Discover book depositorys huge selection of michael spivak books online. What are the prerequisites for michael spivak s monumental a comprehensive introduction to differential geometry. I only know him through his wonderful expositions of mathematical analysis, differential geometry, and topology. A comprehensive introduction to differential geometry cern. As a college freshman with three semesters of calculus under my belt, i found this book to be informative and engaging, even though it started back at square one.
Curve, frenet frame, curvature, torsion, hypersurface, fundamental forms, principal curvature, gaussian curvature, minkowski curvature, manifold, tensor eld, connection, geodesic curve summary. Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. Buy a comprehensive intro to diffe geometry third edition with corrections by spivak, michael isbn. What are the prerequisites for michael spivaks monumental a comprehensive introduction to differential geometry.
Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Spivak, michael and a great selection of similar new, used and collectible books available now at great prices. Spivak s fivevolume textbook a comprehensive introduction to differential geometry states in its preface that calculus on manifolds serves as a prerequisite for a course based on this text. This book is a monographical work on natural bundles and natural operators in differential geometry and this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry. You can choose to develop the subject with or without coordinates. This is the complete fivevolume set of michael spivaks great american differential geometry book, a comprehensive introduction to differential geometry third edition, publishorperish, inc. Comprehensive introduction to differential geometry volumes 1 and 2 by. It is based on the lectures given by the author at e otv os. In fact, several of the concepts introduced in calculus on manifolds reappear in the first volume of this classic work in more sophisticated settings.
The more descriptive guide by hilbert and cohnvossen 1is also highly recommended. Publish or perish, incorporated, 1975 mathematics 474 pages. Spivak begins to study the classical parts of differential geometry. The only prerequisite for volume ii is a careful study of volume i. For me, volume 2 is the most useful of michael spivaks 5volume 1970 dg book series because it presents connections for tensor bundles and general fibre bundles, whereas volume 1 presents only differential topology i. What book a good introduction to differential geometry.
As for a recommended textbook, i hear good things about banchoff and lovett its quite cheap too, but i have yet to go through the material. And i learned that 90% of these three volumes is about a the imbedding of manifolds in manifolds and b the extrinsic properties of the imbedded manifold relative to the containing manifold. Jeffrey lee, manifolds and differential geometry, chapters 12 and center around the notions of metric and connection. A comprehensive introduction to differential geometry, volume. Is spivaks a comprehensive introduction to differential geometry a. Everything is motivated with the utmost careall the abstract topological stuff in the first volume is made completely natural in setting up the geometric content of the second volume. The treatment of curvature of curves and surfaces in the first two chapters are really good. This book is the first volume of the 3rd edition in a five volume series on differential geometry. Comprehensive introduction to differential geometry, complete five. A comprehensive introduction to differential geometry,volume two by michael spivak and a great selection of related books, art and collectibles available now at. Other readers will always be interested in your opinion of the books youve read.
This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a euclidean space of three dimensions. Spivak is the author of the fivevolume a comprehensive introduction to differential geometry. Comprehensive introduction to differential geometry, complete fivevolume set book. An excellent reference for the classical treatment of di. This book mostly focuses on classical differential geometry ie curves and surfaces in r3. Written by an outstanding teacher and mathematician, it explains the material in the most effective way, using vector notation and technique. This was one of the books that helped me decide to get a phd in math even though i didnt officially study differential geometry. Spivak really loves differential geometry, as these books show i will restrict myself to the first two volumes, for i am unfamiliar with the rest. A comprehensive introduction to differential geometry, volume 2 a comprehensive introduction to differential geometry, michael spivak, isbn 0914098837, 9780914098836 author. He is the author of the fivevolume comprehensive introduction to differential geometry. Submanifoldsofrn a submanifold of rn of dimension nis a subset of rn which is locally di. Its a pity that its difficult to find biographical information about him.
The focus here is on the foundations of curvature and connections. Spivaks books read like chalkboard lectures by a superb lecturer. This is the complete fivevolume set of michael spivaks great american differential geometry book, a comprehensive introduction to. Based on my reading of vol 1 and my browsing of vol 2 of this series, there is no doubt that michael spivak and differential geometry are a delightful combination. Free differential geometry books download ebooks online. Free download one of the acknowledged classics of marketing f.
I dont know if you are being pretentious or not but i have not met anyone who would ever recommend langs book as a first exposure to differential geometry. As the summary states, this book is really more an introduction to the study of analysis, and as such has few computations, a. A comprehensive introduction to differential geometry, volume 5 by. Jan 24, 20 spivak really loves differential geometry, as these books show i will restrict myself to the first two volumes, for i am unfamiliar with the rest. A comprehensive introduction to differential geometry, vol. This book could be read as an introduction, but it is intended to be especially useful for clarifying and organising concepts after the reader has already experienced introductory courses. His book calculus takes a very rigorous and theoretical approach to michael david spivak is a mathematician specializing in differential geometry, an expositor of. Everyday low prices and free delivery on eligible orders. A comprehensive introduction to differential geometry series. On this page geometry a comprehensive introduction to differential geometry series by spivak there is a listing of the table of contents. A comprehensive introduction to differential geometry volume 1. What are the prerequisites for michael spivaks monumental a. In addition to this current volume 1965, he is also well known for his introductory but rigorous textbook calculus 1967, 4th ed. Will merry, differential geometry beautifully written notes with problems sheets.
A comprehensive introduction to differential geometry book. Michael spivak michael david spivak born may 25, 1940 is an american mathematician specializing in differential geometry, an expositor of mathematics, and the founder of publishorperish press. Despite of the mess at the description of the product, which confuses the customers, the service was good. His book calculus takes a very rigorous and theoretical approach to. The person recommended langs book as an introduction to differential geometry. Besides the standard spivak, the other canonical choice would be kobayashinomizus foundations of differential geometry, which is by no means easy going. Are these 5 volumes selfconsistent in the sense that a knowledge of the prerequisites of vol. A comprehensive introduction to differential geometry 5 volume. Michael david spivak is a mathematician specializing in differential geometry, an expositor of mathematics, and the founder of publishorperish press. Sold only as individual volumes see isbns 09140988450914098853 volumes 1 and 2 michael spivak. For me, volume 2 is the most useful of michael spivak s 5volume 1970 dg book series because it presents connections for tensor bundles and general fibre bundles, whereas volume 1 presents only differential topology i. Comprehensive introduction to differential geometry. A comprehensive introduction to differential geometry, volume 3. This is the complete fivevolume set of michael spivak s great american differential geometry book, a comprehensive introduction to differential geometry third edition, publishorperish, inc.
The basic library list committee strongly recommends this book for. What is the best self study book on differential geometry for. A file bundled with spivaks calculus on manifolds revised edition, addisonwesley, 1968 as an appendix is also available. Elementary differential geometry by barrett oneill is another good book. Buy a comprehensive introduction to differential geometry by spivak, michael isbn. The theory of plane and space curves and surfaces in the threedimensional euclidean space formed the basis for development of differential geometry during. Whereas barrett oneill manages gets to some serious differential geometry while working over low.
Comprehensive introduction differential geometry abebooks. Michael spivak is one of my favourite mathematicians and expositors of mathematics. Here are my lists of differential geometry books and mathematical logic books. There is a new book by jeffrey lee called manifolds and differential geometry in the ams graduate studies series. Subject category mathematical physics and mathematics. Michael spivak books list of books by author michael spivak. The aim of this textbook is to give an introduction to di erential geometry. Theres a choice when writing a differential geometry textbook. Spivaks most recent book, physics for mathematicians. To see what your friends thought of this book, please sign up.
A comprehensive introduction to differential geometry 5. Applied differential geometry a modern introduction vladimir g ivancevic defence science and technology organisation, australia tijana t ivancevic the university of adelaide, australia n e w j e r s e y l o n d o n s i n g a p o r e b e i j i n g s h a n g h a i h o n g k o n g ta i p e i c h e n n a i. Isbn 0914098810 this book at amazon 9780914098812 this book. Dg without connections or metrics and some riemannian geometry and lie group geometry. Is spivaks a comprehensive introduction to differential geometry a good. Publish or perish, incorporated, 1999 geometry, differential 489 pages. A comprehensive introduction to differential geometry. Michael spivak brandeis university calculus on manifolds a modern approach to classical theorems of advanced calculus addisonwesley publishing company the advanced book program reading, massachusetts menlo park, california new york don mills, ontario wokingham, england amsterdam bonn. I only read the first edition, but i thought it was written fairly well and did a good job of developing geometric intuition because of the number of pictures. Spivaks fivevolume textbook a comprehensive introduction to differential geometry states in its preface that calculus on manifolds serves as a prerequisite for a course based on this text. As the summary states, this book is really more an introduction to the study of analysis, and as such has few computations, a fact which some find disappointing.
Is spivaks a comprehensive introduction to differential. Applied differential geometry a modern introduction vladimir g ivancevic defence science and technology organisation, australia tijana t ivancevic the university of adelaide, australia n e w j e r s e y l o n d o n s i n g a p o r e b e i j i n g s h a n g. Michael david spivak born may 25, 1940 is an american mathematician specializing in differential geometry, an expositor of mathematics, and the founder of publishorperish press. Teaching myself differential topology and differential geometry. Lees book, nice though it is, being a book on basic manifold theory is a language book with respect to differential geometry not even covariant derivatives are defined in it differential geometry needs to have differentiation happening. This book is the second volume of the 3rd edition in a five volume series on differential geometry. My book tries to give enough theorems to explain the definitions.
475 274 1176 1335 791 1234 1315 870 1216 1467 311 1600 1556 465 912 356 101 621 1531 168 1333 1147 1281 1098 882 280 813 144 147 8 1606 605 824 1293 859 1330 127 904 1494 1019 255 1327 501