This text explores the standard problem-solving techniques of multivariable
mathematics integrating vector algebra ideas with multivariable
calculus and differential equations.
offers flexibility in coverage topics can be
covered in a variety of orders, and subsections (which are presented
in order of decreasing importance) can be omitted if desired.
provides proofs and includes the definitions and statements
of theorems to show how the subject matter can be organized around
a few central ideas.
NEWincludes new sections on:
flow lines and flows.
centroids and moments.
arc-length and curvature.
NEWpresents refined method for solving linear
systems using exponential matrices.
NEWadds a chapter on infinite series
with application to differential equations.
contains an abundance of applications and worked
examples and discussion problems.
provides many routine, computational exercises illuminating
both theory and practice.
NEWprovides 50% more problems.
2. Dot and Cross Products.
3. Equations and Matrices.
6. Vector Differential Calculus.
7. Multiple Integration.
8. Integrals and Derivatives on Curves.
9. Vector Field Theory.
10. First-Order Differential Equations.
11. Constant-Coefficient Equations.
12. Introduction to Systems.
13. Matrix Methods.
14. Infinite Series.
Appendix: Finding Indefinite Integrals.
Ansaers and Hints.