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Produktbild: University Calculus: Early Transcendentals, Multivariable
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University Calculus: Early Transcendentals, Multivariable

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

28.09.2024

Verlag

Pearson Education Limited

Seitenzahl

576

Maße (L/B/H)

27,6/21,6/3,2 cm

Gewicht

1418 g

Auflage

4

Sprache

Englisch

ISBN

978-0-13-516511-9

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

28.09.2024

Verlag

Pearson Education Limited

Seitenzahl

576

Maße (L/B/H)

27,6/21,6/3,2 cm

Gewicht

1418 g

Auflage

4

Sprache

Englisch

ISBN

978-0-13-516511-9

Herstelleradresse

Pearson
St.-Martin-Straße 82
81541 München
DE

Email: salesde@pearson.com

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  • Produktbild: University Calculus: Early Transcendentals, Multivariable





    1. Functions



      • 1.1 Functions and Their Graphs


      • 1.2 Combining Functions; Shifting and Scaling Graphs


      • 1.3 Trigonometric Functions


      • 1.4 Graphing with Software


      • 1.5 Exponential Functions


      • 1.6 Inverse Functions and Logarithms







    2. Limits and Continuity



      • 2.1 Rates of Change and Tangent Lines to Curves


      • 2.2 Limit of a Function and Limit Laws


      • 2.3 The Precise Definition of a Limit


      • 2.4 One-Sided Limits


      • 2.5 Continuity


      • 2.6 Limits Involving Infinity; Asymptotes of Graphs







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    3. Derivatives



      • 3.1 Tangent Lines and the Derivative at a Point


      • 3.2 The Derivative as a Function


      • 3.3 Differentiation Rules


      • 3.4 The Derivative as a Rate of Change


      • 3.5 Derivatives of Trigonometric Functions


      • 3.6 The Chain Rule


      • 3.7 Implicit Differentiation


      • 3.8 Derivatives of Inverse Functions and Logarithms


      • 3.9 Inverse Trigonometric Functions


      • 3.10 Related Rates


      • 3.11 Linearization and Differentials







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    4. Applications of Derivatives



      • 4.1 Extreme Values of Functions on Closed Intervals


      • 4.2 The Mean Value Theorem


      • 4.3 Monotonic Functions and the First Derivative Test


      • 4.4 Concavity and Curve Sketching


      • 4.5 Indeterminate Forms and LHôpitals Rule


      • 4.6 Applied Optimization


      • 4.7 Newtons Method


      • 4.8 Antiderivatives







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    5. Integrals



      • 5.1 Area and Estimating with Finite Sums


      • 5.2 Sigma Notation and Limits of Finite Sums


      • 5.3 The Definite Integral


      • 5.4 The Fundamental Theorem of Calculus


      • 5.5 Indefinite Integrals and the Substitution Method


      • 5.6 Definite Integral Substitutions and the Area Between Curves







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    6. Applications of Definite Integrals



      • 6.1 Volumes Using Cross-Sections


      • 6.2 Volumes Using Cylindrical Shells


      • 6.3 Arc Length


      • 6.4 Areas of Surfaces of Revolution


      • 6.5 Work


      • 6.6 Moments and Centers of Mass







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    7. Integrals and Transcendental Functions



      • 7.1 The Logarithm Defined as an Integral


      • 7.2 Exponential Change and Separable Differential Equations


      • 7.3 Hyperbolic Functions







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    8. Techniques of Integration



      • 8.1 Integration by Parts


      • 8.2 Trigonometric Integrals


      • 8.3 Trigonometric Substitutions


      • 8.4 Integration of Rational Functions by Partial Fractions


      • 8.5 Integral Tables and Computer Algebra Systems


      • 8.6 Numerical Integration


      • 8.7 Improper Integrals







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    9. Infinite Sequences and Series



      • 9.1 Sequences


      • 9.2 Infinite Series


      • 9.3 The Integral Test


      • 9.4 Comparison Tests


      • 9.5 Absolute Convergence; The Ratio and Root Tests


      • 9.6 Alternating Series and Conditional Convergence


      • 9.7 Power Series


      • 9.8 Taylor and Maclaurin Series


      • 9.9 Convergence of Taylor Series


      • 9.10 Applications of Taylor Series







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    10. Parametric Equations and Polar Coordinates



      • 10.1 Parametrizations of Plane Curves


      • 10.2 Calculus with Parametric Curves


      • 10.3 Polar Coordinates


      • 10.4 Graphing Polar Coordinate Equations


      • 10.5 Areas and Lengths in Polar Coordinates







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    11. Vectors and the Geometry of Space



      • 11.1 Three-Dimensional Coordinate Systems


      • 11.2 Vectors


      • 11.3 The Dot Product


      • 11.4 The Cross Product


      • 11.5 Lines and Planes in Space


      • 11.6 Cylinders and Quadric Surfaces







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    12. Vector-Valued Functions and Motion in Space



      • 12.1 Curves in Space and Their Tangents


      • 12.2 Integrals of Vector Functions; Projectile Motion


      • 12.3 Arc Length in Space


      • 12.4 Curvature and Normal Vectors of a Curve


      • 12.5 Tangential and Normal Components of Acceleration


      • 12.6 Velocity and Acceleration in Polar Coordinates







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    13. Partial Derivatives



      • 13.1 Functions of Several Variables


      • 13.2 Limits and Continuity in Higher Dimensions


      • 13.3 Partial Derivatives


      • 13.4 The Chain Rule


      • 13.5 Directional Derivatives and Gradient Vectors


      • 13.6 Tangent Planes and Differentials


      • 13.7 Extreme Values and Saddle Points


      • 13.8 Lagrange Multiplier







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    14. Multiple Integrals



      • 14.1 Double and Iterated Integrals over Rectangles


      • 14.2 Double Integrals over General Regions


      • 14.3 Area by Double Integration


      • 14.4 Double Integrals in Polar Form


      • 14.5 Triple Integrals in Rectangular Coordinates


      • 14.6 Applications


      • 14.7 Triple Integrals in Cylindrical and Spherical Coordinates


      • 14.8 Substitutions in Multiple Integrals







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    15. Integrals and Vector Fields



      • 15.1 Line Integrals of Scalar Functions


      • 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux


      • 15.3 Path Independence, Conservative Fields, and Potential Functions


      • 15.4 Greens Theorem in the Plane


      • 15.5 Surfaces and Area


      • 15.6 Surface Integrals


      • 15.7 Stokes Theorem


      • 15.8 The Divergence Theorem and a Unified Theory







      • Questions to Guide Your Review



      • Practice Exercises



      • Additional and Advanced Exercises







    16. First-Order Differential Equations (online at bit.ly/2pzYlEq)



      • 16.1 Solutions, Slope Fields, and Eulers Method


      • 16.2 First-Order Linear Equations


      • 16.3 Applications


      • 16.4 Graphical Solutions of Autonomous Equations


      • 16.5 Systems of Equations and Phase Planes







    17. Second-Order Differential Equations (online at bit.ly/2IHCJyE)



      • 17.1 Second-Order Linear Equations


      • 17.2 Non-homogeneous Linear Equations


      • 17.3 Applications


      • 17.4 Euler Equations


      • 17.5 Power-Series Solutions







    Appendix


    • A.1 Real Numbers and the Real Line


    • A.2 Mathematical Induction


    • A.3 Lines and Circles


    • A.4 Conic Sections


    • A.5 Proofs of Limit Theorems


    • A.6 Commonly Occurring Limits


    • A.7 Theory of the Real Numbers


    • A.8 Complex Numbers


    • A.9 The Distributive Law for Vector Cross Products


    • A.10 The Mixed Derivative Theorem and the increment Theorem



    Additional Topics (online)


    • B.1 Relative Rates of Growth


    • B.2 Probability


    • B.3 Conics in Polar Coordinates


    • B.4 Taylors Formula for Two Variables


    • B.5 Partial Derivatives with Constrained Variables



    Odd Answers