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Multivariable Calculus (9th Edition) by Ron Larson, Bruce H. Edwards



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Multivariable Calculus (9th Edition) by Ron Larson , The Pennsylvania State University, The Behrend College and Bruce H. Edwards , University of Florida.
Explorations provide students with unique challenges to study concepts that have not yet been formally covered. They allow students to learn by discovery and introduce topics related to ones they are presently studying. By exploring topics in this way, students are encouraged to think outside the box. Historical Notes provide students with background information on the foundations of calculus, and Biographies help humanize calculus and teach students about the people who contributed to its formal creation. Putnam Exam questions appear in selected sections and are drawn from actual Putnam Exams. These exercises will push the limits of students’ understanding of calculus and provide extra challenges for motivated students.
Theorems provide the conceptual framework for calculus. Theorems are clearly stated and separated from the rest of the text by boxes for quick visual reference. Key proofs often follow the theorem, and other proofs are provided in an in-text appendix. As with the theorems, definitions are clearly stated using precise, formal wording and are separated from the text by boxes for quick visual reference.

Multivariable Calculus (9th Edition) by Ron Larson, Bruce H. Edwards cover the following topics.


  • 11. Vectors and the Geometry of Space
    11.1 Vectors in the Plane
    11.2 Space Coordinates and Vectors in Space
    11.3 The Dot Product of Two Vectors
    11.4 The Cross Product of Two Vectors in Space
    11.5 Lines and Planes in Space
    11.6 Surfaces in Space
    11.7 Cylindrical and Spherical Coordinates

  • 12. Vector-Valued Functions
    12.1 Vector-Valued Functions
    12.2 Differentiation and Integration of Vector-Valued Functions
    12.3 Velocity and Acceleration
    12.4 Tangent Vectors and Normal Vectors
    12.5 Arc Length and Curvature

  • 13. Functions of Several Variables
    13.1 Introduction to Functions of Several Variables
    13.2 Limits and Continuity
    13.3 Partial Derivatives
    13.4 Differentials
    13.5 Chain Rules for Functions of Several Variables
    13.6 Directional Derivatives and Gradients
    13.7 Tangent Planes and Normal Lines
    13.8 Extrema of Functions of Two Variables
    13.9 Applications of Extrema of Functions of Two Variables
    13.10 Lagrange Multipliers

  • 14. Multiple Integration
    14.1 Iterated Integrals and Area in the Plane
    14.2 Double Integrals and Volume
    14.3 Change of Variables: Polar Coordinates
    14.4 Center of Mass and Moments of Inertia
    14.5 Surface Area
    14.6 Triple Integrals and Applications
    14.7 Triple Integrals in Cylindrical and Spherical Coordinates
    14.8 Change of Variables: Jacobians

  • 15. Vector Analysis
    15.1 Vector Fields
    15.2 Line Integrals
    15.3 Conservative Vector Fields and Independence of Path
    15.4 Green
    s Theorem
    15.5 Parametric Surfaces
    15.6 Surface Integrals
    15.7 Divergence Theorem
    15.8 Stokes
    s Theorem

  • 16. Additional Topics in Differential Equations
    16.1 Exact First-Order Equations
    16.2 Second-Order Homogeneous Linear Equations
    16.3 Second-Order Nonhomogeneous Linear Equations
    16.4 Series Solutions of Differential Equations

  • Appendix
    A.Proofs of Selected Theorems A2
    B.Integration Tables A21
    C.Precalculus Review(Online)
    D.Rotation and the General Second-Degree Equation (Online)
    E.Complex Numbers(Online)
    F.Business and Economic Applications (Online)

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