11.1 Three-Dimensional Coordinate Systems  

11.2 Vectors 

 11.3 The Dot Product  

 11.4 The Vector or Cross Product    

  11.5 Equations of Lines and Planes  

11.6 Cylinders and Quadric Surfaces 

       Chapter 12. Vector Valued Functions

 12.1 Vector-Valued Functions and Space Curves 

  12.2 Calculus of Vector Functions 

12.3 Arc Length and Curvature   

*12.4 Motion Along A Space Curve: Velocity and Acceleration

       Chapter 13. Partial Derivatives

 13.1 Multivariate Functions 

 13.2 Limits and Continuity of Multivariate Functions  

13.3 Partial Derivatives  

13.4 Differentiability and Total Differentials 

13.5 The Chain Rule

 13.6 Directional Derivatives and Gradient 

13.7 Tangent Plane and Differentiability  

13.8 Extrema of Multivariate Functions 

13.9 Lagrange Multiplier  

     Chapter 14. Multiple Integrals

 14.1 Double Integrals 

 14.2 Double Integrals in Polar Coordinates 

14.3 Surface Area 

 14.4 Cylindrical Coordinates and Spherical Coordinates 

14.5 Triple Integrals  

 14.6 Triple Integrals in Cylindrical and Spherical Coordinates  

14.7 Change of Variables in Multiple Integrals 

       Chapter 15. Vector Calculus

 15.1 Vector Differentiation

 15.2 Line Integrals 

15.3 Independence of the Path   

 15.4 Green’s Theorem in Plane  

15.5 Curl and Divergence    

 15.6 Surface and Area  

15.7 Surface Integrals

 15.8 Stokes’ Theorem   

15.9 Divergence Theorem 

References

Index