The ebook
Elementary Calculus
is based on material originally written by H.J. Keisler. For more information please read the
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Index
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Real and Hyperreal Numbers
Differentiation
Continuous Functions
Integral
Limits, Analytic Geometry, and Approximations
Applications of the Integral
Trigonometric Functions
Trigonometry
Derivatives of Trigonometric Functions
Inverse Trigonometric Functions
Inverse Trigonometric Functions
Theorem 1: Inverse Function
Inverse Trigonometric Function - Definitions
Inverse Function Theorem
Theorem 2:
Theorem 3:
Examples
Example 1: Arc Sine
Example 2: Arc Sine
Example 3: Arc Tangent
Example 4: Arc Tangent
Example 5: Arc Sine and Arc Cosine
Example 6: Area Under a Curve
Example 7: Region Between Curve and Axis
Problems
Integration by Parts
Integrals of Powers of Trigonometric Functions
Trigonometric Substitututions
Polar Coordinates
Slopes And Curve Sketching in Polar Coordinates
Area in Polar Coordinates
Length of a Curve in Polar Coordinates
Extra Problems for Chapter 7
Exponential and Logartihmic Functions
Infinite Series
Vectors
Partial Differentiation
Multiple Integrals
Vector Calculus
Differential Equations
Appendix et Addenda
Last Update: 2011-01-22