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SAT Preparation We have taken all 8 math practice tests (432 problems) in "The Offical SAT Study Guide" by the College Board in 100+ videos ... [More] GMAT Preparation We have taken all 400+ data sufficiency and math problems in "The Official Guide for GMAT Review" by the GMAC in 100+ videos below. ... [More] Algebra 1 Variable Expressions Order of Operations Patterns and Equations Equations and Inequalities Domain and Range of a Function Functions as Graphs Word Problem Solving Plan 1 Word Problem Solving Strategies Integers and Rational Numbers Addition of Rational Numbers Subraction of Rational Numbers Multiplication of Rational Numbers Distributive Property Division of Rational Numbers Square Roots and Real Numbers Problem Solving Word Problems 2 One Step Equations Two-Step Equations Multi-Step Equations Equations with Variables on Both Sides Ratio and Proportion Scale and Indirect Measurement Percent Problems Word Problem Solving 3 The Coordinate Plane Graphing Using Intercepts Graphs of Linear Equations Slope and Rate of Change Graphs Using Slope-Intercept Form Direct Variation Models Linear Function Graphs Word Problem Solving 4 Linear Equations in Slope Intercept Form Linear Equations in Point Slope Form Linear Equations in Standard Form Equations of Parallel and Perpendicular Lines Fitting a Line to Data Predicting with Linear Models Using a Linear Model Inequalities Using Addition and Subtraction Inequalities Using Multiplication and Division Multi-Step Inequalities Compound Inequalities Absolute Value Equations Absolute Value Inequalities Graphing Inequalities Solving Linear Systems by Graphing Solving Linear Systems by Substitution Solving Systems of Equations by Elimination Solving Systems of Equations by Multiplication Special Types of Linear Systems Systems of Linear Inequalities Exponent Properties Involving Products Exponent Properties Involving Quotients Zero, Negative, and Fractional Exponents Scientific Notation Exponential Growth Functions Exponential Decay Functions Geometric Sequences (Introduction) Word Problem Solving- Exponential Growth and Decay Addition and Subtraction of Polynomials Multiplication of Polynomials Special Products of Binomials Polynomial Equations in Factored Form Factoring Quadratic Expressions Factoring Special Products Factor by Grouping and Factoring Completely Graphs of Quadratic Functions Solving Quadratic Equations by Graphing Solving Quadratic Equations by Square Roots Solving Quadratic Equations by Completing the Square Using the Quadratic Formula Proof of Quadratic Formula Discriminant of Quadratic Equations Khan Academy Vision and Social Return Linear, Quadratic, and Exponential Models Identifying Quadratic Models Identifying Exponential Models Quadratic Regression Graphs of Square Root Functions Radical Expressions with Higher Roots More Simplifying Radical Expressions How to Rationalize a Denominator Extraneous Solutions to Radical Equations Radical Equation Examples More Involved Radical Equation Example Pythagorean Theorem Distance Formula Midpoint Formula Visual Pythagorean Theorem Proof Average or Central Tendency: Arithmetic Mean, Median, and Mode Range, Variance and Standard Deviation as Measures of Dispersion Stem and Leaf Plots Histograms Box-and-whisker Plot Proportionality Asymptotes of Rational Functions Another Rational Function Graph Example A Third Example of Graphing a Rational Function Polynomial Division Simplifying Rational Expressions Multiplying and Dividing Rational Expressions Adding Rational Expressions Example 1 Adding Rational Expressions Example 2 Adding Rational Expressions Example 3 Solving Rational Equations Two more examples of solving rational equations Surveys and Samples Algebra Algebra: Linear Equations 1 Algebra: Linear Equations 2 Algebra: Linear Equations 3 Algebra: Linear Equations 4 Algebra: Solving Inequalities Algebra: graphing lines 1 Algebra: Slope and Y-intercept intuition Algebra: Slope Algebra: Slope 2 Algebra: Slope 3 Algebra: Equation of a line Slope and Y-intercept Intuition Averages Integer sums Taking percentages Growing by a percentage Another Percent Word Problem More percent problems systems of equations Introduction to Ratios (new HD version) Ratio problem with basic algebra (new HD) More advanced ratio problem--with Algebra (HD version) Alternate Solution to Ratio Problem (HD Version) Introduction to Ratios Advanced ratio problems Age word problems 1 Age word problems 2 Age word problems 3 Level 1 multiplying expressions Solving a quadratic by factoring i and Imaginary numbers Complex Numbers (part 1) Complex Numbers (part 2) Introduction to the quadratic equation Quadratic Equation part 2 Completing the square Quadratic Formula (proof) Quadratic Inequalities Quadratic Inequalities (Visual Explanation) Introduction to functions Functions Part 2 Functions (Part III) Functions (part 4) Domain of a function Proof: log a + log b = log ab Proof: A(log B) = log (B^A), log A - log B = log (A/B) Proof: log_a (B) = (log_x (B))/(log_x (A)) Algebraic Long Division Introduction to Conic Sections Conic Sections: Intro to Circles Conic Sections: Intro to Ellipses Conic Sections: Intro to Hyperbolas Conic Sections: Hyperbolas 2 Conic Sections: Hyperbolas 3 Identifying Conics 1 Identifying Conics 2 Conic Identification 3 Foci of an Ellipse Foci of a Hyperbola Proof: Hyperbola Foci Partial Fraction Expansion 1 Partial Fraction Expansion 2 Partial Fraction Expansion 3 Parabola Focus and Directrix 1 Focus and Directrix of a Parabola 2 Two Passing Bicycles Word Problem Passed Bike Word Problem Passing Trains Overtaking Word Problem Early Train Word Problem Officer on Horseback Rational Inequalities Rational Inequalities 2 Interesting Polynomial Coefficient Problem Geometric series sum to figure out mortgage payments Example of Solving for a Variable Absolute Value and Number Lines Absolute Value Equation Example California Standards Test: Algebra I CA Algebra I: Number Properties and Absolute Value CA Algebra I: Simplifying Expressions CA Algebra I: Simple Logical Arguments CA Algebra I: Graphing Inequalities CA Algebra I: Slope and Y-intercept CA Algebra I: Systems of Inequalities CA Algebra I: Simplying Expressions CA Algebra I: Factoring Quadratics CA Algebra I: Completing the Square CA Algebra I: Quadratic Equation CA Algebra I: Quadratic Roots CA Algebra I: Rational Expressions CA Algebra I: Rational Expressions CA Algebra I: Word Problems CA Algebra I: More Word Problems CA Algebra I: Functions California Standards Test: Algebra II California Standards Test: Algebra II California Standards Test: Algebra II (Graphing Inequalities CA Standards: Algebra II (Algebraic Division/Multiplication) CA Standards: Algebra II Algebra II: Simplifying Polynomials Algebra II: Imaginary and Complex Numbers Algebra II: Complex numbers and conjugates Algebra II: Quadratics and Shifts Algebra II: Shifting Quadratic Graphs Algebra ||: Conic Sections Algebra II: Circles and Logarithms Algebra II: Logarithms Exponential Growth Algebra II: Logarithms and more Algebra II: Functions, Combinatorics Algebra II: binomial Expansion and Combinatorics Algebra II: Binomial Expansions, Geometric Series Sum Algebra II: Functions and Probability Algebra II: Probability and Statistics Algebra II: Mean and Standard Deviation Arithmetic Basic Addition Addition 2 Level 2 Addition Addition 3 Addition 4 Basic Subtraction Subtraction 2 Subtraction 3: Introduction to Borrowing or Regrouping Alternate mental subtraction method Level 4 Subtraction Why borrowing works Adding Decimals Subtracting decimals Basic Multiplication Multiplication 2: The Multiplication Tables Multiplication 3: 10,11,12 times tables Multiplication 4: 2-digit times 1-digit number Multiplication 5: 2-digit times a 2-digit number Multiplication 6: Multiple Digit Numbers Multiplication 7: Old video giving more examples Mulitplication 8: Multiplying decimals (Old video) Lattice Multiplication Why Lattice Multiplication Works Division 1 Division 2 Division 3: More long division and remainder examples Level 4 division Converting fractions to decimals Percent and decimals Dividing decimal Ordering numeric expressions Greatest Common Divisor Least Common Multiple Equivalent fractions Mixed numbers and improper fractions Pre-algebra Adding/Subtracting negative numbers Multiplying and dividing negative numbers Adding and subtracting fractions Multiplying fractions Dividing fractions Introduction to Order of Operations More Complicated Order of Operations Example Level 1 Exponents Level 2 Exponents Level 3 exponents Negative Exponent Intuition Exponent Rules Part 1 Exponent Rules Part 2 Simplifying radicals Introduction to Logarithms Unit conversion Speed translation Introduction to logarithm properties Introduction to logarithm properties (part 2) Scientific Notation Scientific Notation Examples Introduction to Ratios (new HD version) Unit Conversion Example: Drug Dosage Geometry Introduction to angles Angles (part 2) Angles (part 3) Angles of parallel lines The Angle Game Similar triangles Similar triangles (part 2) Angle Game (part 2) Area and Perimeter Circles: Radius, Diameter and Circumference Area of a circle Introduction to the Pythagorean Theorem Pythagorean Theorem II 45-45-90 Triangles Intro to 30-60-90 Triangles 30-60-90 Triangles II Heron's Formula Part 1 of Proof of Heron's Formula Part 2 of the Proof of Heron's Formula An inscribed angle is half of a central angle that subtends the same arc Area of Inscribed Equilateral Triangle (some basic trig used) Right Triangles Inscribed in Circles (Proof) California Standards Test: Geometry CA Geometry: deductive reasoning CA Geometry: Proof by Contradiction CA Geometry: More Proofs CA Geometry: Similar Triangles CA Geometry: Similar Triangles CA Geometry: More on cogruent and similar triangles CA Geometry: Triangles and Parallelograms CA Geometry: Area, Pythagorean Theorem CA Geometry: Area, Circumference, Volume CA Geometry: Pythagorean Theorem, Area CA Geometry: Exterior Angles CA Geometry: Deducing Angle Measures CA Geometry: Pythagorean Theorem, Compass Constructions CA Geometry: Compass Construction CA Geometry: Basic Trigonometry CA Geometry: More Trig CA Geometry: Circle Area Chords Tangent CA Geometry: Secants and Translations

Chemistry Introduction to the atom Orbitals More on orbitals and electron configuration Electron Configurations Electron Configurations 2 Valence Electrons Groups of the Periodic Table Periodic Table Trends: Ionization Energy Other Periodic Table Trends Ionic, Covalent, and Metallic Bonds Molecular and Empirical Formulas The Mole and Avogadro's Number Formula from Mass Composition Another mass composition problem Balancing Chemical Equations Stoichiometry Stoichiometry: Limiting Reagent Ideal Gas Equation: PV=nRT Ideal Gas Equation Example 1 Ideal Gas Equation Example 2 Ideal Gas Equation Example 3 Ideal Gas Example 4 Partial Pressure States of Matter States of Matter Follow-Up Specific Heat, Heat of Fusion and Vaporization Chilling Water Problem Phase Diagrams Van Der Waals Forces Covalent Networks, Metallic, and Ionic Crystals Vapor Pressure Suspensions, Colloids and Solutions Solubility Boiling Point Elevation and Freezing Point Supression Introduction to Kinetics Reactions in Equilibrium Mini-Video on Ion Size Keq Intuition (mathy and not necessary to progress) Keq derivation intuition (can skip; bit mathy) Heterogenous Equilibrium Le Chatelier's Principle Introduction to pH, pOH, and pKw Acid Base Introduction pH, pOH of Strong Acids and Bases pH of a Weak Acid pH of a Weak Base Conjugate Acids and Bases pKa and pKb Relationship Buffers Strong Acid Titration Weak Acid Titration Half Equivalence Point Titration Roundup Introduction to Oxidation States More on Oxidation States Hydrogen Peroxide Correction Redox Reactions Galvanic Cells Types of Decay Half-Life Exponential Decay Formula Proof (can skip, involves Calculus) Introduction to Exponential Decay More Exponential Decay Examples Macrostates and Microstates Quasistatic and Reversible Processes First Law of Thermodynamics/ Internal Energy More on Internal Energy Work from Expansion PV-diagrams and Expansion Work Proof: U=(3/2)PV or U=(3/2)nRT Work Done by Isothermic Process Carnot Cycle and Carnot Engine Proof: Volume Ratios in a Carnot Cycle Proof: S (or Entropy) is a valid state variable Thermodynamic Entropy Definition Clarification Reconciling Thermodynamic and State Definitions of Entropy Entropy Intuition Maxwell's Demon More on Entropy Efficiency of a Carnot Engine Carnot Efficiency 2: Reversing the Cycle Carnot Efficiency 3: Proving that it is the most efficient Enthalpy Heat of Formation Hess's Law and Reaction Enthalpy Change Gibbs Free Energy and Spontaneity Gibbs Free Energy Example More rigorous Gibbs Free Energy/ Spontaneity Relationship A look at a seductive but wrong Gibbs/Spontaneity Proof Stoichiometry Example Problem 1 Stoichiometry Example Problem 2 Limiting Reactant Example Problem 1 Empirical and Molecular Formulas from Stoichiometry Example of Finding Reactant Empirical Formula Stoichiometry of a Reaction in Solution Another Stoichiometry Example in a Solution Brain Teasers Liar Truthteller Brain Teaser Toggler Brain Teaser Alien Abduction Brain Teaser Brain Teaser: Blue Forehead Room Blue Forehead Room Solution Forehead Numbers Brain Teaser Light Bulb Switching Brain Teaser Path Counting Brain Teaser 3-D Path Counting Brain Teaser Current Economics 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 Banking and Money Banking 1 Banking 2: A bank's income statement Banking 3: Fractional Reserve Banking Banking 4: Multiplier effect and the money supply Banking 5: Introduction to Bank Notes Banking 6: Bank Notes and Checks Banking 7: Giving out loans without giving out gold Banking 8: Reserve Ratios Banking 9: More on Reserve Ratios (Bad sound) Banking 10: Introduction to leverage (bad sound) Banking 11: A reserve bank Banking 12: Treasuries (government debt) Banking 13: Open Market Operations Banking 14: Fed Funds Rate Banking 15: More on the Fed Funds Rate Banking 16: Why target rates vs. money supply Banking 17: What happened to the gold? Banking 18: Big Picture Discussion The Discount Rate Repurchase Agreements (Repo transactions) Federal Reserve Balance Sheet Fractional Reserve Banking Commentary 1 FRB Commentary 2: Deposit Insurance FRB Commentary 3: Big Picture Venture Capital and Capital Markets Raising money for a startup Getting a seed round from a VC Going back to the till: Series B An IPO More on IPOs Equity vs. Debt Bonds vs. Stocks Chapter 7:Bankruptcy Liquidation Chapter 11: Bankruptcy Restructuring Finance 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) Raising money for a startup Getting a seed round from a VC Going back to the till: Series B An IPO More on IPOs Bonds vs. Stocks Chapter 7:Bankruptcy Liquidation Chapter 11: Bankruptcy Restructuring Return on capital 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. Comsumption 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 What it means to buy a company's stock 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 Valuation and Investing Price and Market Capitalization Introduction to the Income Statement Earnings and EPS Introduction to the Price-to-Earnings Ratio P/E Discussion ROA Discussion 1 ROA Discussion 2 Depreciation Amortization P/E Conundrum Enterprise Value EBITDA Credit Crisis The housing price conundrum Housing price conundrum (part 2) Housing Price Conundrum (part 3) Housing Conundrum (part 4) Mortgage-Backed Securities I Mortgage-backed securities II Mortgage-backed securities III Collateralized Debt Obligation (CDO) Bailout 13: Does the bailout have a chance of working? Credit Default Swaps Credit Default Swaps 2 Wealth Destruction 1 Wealth Destruction 2 Geithner Plan Geithner Plan I Geithner Plan II Geithner Plan 2.5 Geithner Plan III Geithner Plan IV Geithner 5: A better solution Paulson 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 14: Possible Solution Bailout 15: More on the solution

Biology Introduction to Evolution and Natural Selection Intelligent Design and Evolution Evolution Clarification Natural Selection and the Owl Butterfly DNA Variation in a Species Chromosomes, Chromatids, Chromatin, etc. Mitosis, Meiosis and Sexual Reproduction Phases of Mitosis Phases of Meiosis Embryonic Stem Cells Cancer Introduction to Heredity Punnett Square Fun Hardy-Weinberg Principle Sex-Linked Traits Bacteria Viruses ATP: Adenosine Triphosphate Introduction to Cellular Respiration Oxidation and Reduction Review From Biological Point-of-View Oxidation and Reduction in Cellular Respiration Glycolysis Krebs / Citric Acid Cycle Electron Transport Chain Oxidative Phosphorylation and Chemiosmosis Photosynthesis Photosynthesis: Light Reactions 1 Photosynthesis: Light Reactions and Photophosphorylation Photosynthesis: Calvin Cycle Photorespiration C-4 Photosynthesis CAM Plants Parts of a cell Diffusion and Osmosis The Lungs and Pulmonary System Red blood cells Circulatory System and the Heart Hemoglobin Anatomy of a Neuron Sodium Potassium Pump Electrotonic and Action Potentials Saltatory Conduction in Neurons Neuronal Synapses (Chemical) Myosin and Actin Tropomyosin and troponin and their role in regulating muscle contraction Role of the Sarcoplasmic Reticulum in Muscle Cells Anatomy of a muscle cell Role of Phagocytes in Innate or Nonspecific Immunity Types of immune responses: Innate and Adaptive. Humoral vs. Cell-Mediated B Lymphocytes (B cells) Professional Antigen Presenting Cells (APC) and MHC II complexes Helper T Cells Cytotoxic T Cells Review of B cells, CD4+ T cells and CD8+ T cells Inflammatory Response The Kidney and Nephron Secondary Active Transport in the Nephron Trigonometry 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 Precalculus 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 Statistics Statistics: The Average Statistics: Sample vs. Population Mean Statistics: Variance of a Population Statistics: Sample Variance 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 Law of Large Numbers Normal Distribution Excel Exercise Introduction to the Normal Distribution ck12.org Normal Distribution Problems: Qualitative sense of normal distributions ck12.org Normal Distribution Problems: z-score ck12.org Normal Distribution Problems: Empirical Rule 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 Probability Probability (part 1) Probability (part 2) Probability (part 3) Probability (part 4) Probability (part 5) Probability (part 6) Probability (part 7) Probability (part 8) Permutations Combinations Probability using Combinations Probability and Combinations (part 2) Conditional Probability and Combinations Birthday Probability Problem 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 Law of Large Numbers Calculus 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 Epsilon Delta Limit Definition 1 Epsilon Delta Limit Definition 2 Calculus: Derivatives 1 (new HD version) Calculus: Derivatives 2 (new HD version) Calculus: Derivatives 2.5 (new HD version) Calculus: Derivatives 1 Calculus: Derivatives 2 Calculus: Derivatives 3 Calculus: Derivatives 4: The Chain Rule Calculus: Derivatives 5 Calculus: Derivatives 6 Derivatives (part 7) Derivatives (part 8) Derivatives (part 9) Proof: d/dx(x^n) Proof: d/dx(sqrt(x)) Proof: d/dx(ln x) = 1/x Proof: d/dx(e^x) = e^x Proofs of Derivatives of Ln(x) and e^x Calculus: Derivative of x^(x^x) Extreme Derivative Word Problem (advanced) Implicit Differentiation Implicit Differentiation (part 2) More implicit differentiation More chain rule and implicit differentiation intuition Trig Implicit Differentiation Example Maxima Minima Slope Intuition Inflection Points and Concavity Intuition Monotonicity Theorem Calculus: Maximum and minimum values on an interval Calculus: Graphing Using Derivatives Calculus Graphing with Derivatives Example Graphing with Calculus Optimization with Calculus 1 Optimization with Calculus 2 Optimization with Calculus 3 Optimization Example 4 Introduction to rate-of-change problems Equation of a tangent line Rates-of-change (part 2) Ladder rate-of-change problem Mean Value Theorem The Indefinite Integral or Anti-derivative Indefinite integrals (part II) Indefinite Integration (part III) Indefinite Integration (part IV) Indefinite Integration (part V) Integration by Parts (part 6 of Indefinite Integration) Indefinite Integration (part 7) Another u-subsitution example Introduction to definite integrals Definite integrals (part II) Definite Integrals (area under a curve) (part III) Definite Integrals (part 4) Definite Integrals (part 5) Definite integral with substitution Integrals: Trig Substitution 1 Integrals: Trig Substitution 2 Integrals: Trig Substitution 3 (long problem) Introduction to differential equations Solid of Revolution (part 1) Solid of Revolution (part 2) Solid of Revolution (part 3) Solid of Revolution (part 4) Solid of Revolution (part 5) Solid of Revolution (part 6) Solid of Revolution (part 7) Solid of Revolution (part 8) Sequences and Series (part 1) Sequences and series (part 2) Polynomial approximation of functions (part 1) Polynomial approximation of functions (part 2) Approximating functions with polynomials (part 3) Polynomial approximation of functions (part 4) Polynomial approximations of functions (part 5) Polynomial approximation of functions (part 6) Polynomial approximation of functions (part 7) Taylor Polynomials Exponential Growth AP Calculus BC Exams: 2008 1 a AP Calculus BC Exams: 2008 1 b&c AP Calculus BC Exams: 2008 1 c&d AP Calculus BC Exams: 2008 1 d Calculus BC 2008 2 a Calculus BC 2008 2 b &c Calculus BC 2008 2d Partial Derivatives Partial Derivatives 2 Gradient 1 Gradient of a scalar field Divergence 1 Divergence 2 Divergence 3 Curl 1 Curl 2 Curl 3 Double Integral 1 Double Integrals 2 Double Integrals 3 Double Integrals 4 Double Integrals 5 Double Integrals 6 Triple Integrals 1 Triple Integrals 2 Triple Integrals 3 ∫(2^ln x)/x dx Antiderivative Example Introduction to the Line Integral Line Integral Example 1 Line Integral Example 2 (part 1) Line Integral Example 2 (part 2) Position Vector Valued Functions Derivative of a position vector valued function Differential of a vector valued function Vector valued function derivative example Line Integrals and Vector Fields Using a line integral to find the work done by a vector field example Parametrization of a Reverse Path Scalar Field Line Integral Independent of Path Direction Vector Field Line Integrals Dependent on Path Direction Path Independence for Line Integrals Closed Curve Line Integrals of Conservative Vector Fields Example of Closed Line Integral of Conservative Field Second Example of Line Integral of Conservative Vector Field Green's Theorem Proof Part 1 Green's Theorem Proof (part 2) Green's Theorem Example 1 Green's Theorem Example 2 Introduction to Parametrizing a Surface with Two Parameters Determining a Position Vector-Valued Function for a Parametrization of Two Parameters Partial Derivatives of Vector-Valued Functions Introduction to the Surface Integral Example of calculating a surface integral part 1 Example of calculating a surface integral part 2 Example of calculating a surface integral part 3 Differential Equations Introduction to differential equations 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 homogenous 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 characterisitic 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 nonhomogenous 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

History French Revolution (Part 1) French Revolution (Part 2) French Revolution (Part 3) - Reign of Terror French Revolution (Part 4) - The Rise of Napoleon Bonaparte Haitian Revolution (Part 1) Haitian Revolution (Part 2) Napoleon and the Wars of the First and Second Coalitions Napoleon and the War of the Third Coalition Napoleon and the War of the Fourth Coalition Napoleon's Peninsular Campaigns Napoleon Forced to Abdicate Linear Algebra Introduction to matrices Matrix multiplication (part 1) Matrix multiplication (part 2) Inverse Matrix (part 1) 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 Linear Algebra: Introduction to Vectors Linear Algebra: Vector Examples Linear Algebra: Parametric Representations of Lines Linear Combinations and Span Linear Algebra: Introduction to Linear Independence More on linear independence Span and Linear Independence Example Linear Subspaces Linear Algebra: Basis of a Subspace Vector Dot Product and Vector Length Proving Vector Dot Product Properties Proof of the Cauchy-Schwarz Inequality Linear Algebra: Vector Triangle Inequality Defining the angle between vectors Defining a plane in R3 with a point and normal vector Linear Algebra: 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 Linear Algebra: Matrix Product Examples Matrix Product Associativity Distributive Property of Matrix Products Linear Algebra: 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 Linear Algebra: Exploring the solution set of Ax=b Linear Algebra: Matrix condition for one-to-one trans Linear Algebra: Simplifying conditions for invertibility Linear Algebra: Showing that Inverses are Linear Linear Algebra: Deriving a method for determining inverses Linear Algebra: Example of Finding Matrix Inverse Linear Algebra: Formula for 2x2 inverse Linear Algebra: 3x3 Determinant Linear Algebra: nxn Determinant Linear Algebra: Determinants along other rows/cols Linear Algebra: Rule of Sarrus of Determinants Linear Algebra: Determinant when row multiplied by scalar Linear Algebra: (correction) scalar muliplication of row Linear Algebra: Determinant when row is added Linear Algebra: Duplicate Row Determinant Linear Algebra: Determinant after row operations Linear Algebra: Upper Triangular Determinant Linear Algebra: Simpler 4x4 determinant Linear Algebra: Determinant and area of a parallelogram Linear Algebra: Determinant as Scaling Factor Linear Algebra: Transpose of a Matrix Linear Algebra: Determinant of Transpose Linear Algebra: Transposes of sums and inverses Linear Algebra: Transpose of a Vector Linear Algebra: Rowspace and Left Nullspace Lin Alg: Visualizations of Left Nullspace and Rowspace Linear Algebra: Orthogonal Complements Linear Algebra: Rank(A) = Rank(transpose of A) Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n Lin Alg: Representing vectors in Rn using subspace members Lin Alg: Orthogonal Complement of the Orthogonal Complement Lin Alg: Orthogonal Complement of the Nullspace Lin Alg: Unique rowspace solution to Ax=b Linear Alg: Rowspace Solution to Ax=b example Lin Alg: Showing that A-transpose x A is invertible Linear Algebra: Projections onto Subspaces Linear Alg: Visualizing a projection onto a plane Lin Alg: A Projection onto a Subspace is a Linear Transforma Linear Algebra: Subspace Projection Matrix Example Lin Alg: Another Example of a Projection Matrix Linear Alg: Projection is closest vector in subspace Linear Algebra: Least Squares Approximation Linear Algebra: Least Squares Examples Linear Algebra: Another Least Squares Example Linear Algebra: Coordinates with Respect to a Basis Linear Algebra: Change of Basis Matrix Lin Alg: Invertible Change of Basis Matrix Lin Alg: Transformation Matrix with Respect to a Basis Lin Alg: Alternate Basis Tranformation Matrix Example Lin Alg: Alternate Basis Tranformation Matrix Example Part 2 Lin Alg: Changing coordinate systems to help find a transformation matrix Linear Algebra: Introduction to Orthonormal Bases Linear Algebra: Coordinates with respect to orthonormal bases Lin Alg: Projections onto subspaces with orthonormal bases Lin Alg: Finding projection onto subspace with orthonormal basis example Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix Lin Alg: Orthogonal matrices preserve angles and lengths Linear Algebra: The Gram-Schmidt Process Linear Algebra: Gram-Schmidt Process Example Linear Algebra: Gram-Schmidt example with 3 basis vectors Linear Algebra: Introduction to Eigenvalues and Eigenvectors Linear Algebra: Proof of formula for determining Eigenvalues Linear Algebra: Example solving for the eigenvalues of a 2x2 matrix Linear Algebra: Finding Eigenvectors and Eigenspaces example Linear Algebra: Eigenvalues of a 3x3 matrix Linear Algebra: Eigenvectors and Eigenspaces for a 3x3 matrix Linear Algebra: Showing that an eigenbasis makes for good coordinate systems Physics Introduction to motion Introduction to motion (part 2) Introduction to motion (part 3) Projectile motion (part 1) Projectile motion (part 2) Projectile motion (part 3) Projectile motion (part 4) Projectile motion (part 5) Projectile motion (part 6) Projectile motion (part 7) Projectile motion (part 8) Projectile motion (part 9) Projectile motion (part 10) 2 dimensional projectile motion (part 1) 2 dimensional projectile motion (part 2) 2-dimensional projectile motion (part 3) 2 dimensional projectile motion part 4 2-dimensional projectile motion part 5 Newton's First Law of Motion Newton's Second Law of Motion Newton's Third Law of Motion Newton's Laws Problems (part 1) Newton's Laws Examples (part 2) Newton's Laws Newton's Laws and vectors Force with Vectors Introduction to Tension Tension (part 2) Mass on Inclined Plane Introduction to friction Friction on an inclined plane A more complicated friction/inclined plane problem Tension in an accelerating system and pie in the face Moving pulley problem (part 1) Moving pulley problem (part 2) Introduction to Momentum Momentum: Ice skater throws a ball 2-dimensional momentum problem 2-dimensional momentum problem (part 2) Introduction to work and energy Work and Energy (part 2) Conservation of Energy Work/Energy problem with Friction Introduction to mechanical advantage Mechanical Advantage (part 2) Mechanical Advantage (part 3) Center of Mass Introduction to Torque Moments Moments (part 2) Unit Vector Notation Unit Vector Notation (part 2) Projectile Motion with Unit Vectors Projectile Motion with Unit Vectors (part 2) Projectile Motion with Ordered Set Notation Introduction to centripetal acceleration (part 1) Centripetal Acceleration (part 2) Centripetal Acceleration (part 3) Visual Proof: a= v^2/r Calculus Proof that a=v^2/r Introduction to angular velocity Conservation of angular momemtum Introduction to Newton's Law of Gravitation Gravitation (part 2) Intro to springs and Hooke's Law Potential energy stored in a spring Spring potential energy example (mistake in math) Introduction to Harmonic Motion Harmonic Motion Part 2 (calculus) Harmonic Motion Part 3 (no calculus) Fluids (part 1) Fluids (part 2) Fluids (part 3) Fluids (part 4) Fluids (part 5) Fluids (part 6) Fluids (part 7) Fluids (part 8) Fluids (part 9) Fluids (part 10) Fluids (part 11) Fluids (part 12) Thermodynamics (part 1) Thermodynamics (part 2) Thermodynamics (part 3) Thermodynamics (part 4) Thermodynamics (part 5) Electrostatics (part 1): Introduction to Charge and Coulomb's Law Electrostatics (part 2) Proof (Advanced): Field from infinite plate (part 1) Proof (Advanced): Field from infinite plate (part 2) Electric Potential Energy Electric Potential Energy (part 2-- involves calculus) Voltage Capacitance Circuits (part 1) Circuits (part 2) Circuits (part 3) Circuits (part 4) Cross product 1 Cross Product 2 Cross Product and Torque Introduction to Magnetism Magnetism 2 Magnetism 3 Magnetism 4 Magnetism 5 Magnetism 6: Magnetic field due to current Magnetism 7 Magnetism 8 Magnetism 9: Electric Motors Magnetism 10: Electric Motors Magnetism 11: Electric Motors Magnetism 12: Induced Current in a Wire The dot product Dot vs. Cross Product Calculating dot and cross products with unit vector notation Introduction to Waves Amplitude, Period, Frequency and Wavelength of Periodic Waves