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18 chapters, from basic math to differential equations. 216 lessons and 1501 practice problems are ready now, with more being added. The first section of every chapter is free.

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01Basic MathArithmetic, exponents, percentages, sets, number systems and geometry: the toolkit everything else uses.
  1. 01.01Addition, Subtraction, Multiplication, and DivisionOrder of Operations · Long Division, Remainders, and FractionsFree
  2. 01.02Exponents and RootsExponent Rules · Roots and Rational Exponents
  3. 01.03Rates, Ratios, and ProportionsUnits of Measure · Rates · Ratios · Proportions
  4. 01.04PercentagesDecimals and Percents · Percent Increase and Percent Decrease
  5. 01.05Variables and ExpressionsVariables
  6. 01.06Equations and Inequalities
  7. 01.07GraphingCartesian Coordinate System · Plotting Points
  8. 01.08SetsSet Notation · Set Operations · Cardinality · Set Relations · Venn Diagrams
  9. 01.09Number SystemsNatural Numbers · Integers · Rational Numbers · Real Numbers · Complex Numbers
  10. 01.10IntervalsOpen and Closed Intervals · Bounded and Unbounded Intervals · Set Operations with Intervals
  11. 01.11AnglesPoints, Lines, and Rays · Angles, Degrees, and Radians
  12. 01.12Planar ShapesPolygons · Perimeter and Area · Circles and Ellipses
02AlgebraFunctions and their graphs, from lines and polynomials to exponentials, logarithms and systems.
  1. 02.01FunctionsFunction Rules · Domain and Implied Domain · Range · Injective and SurjectiveFree
  2. 02.02Function OperationsAddition and Subtraction · Multiplication and Division · Composition
  3. 02.03TransformationsVertical Shifting · Horizontal Shifting · Vertical Scaling · Horizontal Scaling
  4. 02.04Inverse Functions
  5. 02.05Linear Functions
  6. 02.06Quadratic and Polynomial Functions
  7. 02.07Rational Functions
  8. 02.08Root Functions
  9. 02.09Exponential Functions
  10. 02.10Logarithmic Functions
  11. 02.11Systems of Equations
  12. 02.12Systems of Inequalities
03TrigonometryTriangles, the unit circle, the six trig functions, identities and the laws of sines and cosines.
  1. 03.01Triangle BasicsFree
  2. 03.02Types of Triangles
  3. 03.03Similar and Congruent Triangles
  4. 03.04Pythagorean Theorem and Special Triangles
  5. 03.05Sine, Cosine, and Tangent
  6. 03.06The Unit Circle
  7. 03.07Secant, Cosecant, and Cotangent
  8. 03.08Trigonometric Identities
  9. 03.09Solving Trigonometric Equations
  10. 03.10Inverse Trigonometric Functions
  11. 03.11The Law of Sines
  12. 03.12The Law of Cosines
04LimitsWhat a function approaches, how to compute it, the precise ε–δ definitions, and continuity.
  1. 04.01Determining Limits GraphicallyFree
  2. 04.02Limit Laws and Basic Limits
  3. 04.03Indeterminate Limits and Algebraic Techniques
  4. 04.04The Squeeze Theorem
  5. 04.05Infinite Valued Limits and Vertical Asymptotes
  6. 04.06Limits at Infinity and Horizontal Asymptotes
  7. 04.07Precise Definition of Finite Limits
  8. 04.08Precise Definition of One-Sided Limits
  9. 04.09Precise Definition of Infinite Valued Limits
  10. 04.10Precise Definition of Limits at Infinity
  11. 04.11Continuity
  12. 04.12The Intermediate Value Theorem
05DerivativesInstantaneous rate of change: the definition, then the rules for every kind of function.
  1. 05.01Definition of the DerivativeFree
  2. 05.02Differentiability
  3. 05.03Derivatives of Power Functions
  4. 05.04Derivatives of Exponential Functions
  5. 05.05Derivatives of Products and Quotients
  6. 05.06Higher-order Derivatives
  7. 05.07Derivatives of Trigonometric Functions
  8. 05.08Derivatives of Compositions
  9. 05.09Implicit Differentiation
  10. 05.10Derivatives of Inverse Functions
  11. 05.11Derivatives of Logarithmic Functions
  12. 05.12Logarithmic Differentiation
06Applications of DerivativesMotion, related rates, approximation, the big theorems, curve sketching and optimization.
  1. 06.01Position, Velocity, and AccelerationFree
  2. 06.02Related Rates
  3. 06.03Linear Approximation
  4. 06.04Critical Points and Critical Values
  5. 06.05The Extreme Value Theorem
  6. 06.06Rolle's Theorem
  7. 06.07The Mean Value Theorem
  8. 06.08Increasing, Decreasing, and Concavity
  9. 06.09First and Second Derivative Tests
  10. 06.10Indeterminate Forms and L'Hôpital's Rule
  11. 06.11Optimization Problems
  12. 06.12Newton's Method
07IntegralsArea under a curve, antiderivatives, the Fundamental Theorem, and techniques of integration.
  1. 07.01Approximating AreaFree
  2. 07.02The Definite Integral
  3. 07.03Antiderivatives of Common Functions
  4. 07.04The Fundamental Theorem of Calculus I
  5. 07.05The Fundamental Theorem of Calculus II
  6. 07.06Variable Substitution
  7. 07.07Integration by Parts
  8. 07.08Antiderivatives of Trigonometric Functions
  9. 07.09Trigonometric Substitution
  10. 07.10Partial Fractions
  11. 07.11Improper Integrals
  12. 07.12Choosing the Right Integration Technique
08Applications of IntegralsAreas, volumes, arc length, surface area, average value and physical applications.
  1. 08.01Derivatives of Integral FunctionsFree
  2. 08.02Net Change and Area Between Curves
  3. 08.03Volume by Slicing
  4. 08.04Solids of Revolution: Disk/Washer Method
  5. 08.05Solids of Revolution: Shell Method
  6. 08.06Average Value of a Function
  7. 08.07Arc Length
  8. 08.08Surface Area of Solids of Revolution
  9. 08.09Tricky Integrals
  10. 08.10Calculating Work
  11. 08.11Center of Mass
  12. 08.12Other Physical Applications
09SequencesLists of numbers that go on forever: notation, convergence, and the theorems behind it.
  1. 09.01Sequence NotationFree
  2. 09.02Arithmetic and Geometric Sequences
  3. 09.03Recursive Sequences
  4. 09.04The Fibonacci Sequence
  5. 09.05Convergence/Divergence
  6. 09.06Increasing/Decreasing
  7. 09.07Bounded/Unbounded
  8. 09.08The Monotone Convergence Theorem
  9. 09.09Subsequences
  10. 09.10The Bolzano–Weierstrass Theorem
  11. 09.11Cauchy Sequences
  12. 09.12The Cauchy Convergence Criterion
10SeriesAdding infinitely many terms: partial sums and every major convergence test.
  1. 10.01Series Notation and IndexingFree
  2. 10.02Sequence of Partial Sums
  3. 10.03Convergence/Divergence
  4. 10.04The Harmonic Series
  5. 10.05Geometric Series
  6. 10.06Telescoping Series
  7. 10.07Divergence Test
  8. 10.08Integral Test and p-series
  9. 10.09Comparison and Limit Comparison Tests
  10. 10.10Alternating Series Test
  11. 10.11Absolute and Conditional Convergence
  12. 10.12Ratio and Root Test
11Applications of SeriesEstimating sums, power series, Taylor and Maclaurin series, and where series show up in practice.
  1. 11.01Estimating the Value of a SeriesIntegral Test Remainders · Alternating Series Test Remainders · Ratio Test RemaindersFree
  2. 11.02The Riemann Series Theorem
  3. 11.03Power Series and Properties
  4. 11.04Taylor and Maclaurin Series
  5. 11.05Maclaurin Series for Trigonometric Functions
  6. 11.06Binomial Series
  7. 11.07Differentiating and Integrating Maclaurin Series
  8. 11.08Solving Limits with Series
  9. 11.09Series in Physics
  10. 11.10Fourier Series
  11. 11.11Infinite Products
  12. 11.12Continued Fractions
12Parametric Equations and Polar CoordinatesCurves traced over time and in polar form: graphing, tangents, area, arc length and surface area.
  1. 12.01Parametric CurvesFree
  2. 12.02Graphing Parametric Curves
  3. 12.03Tangent Lines to Parametric Curves
  4. 12.04Area Under Parametric Curves
  5. 12.05Arc Length of Parametric Curves
  6. 12.06Surface Area of Solids of Revolution with Parametric Curves
  7. 12.07Polar Coordinates
  8. 12.08Graphing in Polar Coordinates
  9. 12.09Differentiation in Polar Coordinates
  10. 12.10Area Enclosed by Polar Curves
  11. 12.11Arc Length of Polar Curves
  12. 12.12Surface Area of Solids of Revolution in Polar Coordinates
13Vectors and 3-Dimensional Coordinate SystemsVectors, products, lines and planes, vector functions, curvature and 3D coordinate systems.
  1. 13.01Vector BasicsFree
  2. 13.02Dot Product
  3. 13.03Cross Product
  4. 13.04Lines and Planes
  5. 13.05Quadric Surfaces
  6. 13.06Vector Functions
  7. 13.07Calculus with Vector Functions
  8. 13.08Tangent, Normal, and Binormal Vectors
  9. 13.09Curvature
  10. 13.10Cylindrical Coordinates
  11. 13.11Spherical Coordinates
  12. 13.12Physical Applications of 3D Coordinate Systems
14Partial DerivativesCalculus of functions of several variables: partials, gradients, and optimization with constraints.
  1. 14.01Functions of Multiple VariablesFree
  2. 14.02Limits and Continuity
  3. 14.03Partial Derivatives
  4. 14.04Higher-Order Partial Derivatives
  5. 14.05Tangent Planes and Linear Approximation
  6. 14.06The Chain Rule
  7. 14.07Directional Derivatives
  8. 14.08The Gradient
  9. 14.09Divergence and Curl
  10. 14.10Relative Extrema
  11. 14.11Absolute Extrema
  12. 14.12Lagrange Multipliers
15Multiple IntegralsDouble and triple integrals in rectangular, polar, cylindrical and spherical coordinates.
  1. 15.01Double Integrals over Rectangular RegionsFree
  2. 15.02Fubini's Theorem
  3. 15.03Double Integrals over General Regions
  4. 15.04Double Integrals in Polar Coordinates
  5. 15.05Surface Area
  6. 15.06Applications of Double Integrals
  7. 15.07Triple Integrals
  8. 15.08Triple Integrals in Cylindrical Coordinates
  9. 15.09Triple Integrals in Spherical Coordinates
  10. 15.10Jacobian Matrices
  11. 15.11Variable Substitution with Multiple Integrals
  12. 15.12Applications of Triple Integrals
16Line and Surface IntegralsVector fields, line and surface integrals, and the theorems of Green, Stokes and Gauss.
  1. 16.01Vector FieldsFree
  2. 16.02Line Integrals
  3. 16.03Line Integrals of Vector Fields
  4. 16.04The Fundamental Theorem for Line Integrals
  5. 16.05Conservative Vector Fields
  6. 16.06Green's Theorem
  7. 16.07Area of Parametric Surfaces
  8. 16.08Surface Integrals
  9. 16.09Surface Integrals of Vector Fields
  10. 16.10Stokes' Theorem
  11. 16.11The Divergence Theorem
  12. 16.12Applications of Line and Surface Integrals
17Ordinary Differential EquationsEquations involving a function and its derivatives: first- and second-order methods and transforms.
  1. 17.01First-Order Differential EquationsFree
  2. 17.02Separable Equations
  3. 17.03Linear First-Order Equations and Integrating Factors
  4. 17.04Exact Equations
  5. 17.05Slope Fields and Euler's Method
  6. 17.06Second-Order Linear Equations
  7. 17.07Undetermined Coefficients
  8. 17.08Variation of Parameters
  9. 17.09Laplace Transforms
  10. 17.10Systems of Differential Equations
  11. 17.11Series Solutions
  12. 17.12Fourier Transforms and Convolutions
18Partial Differential EquationsEquations in several variables: classification, separation of variables, and the classic PDEs.
  1. 18.01Introduction to PDEsFree
  2. 18.02Classification of PDEs
  3. 18.03Separation of Variables
  4. 18.04Fourier Series Solutions
  5. 18.05The Heat Equation
  6. 18.06The Wave Equation
  7. 18.07Laplace's Equation
  8. 18.08Boundary Value Problems
  9. 18.09Sturm–Liouville Problems
  10. 18.10PDEs in Polar and Cylindrical Coordinates
  11. 18.11Fourier Transform Methods
  12. 18.12Numerical Methods for PDEs