Calculus
Explore 73 sections in textbook order, from preparation through limits, derivatives, integrals and series. Learn the ideas, work through examples, and practise your next step.
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73 lessons in textbook order.
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Preparation · Preparation for Calculus
4 lessons
Graphs and Models
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Explore lesson ↗P.2Linear Models and Rates of Change
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Explore lesson ↗P.3Functions and Their Graphs
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Explore lesson ↗P.4Fitting Models to Data
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Explore lesson ↗Chapter 1 · Limits and Their Properties
5 lessons
A Preview of Calculus
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Explore lesson ↗1.2Finding Limits Graphically and Numerically
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Explore lesson ↗1.3Evaluating Limits Analytically
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Explore lesson ↗1.4Continuity and One-Sided Limits
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Explore lesson ↗1.5Infinite Limits
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Explore lesson ↗Chapter 2 · Differentiation
6 lessons
The Derivative and the Tangent Line Problem
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Explore lesson ↗2.2Basic Differentiation Rules and Rates of Change
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Explore lesson ↗2.3Product and Quotient Rules and Higher-Order Derivatives
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Explore lesson ↗2.4The Chain Rule
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Explore lesson ↗2.5Implicit Differentiation
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Explore lesson ↗2.6Related Rates
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Explore lesson ↗Chapter 3 · Applications of Differentiation
9 lessons
Extrema on an Interval
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Explore lesson ↗3.2Rolle’s Theorem and the Mean Value Theorem
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Explore lesson ↗3.3Increasing and Decreasing Functions and the First Derivative Test
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Explore lesson ↗3.4Concavity and the Second Derivative Test
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Explore lesson ↗3.5Limits at Infinity
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Explore lesson ↗3.6A Summary of Curve Sketching
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Explore lesson ↗3.7Optimization Problems
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Explore lesson ↗3.8Newton’s Method
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Explore lesson ↗3.9Differentials
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Explore lesson ↗Chapter 4 · Integration
6 lessons
Antiderivatives and Indefinite Integration
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Explore lesson ↗4.2Area
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Explore lesson ↗4.3Riemann Sums and Definite Integrals
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Explore lesson ↗4.4The Fundamental Theorem of Calculus
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Explore lesson ↗4.5Integration by Substitution
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Explore lesson ↗4.6Numerical Integration
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Explore lesson ↗Chapter 5 · Logarithmic, Exponential, and Other Transcendental Functions
8 lessons
The Natural Logarithmic Function: Differentiation
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Explore lesson ↗5.2The Natural Logarithmic Function: Integration
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Explore lesson ↗5.3Inverse Functions
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Explore lesson ↗5.4Exponential Functions: Differentiation and Integration
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Explore lesson ↗5.5Bases Other than e and Applications
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Explore lesson ↗5.6Inverse Trigonometric Functions: Differentiation
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Explore lesson ↗5.7Inverse Trigonometric Functions: Integration
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Explore lesson ↗5.8Hyperbolic Functions
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Explore lesson ↗Chapter 6 · Differential Equations
4 lessons
Slope Fields and Euler’s Method
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Explore lesson ↗6.2Differential Equations: Growth and Decay
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Explore lesson ↗6.3Separation of Variables and the Logistic Equation
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Explore lesson ↗6.4First-Order Linear Differential Equations
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Explore lesson ↗Chapter 7 · Applications of Integration
7 lessons
Area of a Region Between Two Curves
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Explore lesson ↗7.2Volume: The Disk Method
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Explore lesson ↗7.3Volume: The Shell Method
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Explore lesson ↗7.4Arc Length and Surfaces of Revolution
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Explore lesson ↗7.5Work
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Explore lesson ↗7.6Moments, Centers of Mass, and Centroids
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Explore lesson ↗7.7Fluid Pressure and Fluid Force
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Explore lesson ↗Chapter 8 · Integration Techniques, L’Hopital’s Rule, and Improper Integrals
8 lessons
Basic Integration Rules
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Explore lesson ↗8.2Integration by Parts
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Explore lesson ↗8.3Trigonometric Integrals
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Explore lesson ↗8.4Trigonometric Substitution
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Explore lesson ↗8.5Partial Fractions
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Explore lesson ↗8.6Integration by Tables and Other Integration Techniques
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Explore lesson ↗8.7Indeterminate Forms and L’Hopital’s Rule
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Explore lesson ↗8.8Improper Integrals
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Explore lesson ↗Chapter 9 · Infinite Series
10 lessons
Sequences
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Explore lesson ↗9.2Series and Convergence
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Explore lesson ↗9.3The Integral Test and p-Series
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Explore lesson ↗9.4Comparisons of Series
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Explore lesson ↗9.5Alternating Series
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Explore lesson ↗9.6The Ratio and Root Tests
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Explore lesson ↗9.7Taylor Polynomials and Approximations
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Explore lesson ↗9.8Power Series
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Explore lesson ↗9.9Representation of Functions by Power Series
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Explore lesson ↗9.10Taylor and Maclaurin Series
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Explore lesson ↗Chapter 10 · Conics, Parametric Equations, and Polar Coordinates
6 lessons
Conics and Calculus
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Explore lesson ↗10.2Plane Curves and Parametric Equations
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Explore lesson ↗10.3Parametric Equations and Calculus
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Explore lesson ↗10.4Polar Coordinates and Polar Graphs
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Explore lesson ↗10.5Area and Arc Length in Polar Coordinates
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Explore lesson ↗10.6Polar Equations of Conics and Kepler’s Laws
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