[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-186580-en":3,"doc-seo-186580-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},186580,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",4,"Exam","Advanced Calculus - Revised Edition","Advanced Calculus is an honors-level textbook built on rigorous one-variable calculus foundations, paired with linear algebra prerequisites. It develops differential calculus on normed vector spaces in the early chapters, then extends to differentiable manifolds through differential and integral calculus. The book emphasizes core results, optional starred sections, and multiple perspectives on key theorems such as the implicit function theorem and calculus of variations, supplemented by exercises.","LYNN H.LO0MIS and SHLOM O STER NBERGDepartment of Mathematics,Harvard University  \n# AD VAN CE D CAL CULU S\n\nREVISED EDITION  \nJONES AND BARTLETT PUBLISHERS  \nBoston  \nLondon  \nEditorial,Sales,and Customer Service Offices:  \nJones and Bartlett Publishers,Inc.One Exeter PlazaBoston,MA 02116  \nJones and Bartlett Publishers InternationalPO Box 1498London W67RSEngland  \nCopyright C1990 by Jones and Bartlett Publishers,Inc.Copyright C1968 by Addison-Wesley Publishing Company,Inc.  \nAll rights reserved.No part of the material protected by this copyright noticemay be reproduced or utilized in any form,electronic or mechanical,includingphotocopying,recording,or by any information storage and retrieval system,without written permission from the copyright owner.  \nPrinted in the United States of America.  \n1098765432  \nLibrary of Congress Cataloging-in-Publication Data  \nLoomis,Lynn H.  \nAdvanced calculus/Lynn H.Loomis and Shlomo Sternberg.-Rev.ed.p.cm.  \nOriginally published:Reading,Mass.:Addison-Wesley Pub.Co.,1968.  \nISBN 0-86720-122-3  \n1.Calculus.I.Sternberg,Shlomo.II.Title.  \nQA303.L871990  \n89-15620  \nS15--dc20  \nCIP  \nK9  \nPREFACE  \nThis book is based on an honors course in advanced calculus that we gave in the1960's.The foundational material,presented in the unstarred sections of Chap-ters 1 through 11,was normally covered,but different applications of this basicmaterial were stressed from year to year,and the book therefore contains morematerial than was covered in any one year.It can accordingly be used(withomissions)as a text for a year's course in advanced calculus,or as a text for athree-semester introduction to analysis.  \nThese prerequisites are a good grounding in the calculus of one variablefrom a mathematically rigorous point of view,together with some acquaintancewith linear algebra.The reader should be familiar with limit and continuity typearguments and have a certain amount of mathematical sophistication.As possi-ble introductory texts,we mention Differential and Integral Caleulus by R.Cou-rant,Calculus by T.Apostol,Calculus by M.Spivak,and Pure Mathematics by  \nG.Hardy.The reader should also have some experience with partial derivatives.  \nIn overall plan the book divides roughly into a first half which develops thecaleulus(principally the differential caleulus)in the setting of normed vectorspaces,and a second half which deals with the calculus of differentiable manifolds.  \nVector space calculus is treated in two chapters,the differential calculus inChapter 3,and the basic theory of ordinary differential equations in Chapter 6.The other early chapters are auxiliary.The first two chapters develop the neces-sary purely algebraic theory of vector spaces,Chapter 4 presents the materialon compactness and completeness needed for the more substantive results ofthe calculus,and Chapter 5 contains a brief account of the extra structure en-countered in scalar product spaces.Chapter 7 is devoted to multilinear(tensor)algebra and is,in the main,a reference chapter for later use.Chapter 8 dealswith the theory of (Riemann)integration on Euelidean spaces and includes(inexercise form)the fundamental facts about the Fourier transform.Chapters 9and 10 develop the differential and integral calculus on manifolds,while Chapter11 treats the exterior calculus of E.Cartan.  \nThe first eleven chapters form a logical unit,each chapter depending on theresults of the preceding chapters.(Of course,many chapters contain materialthat can be omitted on first reading;this is generally found in starred sections.)  \nOn the other hand,Chapters 12,13,and the latter parts of Chapters 6 and 11are independent of each other,and are to be regarded as illustrative applicationsof the methods developed in the earlier chapters.Presented here are elementarySturm-Liouville theory and Fourier series,elementary differential geometry,potential theory,and classical mechanics.We usually covered only one or twoof these topics in our one-year course.  \nWe have not ","cbCaieQ2D849pdpo","https://ap.wps.com/l/cbCaieQ2D849pdpo","pdf",31730715,1,592,"English","en",105,"# Preface\n## Prerequisites and overall plan\n## Structure by chapters","[{\"question\":\"What prerequisites does Advanced Calculus require?\",\"answer\":\"The text expects a rigorous grounding in one-variable calculus, familiarity with linear algebra, limit/continuity arguments, and experience with partial derivatives and mathematical sophistication.\"},{\"question\":\"How is the book organized across the chapters?\",\"answer\":\"The first half focuses on vector space calculus and principally differential calculus in normed vector spaces, while the second half develops calculus on differentiable manifolds through differential and integral topics.\"},{\"question\":\"How does the book handle key theorems and proofs?\",\"answer\":\"It revisits the same material from different viewpoints; for example, it presents the contraction mapping fixed-point theorem as a basis for the implicit function theorem while also outlining Newton’s method and sketching additional proofs in exercises.\"}]","Advanced Calculus - Revised Edition | 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prerequisites does Advanced Calculus require?","Question",{"text":75,"@type":76},"The text expects a rigorous grounding in one-variable calculus, familiarity with linear algebra, limit/continuity arguments, and experience with partial derivatives and mathematical sophistication.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the book organized across the chapters?",{"text":80,"@type":76},"The first half focuses on vector space calculus and principally differential calculus in normed vector spaces, while the second half develops calculus on differentiable manifolds through differential and integral topics.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the book handle key theorems and proofs?",{"text":84,"@type":76},"It revisits the same material from different viewpoints; for example, it presents the contraction mapping fixed-point theorem as a basis for the implicit function theorem while also outlining Newton’s method and sketching additional proofs in 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