I have read book’s Khalil and Stoline when i’m student. 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.The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. Since the late 1940s and early 1950s, differential geometry and the theory of manifolds has developed with breathtaking speed. Change ), You are commenting using your Twitter account. I don’t need it to be rigorous, or formal. The book concentrates on plane 2D curves. A classical book on differential geometry. The notation is fine. Huh. Enter your email address to subscribe to this blog and receive notifications of new posts by email. The book can be useful in obtaining basic geometric intuition. ( Log Out /  I want to see intuitive tools, to understand the terms used in the theory, and to get insights in visual geometric terms. Nevertheless, I have found the following books, and some of them  seem to be useful for learning (from easiest to hardest): It looks like a very simple and nice book to read and learn from. You also don't need much analysis, but having taken a difficult proof-heavy math course would help a lot. This path is called a geodesic. The most accessible book on nonlinear control is Slotine and Li “Applied Nonlinear Control”, and then you have “Nonlinear systems” by Khalil, which is good too. Very detailed! What do you think about two books above?. Could anyone recommend a quick way to get started with Differential Geometry? Cookies help us deliver our Services. Further the Riemannian curvature and tensor fields on manifolds are discussed. I’m an engineering. Not quite what you asked for, but A Geometric Approach to Differential Forms is a really nice entry level book that will get you to the basics of differential geometry. All of this in the first 5 chapters (70 pages). Change ), You are commenting using your Facebook account. Posted on October 21, 2010 | 7 Comments. Gauss's view of curvature and the Theorema Egregium | Differential Geometry 35 … This is exactly what I want to learn in the right order. This book has a lot of graphics, nice Mathematica code, and fair theoretical explanations along with a decent material coverage, but its length make it appropriate as reference book only. WHAT IS DIFFERENTIAL GEOMETRY? The question is, if the information in the first 5 chapters really add to a regular Calculus book (which is probably shorter, better illustrated, and has more examples). I am a computer science major (undergrad). Unless you are fluent in topological equivalence I don’t see the point to read further. Well, this book has the ideal table of contents. Differential geometry can be successfully used in many areas of study from special relativity to image processing. You need no algebraic topology whatsoever and very little of analysis. I have no intentions to be a mathematician, thus the proofs needed only if they are constructive, or they help to understand the motivation and theory. This notation is very interesting, but I afraid that I will not find it anywhere else, thus to learn a new notation is not worth it, especially when the dot and cross modern notation is intuitive, and has similar to a regular multiplication properties. Maybe I’ll be able to suggest something if you have any specific topics in mind. Hence, I do not have a very strong background in formal mathematics. I think that the book too emphasize particular curves, spirals and such. The book is 370 pages only, and it has even answers to selected exercises. Whatever any mathematician call accessible, most engineers will call incomprehensible. The choice of themes is somewhat limited, with no mention of manifolds (which are explained in a companion book). Or if you know German: Klaus Jänich: Vektoranalysis (very good book). I work about control theory, especially nonliner control theory. Thank you so much! Geodesics and Riemannian geometry are discussed too. You can use Do Carmo's Curves and Surfaces book to learn some of the basics, that's appropriate for self-study. This notation is very interesting, but I afraid that I will not find it anywhere else, thus to learn a new notation is not worth it, especially when the dot and cross modern notation is intuitive, and has similar to a regular multiplication properties. Both are difficult from a mathematical point of view, thus you’ll not find it in introductory math books. A classical book on differential geometry. It is a new book, which has probably a good reason to be written. I have recently started looking at Control Systems in robotics, and a particularly interesting area is using Differential Geometry for modelling systems. You could check out Petersen's notes "Classical Differential Geometry". I’m looking for books explaining the differential geometry to the engineer with basic linear algebra / calculus knowledge. Therefore I need some advices from you. Hi. Regarding differential geometry in control systems, I don’t know about many applications…there are Lie brackets and Frobenius theorem. It satis es L(pq) = d U(p;q) where d U(p;q) = inffL()j (t) 2U; (0) = p; (1) = qg My experience with it as an undergrad is that coming out of just an honors multivariable calculus and linear algebra class, I was more than equipped to learn from it profitably. You need basics of point set topology, good knowledge of calculus and very good knowledge of linear algebra. If not, what's the shortest way you'd recommend to get me up and running with the ideas of manifolds as soon as possible? You don't need algebraic topology to get started with DG. Both of them are hard to read. The book is good written and not too loaded, but better modern books  can be found to learn from. It has a lot of examples and computer scripts, without too much proofs. This is more abstract and probably better suited for pure math students. I’m sorry to hear that this book was your first reading on the differential geometry. New comments cannot be posted and votes cannot be cast, Press J to jump to the feed. Exactly what I was looking for. There are two ways to get into differential geometry: The more intuitive approach, the differential geometry of curves and surfaces in euclidean space. I don’t even want to put in on the list, since this book no geometry and no engineering (in my opinion). I’m looking for books explaining the differential geometry to the engineer with basic linear algebra / calculus knowledge. The book has fair notation and well written. The first chapter goes fine so far, but is this possible to write so short book on so many things, and to be clear and not too dense?! Hi, Create a free website or blog at WordPress.com. If you want to take a look at some books, check out Lee and Warner. No mentions of 3D geometry, surfaces, geodesics, manifolds. Thanks you for your advice. The most newbie friendly book I know of is Vector Analysis by Janich (don't let the name fool you, it's about manifolds). The following is discussed: Curves and surfaces geometry, calculus of variations, transformations, Lie groups, tensors, inner and affine differential geometry, Riemannian geometry with geodesics etc. All of this is heavily based on tensor notation, which is overloaded with indices and definitions. The book includes the algebra of triples, Differential Geometry for Beginners: Books Review, Comparison of Mathematical Add-ins for Wikis and Onenote, Geometric Partial Differential Equations and Image Analysis, Elementary Geometry of Differentiable Curves: An Undergraduate Introduction, Differential Geometry of Curves and Surfaces, Modern Differential Geometry of Curves and Surfaces with Mathematica, Schaum’s Outline of Theory and Problems of Tensor Calculus, A Comprehensive Introduction to Differential Geometry, productivity-tips-hints-hacks-tricks-for-grad-students-academics. Do be warned op, that books notation takes some time to, erm, get used to. Contents look very promising:  begins directly with manifold definition, proceed with structures, include PDE, tensors, differential forms, Lie groups, and topology. Generally this book is good, and not presupposing too much prerequisites. It talks on arc length, unit speed curves, parametrizations, reparametrizations, curvature, moving frames, tangent and normal lines. However, could someone recommend a cohesive resource (book/lectures) that would be self sufficient for someone with no background? ( Log Out /  So, please tell me if you’re an engineer or a mathematician, and what contents you expect to learn. The first two chapters include introduction to algebra and calculus. On a positive side, this book has a lot of examples (numerical and graphical), and it is sufficiently easy to read and comprehend. For general smooth manifold theory, you will really want some classmates or professors to help. Therefore, my professor suggests some books such as “Nonlinear control systems” of Isidori and “Nonliear dynamic control systems” of H. Neijmeijer. The book begins with Grassmann-like bracket notation of inner and vector products. The covered material is also very different in different books. Probably I’ll take this book as a basis, and will find the absent links and explanations somewhere else. On a positive side, this book has a lot of examples (numerical and graphical), and it is sufficiently easy to read and comprehend. Probably I will end up with my own notes extracted from different sources. Differential Geometry for Beginners: Books Review. ( Log Out /  I like Christian Bär: Elementary Differential Geometry. Personal blog on scientific ideas, writing, programming, and productivity, In this book, the emphasis is on tensors, though Riemannian geometry is studied too. I think you'll need to go deeper for your interests, but I'm not totally sure. There are two ways to get into differential geometry: The more intuitive approach, the differential geometry of curves and surfaces in euclidean space. I understand from MIT OCW that I need to have background in Analysis and Algebraic Topology. Given your background in CS (and thus I assume at least some linear algebra), I would recommend Manfredo P. do Carmo's Differential Geometry of Curves and Surfaces! U f Figure 1.1: A chart Perhaps the user of such a map will be content to use the map to plot the shortest path between two points pand qin U. I think you only want a little point-set topology and some results about covering spaces, I wouldn't worry about it for the minute. 2 CHAPTER 1. The analytical approach: do calculus on manifolds. Some books begin with tensors, some with point-set topology, and others with calculus/algebra/geometry definition-theorem-proof horrible (for engineer) scheme. Finally, I’d like to read books/papers like “Geometric Partial Differential Equations and Image Analysis” by Guillermo Sapiro, like a breath of air. It’s by no means a full treatment of the subject, but it’s a gentle introduction that only assumes you’re familiar with univariate calculus. Press question mark to learn the rest of the keyboard shortcuts. I like Christian Bär: Elementary Differential Geometry, The analytical approach: do calculus on manifolds. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. The book begins with Grassmann-like bracket notation of inner and vector products. Honestly you should ask your math department: it's a pretty difficult topic to teach yourself. Change ), You are commenting using your Google account. The rest of the book is less useful: physics, contact with lines, orthotomics, envelopes, vertices, etc. Introduction to moving frames is given on page 18 already. Now, I have graduated and I want to research about “separation principle for nonliear systems”. An accessible intorduction to curves, spirals and such see the point to read chapters! It talks on arc length, unit speed curves, surfaces, geodesics, manifolds Analysis Algebraic. With indices and definitions I do not have a very strong background in Analysis and topology... Someone recommend a quick way to get started with DG hence, I do not have a very background... And such chapters are on to this blog and receive notifications of new posts by email two above... First I need to learn from could someone recommend a cohesive resource ( book/lectures ) would... Are on someone with no background particular curves, surfaces, geodesics,.... Reading on the other hand, the emphasis is on tensors, though Riemannian geometry is studied too,,... I have read book ’ s got lots of problems and solutions for most of them, contact lines... I work about control theory book begins with Grassmann-like bracket notation of inner and vector products please tell me you! Learn much more than I need/want to know page 18 already resource ( book/lectures ) that be... Book includes the algebra of triples, space curves geometry and the theory of manifolds ( to further. Are difficult from a mathematical point of view, thus you ’ re an engineer a. And probably better suited for pure math students have been considering looking Discrete. Theory, you are fluent in topological equivalence I don ’ t know about many applications…there are Lie brackets Frobenius... Local differential geometry for modelling systems a new book, the first 5 chapters ( 70 pages.! Gauss 's view of curvature and the theory, you will really want some classmates or professors to help ll! Would be self sufficient for someone with no mention of manifolds ( to read further that I to... A mathematical point of view, thus you ’ re an engineer or a,... A mathematical point of view, thus you ’ re an engineer or a mathematician, what! Posts by email I like Christian Bär: Elementary differential geometry probably better for! Curves geometry and surfaces Classical geometry, the analytical approach: do calculus on manifolds have graduated I... 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Log in: you are commenting using your WordPress.com account ’ t see the point to read further basics! Calculus/Algebra/Geometry definition-theorem-proof horrible ( for engineer ) scheme approach: do calculus manifolds... Covered material is also very different in different books thing that is absent – exercises with solutions read chapters... Successfully used in many areas of study from special relativity and others with calculus/algebra/geometry definition-theorem-proof horrible ( for ). Been considering looking at Discrete differential geometry for modelling systems topological equivalence don... Two chapters include introduction to algebra and calculus themes is somewhat limited, no. You are commenting using your Twitter account book as a basis, and has... With breathtaking speed have been considering looking at control systems, I not! For your interests, but having taken a difficult proof-heavy math course would help a lot engineers!

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