Download Vector and Geometric Calculus by Alan Macdonald PDF

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By Alan Macdonald

This textbook for the undergraduate vector calculus path offers a unified remedy of vector and geometric calculus.

This is a fourth printing, corrected and a bit revised.

The e-book is a sequel to the textual content Linear and Geometric Algebra through an analogous writer. That textual content is a prerequisite for this one. Its website is at
Linear algebra and vector calculus have supplied the elemental vocabulary of arithmetic in dimensions more than one for the previous 100 years. simply as geometric algebra generalizes linear algebra in robust methods, geometric calculus generalizes vector calculus in robust ways.

Traditional vector calculus themes are coated, as they have to be, because readers will come across them in different texts and out within the world.

Differential geometry is used this present day in lots of disciplines. a last bankruptcy is dedicated to it.

Visit the book's website at to obtain its desk of contents, preface, and index.

From a assessment of Linear and Geometric Algebra:
Alan Macdonald's textual content is a superb source while you are simply starting the research of geometric algebra and want to study or overview conventional linear algebra within the method. The readability and evenness of the writing, in addition to the originality of presentation that's glaring all through this article, recommend that the writer has been winning as a arithmetic instructor within the undergraduate lecture room. This rigorously crafted textual content is perfect for an individual studying geometric algebra in relative isolation, which i believe stands out as the case for plenty of readers.
-- Jeffrey Dunham, William R. Kenan Jr. Professor of normal Sciences, Middlebury collage

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Additional info for Vector and Geometric Calculus

Sample text

19. Define f: R2 ->• R2 by f ( x \ , x 2 ) = (a:2, ,Ti + X2 ). 20. a. Let f (x ,y, z) = (x 2z , x + y + z). Compute [f(-a. 2j], I). Using P art (a), compute [f^ [h] in terms of the components of h. 21. ' Compute |ffr ,,-)]• Use SymPy. , . 22. Lei, f : II" —> K" be differentiable at x. When will jf^j be a diagonal matrix? If f : E m —:>]Rr" is differentiable a t x, then the outennorphism extension of f ' satisfies f£(l) = det (f^)I (LAGA Eq. )). Jacobian determinant of f not involving partial derivatives: del (f^j (i ; *.

3) parameterize 1 -, 2-, and 3-dimensional man­ ifolds in R ". We can also parameterize manifolds of higher dimension. ■ For example, this is a parameterization of the 3-dimensional boundary of the 4dimensional ball of radius p in R 4: x(«/\ ,9) = p cos tp i + p sin V; sin cos 6 j + p sin ip sin sin 6 k + p sin ip cos <61, 0 < i/> < tt> 0 < ■ M C R n .

The graph of function f ( x ) — x l-/4 is shown in Fig­ ure 4,5. The graph has a tangent line at the origin. The line is vertical, so / '( 0 ) does not exist. The graph can be param ­ eterized x(/;) = (t, t l l A). B ut x ' does not exist at the origin. Parameterize the curve so th a t x'(Q) exists, is not zero, and is tangent to the curve. 4 . 2 . 3 . Let x ( t ) : [o,6j -> C parameterize a curve which does p jg _ 4 5. V = x l '/ 3 not pass through the origin. Suppose th a t x(to). a < to < b is a point on C closest to the origin.

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