differential geometry for beginners

In conclusion, for mathematics only. ( Log Out /  Now, I have graduated and I want to research about “separation principle for nonliear systems”. 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! 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 first two chapters include introduction to algebra and calculus. I’m afraid not. Spivak wrote a short and good book. Change ). Hi. Create a free website or blog at WordPress.com. 2 CHAPTER 1. Hence, I do not have a very strong background in formal mathematics. ( Log Out /  Change ), You are commenting using your Google account. Gauss's view of curvature and the Theorema Egregium | Differential Geometry 35 … However, could someone recommend a cohesive resource (book/lectures) that would be self sufficient for someone with no background? I have recently started looking at Control Systems in robotics, and a particularly interesting area is using Differential Geometry for modelling systems. Cookies help us deliver our Services. 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. The book begins with Grassmann-like bracket notation of inner and vector products. The covered material is also very different in different books. There are two ways to get into differential geometry: The more intuitive approach, the differential geometry of curves and surfaces in euclidean space. Denote this shortest path by pq. Generally this book is good, and not presupposing too much prerequisites. Differential geometry can be successfully used in many areas of study from special relativity to image processing. Very detailed! The book has fair notation and well written. Yes, probably I can recommend you a book, but first I need a few details from you. Or if you know German: Klaus Jänich: Vektoranalysis (very good book). Could anyone recommend a quick way to get started with Differential Geometry? I’m sorry to hear that this book was your first reading on the differential geometry. You need basics of point set topology, good knowledge of calculus and very good knowledge of linear algebra. You could check out Petersen's notes "Classical Differential Geometry". You need no algebraic topology whatsoever and very little of analysis. I think you'll need to go deeper for your interests, but I'm not totally sure. Some books begin with tensors, some with point-set topology, and others with calculus/algebra/geometry definition-theorem-proof horrible (for engineer) scheme. I like Christian Bär: Elementary Differential Geometry, The analytical approach: do calculus on manifolds. If you want to take a look at some books, check out Lee and Warner. Exactly what I was looking for. Enter your email address to subscribe to this blog and receive notifications of new posts by email. I am in a similar position and have been considering looking at Discrete Differential Geometry related materials. I want to see intuitive tools, to understand the terms used in the theory, and to get insights in visual geometric terms. You can use Do Carmo's Curves and Surfaces book to learn some of the basics, that's appropriate for self-study. A classical book on differential geometry. Change ), You are commenting using your Facebook account. This is about applying differential geometry to computer graphics (and the linked course is aimed at CS students), which might be approachable with your background. 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. A Geometric Approach to Differential Forms, Petersen's notes "Classical Differential Geometry". The choice of themes is somewhat limited, with no mention of manifolds (which are explained in a companion book). 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. What do you think about two books above?. The notation is fine. 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. The rest of the book is less useful: physics, contact with lines, orthotomics, envelopes, vertices, etc. This is more abstract and probably better suited for pure math students. Since the late 1940s and early 1950s, differential geometry and the theory of manifolds has developed with breathtaking speed. Both are difficult from a mathematical point of view, thus you’ll not find it in introductory math books. By using our Services or clicking I agree, you agree to our use of cookies. Change ), You are commenting using your Twitter account. It talks on arc length, unit speed curves, parametrizations, reparametrizations, curvature, moving frames, tangent and normal lines. Unless you are fluent in topological equivalence I don’t see the point to read further. The book is 370 pages only, and it has even answers to selected exercises. 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?! I think that the book too emphasize particular curves, spirals and such. Therefore, my professor suggests some books such as “Nonlinear control systems” of Isidori and “Nonliear dynamic control systems” of H. Neijmeijer. I don’t need it to be rigorous, or formal. 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. The book begins with Grassmann-like bracket notation of inner and vector products. Posted on October 21, 2010 | 7 Comments. Contents look very promising:  begins directly with manifold definition, proceed with structures, include PDE, tensors, differential forms, Lie groups, and topology. ( Log Out /  But I think it is not the best book. It includes local and global curves and surfaces geometry. So, please tell me if you’re an engineer or a mathematician, and what contents you expect to learn. On a positive side, this book has a lot of examples (numerical and graphical), and it is sufficiently easy to read and comprehend. The book concentrates on plane 2D curves. I have read book’s Khalil and Stoline when i’m student. 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. The book is focussed on curve and surface local differential geometry. I feel that it isn’t detail.

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