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Calculus A New Horizon Combined 6th Edition by Howard Anton



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Calculus A New Horizon Combined 6th Edition written by Howard Anton . This text is aimed at future engineers and professional scientists. Applications modules at the ends of chapters demonstrate the need to relate theoretical mathematical concepts to real world examples. These modules examine problem-solving as it occurs in industry or research settings, such as the use of wavelets in music and voice synthesis and in FBI fingerprint analysis and storage.

Calculus A New Horizon Combined 6th Edition written by Howard Anton cover the following topics.


  • 1. Functions
    1.1 Functions and the Analysis of Graphical lnformation
    1.2 Properties of Functions
    1.3 Graphing Functions on Calculators and Computers; Computer Algebra Systems
    1.4 New Functions {rom Old
    1.5 Mathematical Models; Linear Models
    1.6 Families of Functions
    1.7 ParametricEquations
    Horizon Module: lteration and Dynamical Systems

  • 2. Limit and AND Continuity
    2.1 Limits (An lntuitive lntroduction)
    2.2 Limits(ComputationalTechniques)
    2.3 Limits (Discussed More Rigorously)
    2.4 Continuity
    2.5 Limits and Continuity of Trigonometric Functions

  • 3. The Derivative
    3.1 Tangent Lines and Rates of Change
    3.2 The Derivative
    3.3 Techniques of.Differentiation
    3.4 Derivatives of Trigonometric Functions
    3.5 The Chain Rule
    3.6 Local LinearApproximation; Differentials
    Horizon Module e: Robotics

  • 4. Logarithmic and Exponential Funtions
    4.1 lnverse Functions
    4.2 Logarithmic and Exponential Functions
    4.3 lmplicitDifferentiation
    4.4 Derivatives of Logarithmic and Exponential Functions
    4.5 Derivatives of Inverse Trigonometric Functions
    4.6 Related Rates
    4.7 L Hopital s Rule; lndeterminate Forms

  • 5. Analysis of Functions and their Graphs
    5.1 Analysis of Functions l: lncrease, Decrease, and Concavity
    5.2 Ana ysis of Functions ll: Relative Extrema; First and Second Derivative Tests
    5.3 Analysis of Functions lll: Applying Technology and the Tools of Calculus
    5.4 Horizontal Module: Functions from Data

  • 6. Application of the derivative
    6.1 Absolute Maxima and Minima
    6.2 Applied Maximum and Minimum Problems
    6.3 Rectilinear Motion (Motion Along a Line)
    6.4 Newton's Method
    6.5 Rolle s Theorem; Mean-Value Theorem

  • 7. Integration
    7.1 An Overview of the Area Problem
    7.2 The lndefinite lntegral; lntegral Curves and Direction Fields
    7.3 lntegration by Substitution
    7.4 Sigma Notation
    7.5 The Definite lntegral
    7.6 The Fundamental Theorem of Calculus
    7.7 Rectilinear Motion Revisited; Average Value
    7.8 Evaluating Definite lntegrals by Substitution
    7.9 Logarithmic Functions from the lntegral Pojnt of View
    7.10 Hor zon Module: Blammo the Human Cannonbal

  • 8. Application of Definite Integral in Geometry and Science and Engineering
    8.1 Area Between Two Curves
    8.2 Volumes by Slicing; Disks and Washers
    8.3 Volumes by Cyhndrrcal Shells
    8.4 Length o{ a Plane Curve
    8.5 Area of a Surface of Revolution
    8.6 Work
    8.7 Fluid Pressure and Force
    8.8 Hyperbolic Functions and Hanging Cables

  • 9. Principle of Integral Equations
    9.1 An Overview of lntegration Methods
    9.2 lntegration by Parts 516
    9.3 Trigonometriclntegrals
    9.4 Trigonometric Substitutions
    9.5 lntegrating Rational Functions by Partial Fractions
    9.6 Using Tables of lntegrals and Computer Algebra Systems
    9.7 Numerical lntegration; Simpson's Rule
    9.8 lmproper lntegrals
    9.9 Honzil [,'locLr e Ri rl::r] les gn

  • 10. Mathematical Methods with Differential Equations
    10.1 Frrst-Order Differential Equations and Applications
    10.2 Direction Fields; Euler's Method
    10.3 Modeling with Differential Equations

  • 11. Infinite Series
    11.1 Sequences
    11.2 Monotone Sequences
    11.3 lnfinite Series
    11.4 Convergence Tests
    1i.5 Taylor and Maclaurin Series
    1i.6 The Comparison, Ratio, and Root Tests
    11.7 Alternating Series; Conditional Convergence
    11.8 Power Series
    11.9 Convergence of Taylor Series; Computational Methods
    11.10 Differentiating and Integrating Power Series; Modeling with Taylor Series

  • 12 Analytical Geometry in Calculus
    12.1 Polar Coordinates
    12.2 Tangent Lines and Arc Length for Parametric and Polar Curves
    12.3 Area in Polar Coordinates
    12.4 Conic Sectrons in Calculus
    12.5 Conic Sectrons in Polar Coordinates
    12.6 Horizon Module: Comet Col sion

  • 13. Three-Dimentional Space; Vectors
    13.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces
    13.2 Vectors
    13.3 Dot Product; Projections
    13.4 Cross Product
    13.5 Parametrjc Equations of Lines
    13.6 Planes in 3-Space
    13.7 Quadric Surfaces
    13.8 Cylindr cal and Spherical Coordinates

  • 14. Vector Values Functions
    l4.l lntroduction to Vector-Valued Functions
    14.2 Calculus of Vector-Valued Functions
    14.3 Change of Parameter; Arc Length
    14.4 Unit Tangent, Normal, and Binormal Vectors
    14.5 Curvature
    14.6 lVotion Along a Curve
    14.7 Kepler's Laws o{ Planetary lVotion

  • 15. Partial Derivative
    15.1 Functions of Two or More Variables
    15.2 Limits and Continuity
    15.3 Partial Derivatives
    15.4 Differentiability and Chain Rules
    15.5 Tangent Planes; Total Differentials for Functrons of Two Variables
    15.6 Directional Derivatives and Grad ents for Functions of Two Variables
    15.7 Differentiability, Directional Derivatives, and Gradients for Functions of Three or More Variables
    15.8 Maxima and Minima of Functions o{ Two Variables
    15.9 Lagrange Multipllers

  • 16. Multiple Integral
    16.1 Double lntegrals
    16.2 Double lntegrals over Nonrectangular Regions 985 f6.3 Double lntegrals in Polar Coordinates
    16.4 Parametric Surfacesi Surface Area
    16.5 Triple lntegrals
    16.6 Centroid, Center of Gravity, Theorem of Pappus
    16.7 Triple lntegrals in Cylindrical and Spherical Coordinates
    16.8 Change ot Variables in lVlultiple Integrals; Jacobians

  • 17. Topics in vector Calculus
    17.l Vector Fields
    17.2 Line lntegrals
    17.3 lndependence of Path; Conservative Vector Fields
    17.4 Green's Theorem
    17.5 Surface Integrals
    17.6 Applications of Surface Integrals; Flux
    17.7 The Divergence Theorem
    17.8 Stokes' Theorem

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