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Simple and convenient calculus guide.

This is a best way for you to learn calculus.

The following contents are provided :

CH 1 Function

 Function and Graphs

 Combining Function

 Trigonometric Function

CH 2 Limits and Continuity

 Limits of Sequences

 The Limit of a Function

 Continuity

CH 3 Derivatives

 Derivatives and Rates of Change

 Derivative as a function

 Differentiation Formulas

 Derivatives of Trigonometric Function

 Chain Rule and Implicit Differentiation

 Linear Approximation and Differential

CH 4 Applications of Differentiation

 Maximum and Minimum Value

 The Mean Value Theorem

 How Derivatives affect the shape of a graph

 Newton's Method

CH 5 Integrals

 Indefinite Integral

 Definite Integral

 Application of Integration

CH 6 Techniques of Integration

 Integration by Part

 Trigonometric Integrals

 Integration of Rational Functions by Partial Fractions

 Integral Formula

CH 7 Inverse Function

 Inverse Function

 Exponential Function and their Derivatives

 logarithmic function

 Inverse Trigonometric Functions

 Hyperbolic Function

 Indeterminate Form and L'Hospital's Rule

CH 8 Infinite Sequences and Series

 Sequence

 Series

 The Integral Test and Estimates of Sums

 The Comparison Test

 Alternating Series

 Absolute Convergence and The Ratio and Root Test

 Power Series

 Taylor and Maclaurin Series

CH 9 Vector

 Three-Dimensional Coordinate system

 Vectors

 The Dot Product

 The Cross Product

 Equation of Line and Planes

CH 10 Vector Functions

 Vector Functions and Space Curve

 Derivatives and Integrals of Vector Function

 Arc Length and Curvature

 Motion in Space: Velocity and Acceleration

CH 11 Partial Derivatives

 Functions of Several Variables

 Limits and Continuity

 Partial Derivatives

 Tangent Planes and Linear Approximations

 The Chain Rule

 Directional Derivatives and the Gradient Vector

 Maximum and Minimum Values

 Lagrange Multipliers

CH 12 Multiple Integrals

 Double Integrals over Rectangles

 Iterated Integrals

 Double Integrals over General Regions

 Double Integrals in Polar Coordinate

 Applications of Double Integrals

 Triple Integrals

 Triple Integrals in Cylindrical Coordinates and Spherical Coordinates

 Change of Variables In Multiple Integrals

CH 13 Vector Calculus

 Vector Fields

 Line Integrals

 The Fundamental Theorem for Line Integrals and Green's Theorem

 Curl and Divergence

 Surface Integrals

 Stokes' Theorem and The Divergence Theorem

Calculus Guide

Ancienne Version de Calculus Guide