Contents

• Chapter 12: Vectors and geometry of space

  • 12.1 Three dimensional coordinate system

  • 12.2 Vectors

  • 12.3 The dot product

  • 12.4 The cross product

  • 12.5 Equations of lines and planes

  • 12.6 Quadratic surfaces

• Chapter 13: Vector functions

  • 13.1 Vector functions and space curves

  • 13.2 Derivatives and integrals of vector functions

  • 13.3 Arc length and curvature

  • 13.4 Motion in space: velocity and acceleration

• Chapter 14: Functions of several variables, partial derivatives

  • 14.1 Functions of several variables

  • 14.2 Limits and continuity

  • 14.3 Partial derivatives

  • 14.4 Tangent planes and linear approximation

  • 14.5 The chain rule

  • 14.6 Directional derivatives and the gradient

  • 14.7 Maximum and minimum values

  • 14.8 Lagrange multipliers

  • 14.9 Taylor series for functions of several variables* (not in the book)

• Chapter 15: Multiple integrals

  • 15.1 Double integrals over rectangles

  • 15.2 Iterated integrals

  • 15.3 Double integrals over general regions

  • 15.4 Double integrals in polar coordinates

  • 15.5 Applications of double integrals

  • 15.6 Surface area

  • 15.7 Triple integrals

  • 15.8 Triple integrals in cylinder coordinates

  • 15.9 Triple integrals in spherical coordinates

  • 15.10 Change of variables in multiple integrals

• Chapter 16: Vector Calculus

  • 16.1 Vector fields

  • 16.2 Line integrals

  • 16.3 The fundamental theorem of line integrals

  • 16.4 Green's theorem

  • 16.5 Curl and divergence

  • 16.6 Parametric surfaces and their areas

  • 16.7 Surface integrals

  • 16.8 Stoke's theorem

  • 16.9 The divergence theorem