Calculus-대학미적분학(영문)

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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 Chage

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

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