Multivariate calculus provides the framework for handling systems having many variables associated with each of several bodies. We introduced variational calculus which covers several important aspect...Multivariate calculus provides the framework for handling systems having many variables associated with each of several bodies. We introduced variational calculus which covers several important aspects of multivariate calculus such as Euler’s variational calculus and Lagrange multipliers. This appendix provides a brief review of a selection of other aspects of multivariate calculus that feature prominently in classical mechanics.
Of course, the xi’s are just ordinary perpendicular Cartesian axes so the volume is just the product of the three sides of the little box, dx1dx2dx3.Imagine this little box, i...Of course, the xi’s are just ordinary perpendicular Cartesian axes so the volume is just the product of the three sides of the little box, dx1dx2dx3.Imagine this little box, its corner closest to the origin at (x1,x2,x3) and its furthest point at the other end of the body diagonal at (x1+dx1,x2+dx2,x3+dx3) Let’s take these two points in the qi coordinates to be at \(\left(q_{1}, q_{2}, q_{3}\right) \text { …
