Calculus Guide

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