CK-12-Calculus

(Marvins-Underground-K-12) #1

  • 1 Functions, Limits, and Continuity Contents

    • 1.1 Equations and Graphs

    • 1.2 Relations and Functions

    • 1.3 Models and Data

    • 1.4 The Calculus

    • 1.5 Finding Limits

    • 1.6 Evaluating Limits

    • 1.7 Continuity

    • 1.8 Infinite Limits



  • 2 Derivatives

    • 2.1 Tangent Lines and Rates of Change

    • 2.2 The Derivative

    • 2.3 Techniques of Differentiation

    • 2.4 Derivatives of Trigonometric Functions

    • 2.5 The Chain Rule

    • 2.6 Implicit Differentiation

    • 2.7 Linearization and Newton’s Method



  • 3 Applications of Derivatives

    • 3.1 Related Rates

    • 3.2 Extrema and the Mean Value Theorem

    • 3.3 The First Derivative Test

    • 3.4 The Second Derivative Test

    • 3.5 Limits at Infinity

    • 3.6 Analyzing the Graph of a Function

    • 3.7 Optimization

    • 3.8 Approximation Errors



  • 4 Integration

    • 4.1 Indefinite Integrals Calculus

    • 4.2 The Initial Value Problem

    • 4.3 The Area Problem

    • 4.4 Definite Integrals

    • 4.5 Evaluating Definite Integrals

    • 4.6 The Fundamental Theorem of Calculus

    • 4.7 Integration by Substitution

    • 4.8 Numerical Integration



  • 5 Applications of Definite Integrals

    • 5.1 Area Between Two Curves

    • 5.2 Volumes

    • 5.3 The Length of a Plane Curve http://www.ck12.org Contents

    • 5.4 Area of a Surface of Revolution

    • 5.5 Applications from Physics, Engineering, and Statistics



  • 6 Transcendental Functions

    • 6.1 Inverse Functions

    • 6.2 Exponential and Logarithmic Functions

    • 6.3 Differentiation and Integration of Logarithmic and Exponential Functions

    • 6.4 Exponential Growth and Decay

    • 6.5 Derivatives and Integrals Involving Inverse Trigonometric Functions

    • 6.6 L’Hospital’s Rule



  • 7 Integration Techniques

    • 7.1 Integration by Substitution

    • 7.2 Integration By Parts

    • 7.3 Integration by Partial Fractions

    • 7.4 Trigonometric Integrals

    • 7.5 Trigonometric Substitutions

    • 7.6 Improper Integrals

    • 7.7 Ordinary Differential Equations



  • 8 Infinite Series

    • 8.1 Sequences

    • 8.2 Infinite Series

    • 8.3 Series Without Negative Terms

    • 8.4 Series With Odd or Even Negative Terms

    • 8.5 Ratio Test, Root Test, and Summary of Tests

    • 8.6 Power Series

    • 8.7 Taylor and Maclaurin Series

    • 8.8 Calculations with Series



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