By Sudhir R. Ghorpade, Balmohan V. Limaye

ISBN-10: 1441916210

ISBN-13: 9781441916211

This self-contained textbook provides an intensive exposition of multivariable calculus. it may be seen as a sequel to the one-variable calculus textual content, A path in Calculus and genuine research, released within the comparable sequence. The emphasis is on correlating common innovations and result of multivariable calculus with their opposite numbers in one-variable calculus. for instance, whilst the overall definition of the quantity of a high-quality is given utilizing triple integrals, the authors clarify why the shell and washing machine equipment of one-variable calculus for computing the quantity of a fantastic of revolution needs to supply an analogous resolution. additional, the booklet contains actual analogues of simple ends up in one-variable calculus, resembling the suggest worth theorem and the elemental theorem of calculus.

This booklet is unusual from others at the topic: it examines themes no longer quite often coated, reminiscent of monotonicity, bimonotonicity, and convexity, including their relation to partial differentiation, cubature principles for approximate overview of double integrals, and conditional in addition to unconditional convergence of double sequence and wrong double integrals. in addition, the emphasis is on a geometrical method of such simple notions as neighborhood extremum and saddle point.

Each bankruptcy comprises designated proofs of correct effects, besides a number of examples and a large selection of workouts of various levels of hassle, making the booklet important to undergraduate and graduate scholars alike. there's additionally an informative component of "Notes and Comments’’ indicating a few novel positive factors of the remedy of issues in that bankruptcy in addition to references to appropriate literature. the one prerequisite for this article is a path in one-variable calculus.

**Read Online or Download A Course in Multivariable Calculus and Analysis (Undergraduate Texts in Mathematics) PDF**

**Best calculus books**

**Download PDF by David S. Kahn: Cracking the AP Calculus AB & BC Exams (2014 Edition)**

Random apartment, Inc.

THE PRINCETON evaluation will get effects. Get all of the prep you want to ace the AP Calculus AB & BC checks with five full-length perform checks, thorough subject studies, and confirmed recommendations that can assist you ranking greater. This book variation has been optimized for on-screen viewing with cross-linked questions, solutions, and explanations.

Inside the e-book: the entire perform & concepts You Need

• five full-length perform exams (3 for AB, 2 for BC) with designated motives

• resolution causes for every perform question

• accomplished topic experiences from content material specialists on all attempt topics

• perform drills on the finish of every chapter

• A cheat sheet of key formulas

• step by step innovations & concepts for each part of the exam

THE PRINCETON evaluation will get effects. Get all of the prep you want to ace the AP Calculus AB & BC checks with five full-length perform assessments, thorough subject experiences, and confirmed suggestions that will help you rating higher.

Inside the ebook: the entire perform & innovations You Need

• five full-length perform exams (3 for AB, 2 for BC) with particular reasons

• resolution motives for every perform question

• finished topic studies from content material specialists on all try topics

• perform drills on the finish of every chapter

• A cheat sheet of key formulas

• step by step techniques & recommendations for each part of the examination

**Extra resources for A Course in Multivariable Calculus and Analysis (Undergraduate Texts in Mathematics)**

**Example text**

Xn ) is uniquely determined by the function f . 37. Let (x0 , y0 ) and (x1 , y1 ) be any two points in R2 and let Γ be a path joining them, that is, Γ is the path given by (x(t), y(t)), t ∈ [α, β], where x, y : [α, β] → R are continuous functions with (x(α), y(α)) = (x0 , y0 ) and (x(β), y(β)) = (x1 , y1 ). Prove that the image of Γ , that is, the set {(x(t), y(t)) : t ∈ [α, β]}, is a closed and path-connected subset of R2 . 38. Let I and J be nonempty intervals in R and let f : I × J → R be any function that is bimonotonically increasing as well as bimonotonically decreasing.

Y y Γ1 Γ x Γ2 Γ3 x Fig. 8. A nonregular path Γ and regular paths Γ1 , Γ2 , Γ3 ; note that Γ1 and Γ2 as well as Γ1 and Γ3 intersect transversally, but Γ2 and Γ3 do not. For example, the path Γ given by (t2 , t3 ), t ∈ [−1, 1], is not a regular path. ) On the other hand, consider the paths Γ1 , Γ2 , and Γ3 given by (t, −t), (t, t), and (2t + t2 , 2t − t2 ), respectively, with t ∈ [−1, 1] in each case. Each of these paths is regular and passes through the origin (0, 0). The tangent vectors to Γ1 , Γ2 , and Γ3 at the origin are (1, −1), (1, 1), and (2, 2), respectively.

Define f, g : [a, b] × [c, d] → R by f (x, y) := φ(x) + ψ(y) and g(x, y) := φ(x)ψ(y). (i) Show that f is of bounded variation on [a, b] × [c, d] if and only if φ is of bounded variation on [a, b] and ψ is of bounded variation on [c, d]. (ii) Assume that φ and ψ are not identically zero, that is, φ(x0 ) = 0 and ψ(y0 ) = 0 for some x0 ∈ [a, b] and y0 ∈ [c, d]. Show that g is of bounded variation on [a, b] × [c, d] if and only if φ is of bounded variation on [a, b] and ψ is of bounded variation on [c, d].

### A Course in Multivariable Calculus and Analysis (Undergraduate Texts in Mathematics) by Sudhir R. Ghorpade, Balmohan V. Limaye

by Kenneth

4.2