By John H. Hubbard

A pupil resolution guide - with recommendations for the 4th version of vector Calculus and Linear Algebra.

**Read Online or Download Vector Calculus, Linear Algebra, and Differential Forms (4th Edition): Student Solution Manual PDF**

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**Additional resources for Vector Calculus, Linear Algebra, and Differential Forms (4th Edition): Student Solution Manual**

**Example text**

1 , . :35, part (b): The locus of A2 I is given by in four unknowns, four expect it to be a so you union of finitely many points. This is not the case; the locus the surface of equation is a 2 + be 1: take any point of this surface and set d -a to find A such that I. There are two exceptional solutions not on this surface, ± I. 33 a. 9. At the origin, all partials exist and are 0, since the function vanishes identically on all three coordinate axes. b. 1, the function is differentiable everywhere except at the origin.

359i) . A3'. 359'i) . 282. Thus ClOOO has 265 digits. 63. 3 a. c: ; I:r - yl +yl Iy . . x yJ. b. Choose C > 0, and find x such that 1/2y'X > which will happen for x > a sufficiently small. From the definition of the derivative, 1 lim -'---- y X 60 Solutions for chapter 2 Thus taking y > x sufficiently close to x, we will find Since this is possible for every C > 0, we see that there cannot exist a number lIt such that IvY - JXI ::; Mly - xl for all x, y > O. 5 a. 083, X2 2x n s = +9 . 08008382306424.

It is best to think of first rotating the into the (x, z)- plane, then rotating it until it is horizontal (or vertical), then rotating it on its own and then rotating it back (in two steps). 1 a m -m1] 1 2 -3 n U j] -7 2 -4 1 2 -:3 b. 1 0 -3 -2 c. 3 a. [! 2 5 -; 1 b. 2 3 1 o [_: [l d [l 1 -3 1 3 2 -4 0 1 0 0 0 1 5 0 1 -2 0 0 i] 0 1 0 0 -1 3 2 3 -1 1 2 1 7 U -1 0 1 [1 2 3 '] [1 0 c. 1). , "adding (-·row i) to row j". You can undo "switching row i and row j" by "switching row i and row j" again.