Calculus References



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

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
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
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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