Calculus Guide

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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
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July 9, 2018
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