Calculus@UTK 241 Table of Contents


241 Syllabus

141 Table of Contents

142 Table of Contents

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9. Vectors and the Geometry of Space

  1. Three-Dimensional Coordinate Systems
  2. Vectors
  3. The Dot Product
  4. The Cross Product
  5. Equations of Lines and Planes
  6. Functions and Surfaces
  7. Cylindrical and Spherical Coordinates

10. Vector Functions

  1. Vector Functions and Space Curves
  2. Derivatives and Integrals of Vector Functions
  3. Arc Length and Curvature
  4. Motion in Space
  5. Parametric Surfaces

11. Partial Derivatives

  1. Functions of Several Variables
  2. Limits and Continuity
  3. Partial Derivatives
  4. Tangent Planes and Linear Approximations
  5. The Chain Rule
  6. Directional Derivatives and the Gradient Vector
  7. Maximum and Minimum Values
  8. Lagrange Multipliers

12. Multiple Integrals

  1. Double Integrals over Rectangles
  2. Iterated Integrals
  3. Double Integrals over General Regions
  4. Double Integrals in Polar Coordinates
  5. Applications of Double Integrals
  6. Surface Area
  7. Triple Integrals
  8. Triple Integrals in Cylindrical and Spherical Coordinates
  9. Change of Variables in Multiple Integrals

13. Vector Calculus

  1. Vector Fields
  2. Line Integrals
  3. The Fundamental Theorem for Line Integrals
  4. Green's Theorem
  5. Curl and Divergence
  6. Surface Integrals
  7. Stokes' Theorem
  8. The Divergence Theorem
  9. Summary


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