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Calculus volume 3

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Cấu trúc

  • Preface

    • 1. About OpenStax

    • 2. About OpenStax's resources

    • 3. About Calculus Volume 3

    • 4. Additional resources

    • 5. About the authors

  • Chapter 1. Parametric Equations and Polar Coordinates

    • 1.1. Parametric Equations*

    • 1.2. Calculus of Parametric Curves*

    • 1.3. Polar Coordinates*

    • 1.4. Area and Arc Length in Polar Coordinates*

    • 1.5. Conic Sections*

    • Glossary

  • Chapter 2. Vectors in Space

    • 2.1. Vectors in the Plane*

    • 2.2. Vectors in Three Dimensions*

    • 2.3. The Dot Product*

    • 2.4. The Cross Product*

    • 2.5. Equations of Lines and Planes in Space*

    • 2.6. Quadric Surfaces*

    • 2.7. Cylindrical and Spherical Coordinates*

    • Glossary

  • Chapter 3. Vector-Valued Functions

    • 3.1. Vector-Valued Functions and Space Curves*

    • 3.2. Calculus of Vector-Valued Functions*

    • 3.3. Arc Length and Curvature*

    • 3.4. Motion in Space*

    • Glossary

  • Chapter 4. Differentiation of Functions of Several Variables

    • 4.1. Functions of Several Variables*

    • 4.2. Limits and Continuity*

    • 4.3. Partial Derivatives*

    • 4.4. Tangent Planes and Linear Approximations*

    • 4.5. The Chain Rule*

    • 4.6. Directional Derivatives and the Gradient*

    • 4.7. Maxima/Minima Problems*

    • 4.8. Lagrange Multipliers*

    • Glossary

  • Chapter 5. Multiple Integration

    • 5.1. Double Integrals over Rectangular Regions*

    • 5.2. Double Integrals over General Regions*

    • 5.3. Double Integrals in Polar Coordinates*

    • 5.4. Triple Integrals*

    • 5.5. Triple Integrals in Cylindrical and Spherical Coordinates*

    • 5.6. Calculating Centers of Mass and Moments of Inertia*

    • 5.7. Change of Variables in Multiple Integrals*

    • Glossary

  • Chapter 6. Vector Calculus

    • 6.1. Vector Fields*

    • 6.2. Line Integrals*

    • 6.3. Conservative Vector Fields*

    • 6.4. Green’s Theorem*

    • 6.5. Divergence and Curl*

    • 6.6. Surface Integrals*

    • 6.7. Stokes’ Theorem*

    • 6.8. The Divergence Theorem*

    • Glossary

  • Chapter 7. Second-Order Differential Equations

    • 7.1. Second-Order Linear Equations*

    • 7.2. Nonhomogeneous Linear Equations*

    • 7.3. Applications*

    • 7.4. Series Solutions of Differential Equations*

    • Glossary

  • Appendix A. Table of Integrals*

    • A.1. Basic Integrals

    • A.2. Trigonometric Integrals

    • A.3. Exponential and Logarithmic Integrals

    • A.4. Hyperbolic Integrals

    • A.5. Inverse Trigonometric Integrals

    • A.6. Integrals Involving a2 + u2, a > 0

    • A.7. Integrals Involving u2 − a2, a > 0

    • A.8. Integrals Involving a2 − u2, a > 0

    • A.9. Integrals Involving 2au − u2, a > 0

    • A.10. Integrals Involving a + bu, a ≠ 0

  • Appendix B. Table of Derivatives*

    • B.1. General Formulas

    • B.2. Trigonometric Functions

    • B.3. Inverse Trigonometric Functions

    • B.4. Exponential and Logarithmic Functions

    • B.5. Hyperbolic Functions

    • B.6. Inverse Hyperbolic Functions

  • Appendix C. Review of Pre-Calculus*

    • C.1. Formulas from Geometry

    • C.2. Formulas from Algebra

    • C.3. Formulas from Trigonometry

  • Solutions

    • Chapter 1

    • Chapter 2

    • Chapter 3

    • Chapter 4

    • Chapter 5

    • Chapter 6

    • Chapter 7

    • Index

  • CalculusVolume3.pdf

    • Blank Page

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