Calculus References|教育線上App不用買

Calculus Reference will help you learn calculus concepts.

◆ Table of Contents ◆

CH 1 Functions

Functions and Graphs

Combining Functions

Trigonometric Functions

CH 2 Limits and Continuity

Limits of Sequences

The Limits of a Function

Continuity

CH 3 Derivatives

Derivatives and Rates of Chage

Derivative as a function

Differentiation Formulas

Derivatives of Trigonometric Functions

Chain Rule and Implicit Differentiation

Linear Approximation and Differential

CH 4 Applications of Differentiation

Maximum and Minimum Values

The Mean Value Theorem

How Derivatives affect the shape of a graph

Newton's Method

CH 5 Integrals

Indefinite Integral

Definite Integral

Applications of Integration

CH 6 Techniques of Integration

Integration by Part

Trigonometric Integrals

Integration of Rational Functions by Partial Fractions

Table of Integration Formulas

CH 7 Inverse Functions

Inverse Functions

Exponential Functions and their Derivatives

Logarithmic Functions

Inverse Trigonometric Functions

Hyperbolic Functions

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 Vectors

Three-Dimensional Coordinate Systems

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 Functions

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 Coordinates

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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