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Calculus References

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    Calculus References

    by: HYUNKYOIC 271 8.4

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    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

    [hyunkyoic math series]

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