3 Hybridized Orbitals and Sigma Bonds. Pi bonds and sp2 Hybridized Orbitals. Newman Projections. Newman Projections 2. Chair and Boat Shapes for Cyclohexane. Double Newman Diagram for Methcyclohexane. 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. Stereoisomers, Enantiomers, Diastereomers, Constitutional Isomers and Meso Compounds. 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. 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. Free Radical Reactions. Alcohols. Alcohol Properties. Resonance. Ether Naming and Introduction. Cyclic ethers and epoxide naming. Ring-opening Sn2 reaction of expoxides. Sn1 and Sn2 epoxide opening discussion. Aromatic Compounds and Huckel's Rule. Naming Benzene Derivatives Introduction. Electrophilic Aromatic Substitution. Bromination of Benzene. Amine Naming Introduction. Amine Naming 2. Amine as Nucleophile in Sn2 Reaction. Amine in Sn2 part 2. Sn1 Amine Reaction. Aldehyde Introduction. Ketone Naming. Friedel Crafts Acylation. Friedel Crafts Acylation Addendum. Keto Enol Tautomerization. Carboxlic Acid Introduction. Carboxylic Acid Naming. Fisher Esterification. Acid Chloride Formation. Amides, Anhydrides, Esters and Acyl Chlorides. Relative Stability of Amides Esters Anhydrides and Acyl Chlorides. Amide Formation from Acyl Chloride. Aldol Reaction.

Videos to help understand the bailout. Bailout 1: Liquidity vs. Solvency. Bailout 2: Book Value. Bailout 3: Book value vs. market value. Bailout 4: Mark-to-model vs. mark-to-market. Bailout 5: Paying off the debt. Bailout 6: Getting an equity infusion. Bailout 7: Bank goes into bankruptcy. Bailout 8: Systemic Risk. Bailout 9: Paulson's Plan. Bailout 10: Moral Hazard. Bailout 11: Why these CDOs could be worth nothing. Bailout 12: Lone Star Transaction. Bailout 13: Does the bailout have a chance of working?. Bailout 14: Possible Solution. Bailout 15: More on the solution.

Non-trigonometry pre-calculus topics. Solid understanding of all of the topics in the "Algebra" playlist should make this playlist pretty digestible. Introduction to Limits (HD). Introduction to Limits. Limit Examples (part 1). Limit Examples (part 2). Limit Examples (part3). Limit Examples w/ brain malfunction on first prob (part 4). Squeeze Theorem. Proof: lim (sin x)/x. More Limits. Sequences and Series (part 1). Sequences and series (part 2). Permutations. Combinations. Binomial Theorem (part 1). Binomial Theorem (part 2). Binomial Theorem (part 3). 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. Polar Coordinates 1. Polar Coordinates 2. Polar Coordinates 3. Parametric Equations 1. Parametric Equations 2. Parametric Equations 3. Parametric Equations 4. Introduction to Function Inverses. Function Inverse Example 1. Function Inverses Example 2. Function Inverses Example 3. Basic Complex Analysis. Exponential form to find complex roots. Complex Conjugates. Series Sum Example. Complex Determinant Example. 2003 AIME II Problem 8. 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).

Basic probability. Should have a reasonable grounding in basic algebra before watching. Basic Probability. Example: Marbles from a bag. Example: Picking a non-blue marble. Example: Picking a yellow marble. Term Life Insurance and Death Probability. Probability with Playing Cards and Venn Diagrams. Addition Rule for Probability. Compound Probability of Independent Events. Getting At Least One Heads. Example: Probability of rolling doubles. LeBron Asks: What are the chances of making 10 free throws in a row?. LeBron Asks: What are the chances of three free throws versus one three pointer?. Frequency Probability and Unfair Coins. Example: Getting two questions right on an exam. Example: Rolling even three times. Introduction to dependent probability. Example: Dependent probability. Example: Is an event independent or dependent?. Example: Bag of unfair coins. Monty Hall Problem. Example: All the ways you can flip a coin. Example: Probability through counting outcomes. Permutations. Combinations. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Generalizing with Binomial Coefficients (bit advanced). Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Conditional Probability and Combinations. Birthday Probability Problem. Random Variables. Discrete and continuous random variables. Probability Density Functions. Expected Value: E(X). Binomial Distribution 1. Binomial Distribution 2. Binomial Distribution 3. Binomial Distribution 4. Expected Value of Binomial Distribution. Poisson Process 1. Poisson Process 2. Law of Large Numbers. Introduction to Random Variables. Probability (part 1). Probability (part 2). Probability (part 3). Probability (part 4). Probability (part 5). Probability (part 6). Probability (part 7). Probability (part 8).

Lectures based on the Singapore Math curriculum. You can follow along through the workbooks available at singaporemath.com. Singapore Math: Grade 3a, Unit 1 (part 1). Singapore Math: Grade 3a Unit 1 (part 2). Singapore Math: Grade 3a, Unit 1 (part 3). Singapore Math: Grade 3a, Unit 1 (part 4). Singapore Math: Grade 3a, Unit 1 (part 5). Singapore Math: Grade 3a, Unit 1 (part 6). Singapore Math: Grade 3a, Unit 1 (part 7). Singapore Math: Grade 3a, Unit 1 (part 8). Singapore Math: Grade 3a, Unit 1 (part 9). Singapore Math: Grade 3a Unit 2 (part 1). Singapore Math: Grade 3a Unit 2 (part 2). Singapore Math: Grade 3a Unit 2 (part 3). Singapore Math: Grade 3a Unit 2 (part 4). Singapore Math: Grade 3a Unit 2 (part 5). Singapore Math: Grade 3a Unit 2 (part 6). Singapore Math: Grade 3a Unit 2 (part 7). Singapore Math: Grade 3a Unit 2 (part 8). Singapore Math: Grade 3a Unit 2 (part 9). Singapore Math: Grade 3a Unit 2 (part 10). Singapore Math: Grade 3a Unit 2 (part 11). Singapore Math: Grade 3a, Unit 1 (part 1). Singapore Math: Grade 3a Unit 1 (part 2). Singapore Math: Grade 3a, Unit 1 (part 3). Singapore Math: Grade 3a, Unit 1 (part 4). Singapore Math: Grade 3a, Unit 1 (part 5). Singapore Math: Grade 3a, Unit 1 (part 6). Singapore Math: Grade 3a, Unit 1 (part 7). Singapore Math: Grade 3a, Unit 1 (part 8). Singapore Math: Grade 3a, Unit 1 (part 9). Singapore Math: Grade 3a Unit 2 (part 1). Singapore Math: Grade 3a Unit 2 (part 2). Singapore Math: Grade 3a Unit 2 (part 3). Singapore Math: Grade 3a Unit 2 (part 4). Singapore Math: Grade 3a Unit 2 (part 5). Singapore Math: Grade 3a Unit 2 (part 6). Singapore Math: Grade 3a Unit 2 (part 7). Singapore Math: Grade 3a Unit 2 (part 8). Singapore Math: Grade 3a Unit 2 (part 9). Singapore Math: Grade 3a Unit 2 (part 10). Singapore Math: Grade 3a Unit 2 (part 11).

Introduction to statistics. We start with the basics of reading and interpretting data and then build into descriptive and inferential statistics that are typically covered in an introductory course on the subject. Overview of Khan Academy statistics. Statistics intro: mean, median and mode. Constructing a box-and-whisker plot. Sample mean versus population mean.. 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. Simulation providing evidence that (n-1) gives us unbiased estimate. Statistics: Standard Deviation. Statistics: Alternate Variance Formulas. Introduction to Random Variables. Probability Density Functions. Binomial Distribution 1. Binomial Distribution 2. Binomial Distribution 3. Binomial Distribution 4. Expected Value: E(X). Expected Value of Binomial Distribution. Poisson Process 1. Poisson Process 2. Introduction to the Normal Distribution. Normal Distribution Excel Exercise. Law of Large Numbers. ck12.org Normal Distribution Problems: Qualitative sense of normal distributions. ck12.org Normal Distribution Problems: Empirical Rule. ck12.org Normal Distribution Problems: z-score. ck12.org Exercise: Standard Normal Distribution and the Empirical Rule. ck12.org: More Empirical Rule and Z-score practice. Central Limit Theorem. Sampling Distribution of the Sample Mean. Sampling Distribution of the Sample Mean 2. Standard Error of the Mean. Sampling Distribution Example Problem. Confidence Interval 1. Confidence Interval Example. Mean and Variance of Bernoulli Distribution Example. Bernoulli Distribution Mean and Variance Formulas. Margin of Error 1. Margin of Error 2. Small Sample Size Confidence Intervals. Hypothesis Testing and P-values. One-Tailed and Two-Tailed Tests. Z-statistics vs. T-statistics. Type 1 Errors. Small Sample Hypothesis Test. T-Statistic Confidence Interval. Large Sample Proportion Hypothesis Testing. Variance of Differences of Random Variables. Difference of Sample Means Distribution. Confidence Interval of Difference of Means. Clarification of Confidence Interval of Difference of Means. Hypothesis Test for Difference of Means. Comparing Population Proportions 1. Comparing Population Proportions 2. Hypothesis Test Comparing Population Proportions. Squared Error of Regression Line. Proof (Part 1) Minimizing Squared Error to Regression Line. Proof Part 2 Minimizing Squared Error to Line. Proof (Part 3) Minimizing Squared Error to Regression Line. Proof (Part 4) Minimizing Squared Error to Regression Line. Regression Line Example. Second Regression Example. R-Squared or Coefficient of Determination. Calculating R-Squared. Covariance and the Regression Line. Correlation and Causality. Chi-Square Distribution Introduction. Pearson's Chi Square Test (Goodness of Fit). Contingency Table Chi-Square Test. ANOVA 1 - Calculating SST (Total Sum of Squares). ANOVA 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).avi. ANOVA 3 -Hypothesis Test with F-Statistic. Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance. Mean Median and Mode. Range and Mid-range. Reading Pictographs. Reading Bar Graphs. Reading Line Graphs. Reading Pie Graphs (Circle Graphs). Misleading Line Graphs. Stem-and-leaf Plots. Box-and-Whisker Plots. Reading Box-and-Whisker Plots. Statistics: The Average. Statistics: Variance of a Population. Statistics: Sample Variance. Deductive Reasoning 1. Deductive Reasoning 2. Deductive Reasoning 3. Inductive Reasoning 1. Inductive Reasoning 2. Inductive Reasoning 3. Inductive Patterns.

Videos on trigonometry. Watch the "Geometry" playlist first if you have trouble understanding the topics covered here. Basic Trigonometry. Basic Trigonometry II. Radians and degrees. Using Trig Functions. Using Trig Functions Part II. The unit circle definition of trigonometric function. Unit Circle Definition of Trig Functions. Graph of the sine function. Graphs of trig functions. Graphing trig functions. More trig graphs. Determining the equation of a trigonometric function. Trigonometric 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 (parr 4 if you watch the proofs). Trig identies part 3 (part 5 if you watch the proofs). Trigonometry word problems (part 1). Trigonometry word problems (part 2). Law of cosines. Navigation Word Problem. Proof: Law of Sines. Ferris Wheel Trig Problem. Ferris Wheel Trig Problem (part 2). Fun Trig Problem. Polar Coordinates 1. Polar Coordinates 2. Polar Coordinates 3. Inverse Trig Functions: Arcsin. Inverse Trig Functions: Arctan. Inverse Trig Functions: Arccos. Trigonometry Identity Review/Fun. Tau versus Pi. IIT JEE Trigonometry Problem 1. IIT JEE Trigonometric Maximum. IIT JEE Trigonometric Constraints. Trigonometric System Example. 2003 AIME II Problem 11.avi. 2003 AIME II Problem 14.