elementary differential geometry pressley solution manual
LINK 1 ENTER SITE >>> Download PDF
LINK 2 ENTER SITE >>> Download PDF
File Name:elementary differential geometry pressley solution manual.pdf
Size: 2858 KB
Type: PDF, ePub, eBook
Category: Book
Uploaded: 26 May 2019, 21:33 PM
Rating: 4.6/5 from 557 votes.
Status: AVAILABLE
Last checked: 9 Minutes ago!
In order to read or download elementary differential geometry pressley solution manual ebook, you need to create a FREE account.
eBook includes PDF, ePub and Kindle version
✔ Register a free 1 month Trial Account.
✔ Download as many books as you like (Personal use)
✔ Cancel the membership at any time if not satisfied.
✔ Join Over 80000 Happy Readers
elementary differential geometry pressley solution manualCancel anytime. Share this document Share or Embed Document Sharing Options Share on Facebook, opens a new window Share on Twitter, opens a new window Share on LinkedIn, opens a new window Share with Email, opens mail client Copy Text Related Interests Sine Trigonometric Functions Line (Geometry) Angle Curve Footer menu Back to top About About Scribd Press Our blog Join our team. Quick navigation Home Books Audiobooks Documents, active. Since this holds for every curve in the surface, ?f is perpendicular to the surface. At least one of u. For the parametrization.The second pair follows by interchanging the roles of. In that case ? and ? must be constant, so.The orthogonal projection of.It now follows from Proposition A.1.6 that ? and ?? have the same area (note that if M is opposite, the area appears to change sign, but it does not because in that case ?? is negatively-oriented when. As S 2 is a closed and bounded subset of R3, it is compact. Hence, U would be compact, and hence closed. The transition map from.At time t, the centre is at (0, 0, ?t) where ? is the speed of the aeroplane. If the propeller is initially along the x-axis, the point initially at (v, 0, 0) is therefore at the point (v cos ?t, v sin ?t, ?t) at time t, where.S F ? ?F is perpendicular to Tp S, it is perpendicular to ?? (t0 ) for every curve. Since S has a (smooth) choice of unit normal.The solution of Exercise 4.4.3 also shows that if the restriction of F to S has a local maximum or a local minimum at p, then. F is perpendicular to the tangent plane of S at p. But ? f is also perpendicular to the tangent plane. Thus, f depends only on r, and hence. From Exercise 4.1.3, there is a straight line on the hyperboloid passing through ? (u), and it takes the form (x.The first two families of surfaces consist of generalized cylinders, the third consists of parallel planes.Then the restriction of. Hence, the restriction of.http://megatex-plast.ru/pub/factory-repair-manual-seat-leon.xml
- Tags:
- elementary differential geometry pressley solutions manual pdf, andrew pressley elementary differential geometry solutions manual, elementary differential geometry pressley solution manual, elementary differential geometry pressley solution manual pdf, elementary differential geometry pressley solution manual answers, elementary differential geometry pressley solution manual free, elementary differential geometry pressley solution manual class.
By applying an isometry of R3 (a translation), we can assume that the vertex of the cone is the origin. By Corollary 6.2.3, the given surface is locally isometric to this surface of revolution.This gives n triangles whose sides are arcs of great circles. This is a parametrization of the tractrix, so. R)? corresponds to the isometry F ? R of S 2. It therefore suffices to prove that every unitary M?obius transformation is a composite of finitely-many special unitary M?obius transformations.It therefore suffices to prove the result in the case where the two great circles coincide.R3 a constant vector,.Thus, for tangent developables, the second fundamental form vanishes everywhere if and only if the surface is part of a plane.The angle ? in Eq. 7.10 is therefore equal to. Note that ? is not unit-speed in general. We could therefore use the preceding exercise but we would need a unit-speed parametrization of the parabola, which is complicated.This proves that (i) is equivalent to (ii). S ? ), the unit normal at p RR covers the whole of S 2.For the second part, if the second fundamental form is a multiple of the first, the Weingarten map is a scalar multiple of the identity map, so every tangent vector is principal and every curve on the surface is a line of curvature. Condition (i) implies that the two principal curvatures are equal everywhere, i.e. every point is an umbilic, so.We can now assume that.Hence ? is a line of curvature by Exercise 8.2.2. Conversely, if ? is both a geodesic and a line of curvature, we may assume.For an example, take S1 and S2 to be the sphere and cylinder in Theorem 6.4.6. (ii) Now suppose that S1 and S2 intersect perpendicularly. Since ?? is also perpendicular to ??, it must be parallel to N 1. Finally, if ? is a geodesic on both S1 and S2, then N? 1 is parallel to N2 and N? 2 is parallel to N1. It follows that N1. Since ?? is (N a unit vector parallel to N1. Indeed, a normal to the ellipsoid is p2, q 2, r2.Let ?http://newayskazakhstan.kz/upload_picture/factory-production-control-manual.xml (u) be a non-zero vector parallel to the ruling through ? (u). Then (i) says that. By Proposition 8.2.9, it suffices to show that every point of S is an umbilic. Suppose for a contradiction that p.By Exercise 9.1.5, ? is a line of curvature, but this contradicts property (i). 9.1.20 Assume that ? is unit-speed, and let r be the radius of the sphere. The curves on S that make a constant angle with.These are, of course, exactly the straight lines in the plane, i.e. the geodesics in the plane.Hence this circle also corresponds to a geodesic on the pseudosphere. For the sphere: (i) true; (ii) false; (iii) false; (iv) false; (v) true; (vi) false; (vii) true.We are 101 given that this is a function of r only, say A(r). It follows that the surface is a plane. So E is a function Rv of U only.Hence, the surface is locally isometric to the plane, and so is flat by the Theorema Egregium. The result is not true without the assumption of orthogonality. Example 10.4.3 gives a parametrization ? (u, v) of S 2 (actually of a hemisphere) with the property that the pre-geodesics on S 2 correspond exactly to the straight lines in the uvplane.It follows that dilations take geodesics to geodesics. Hence, any composite of local isometries and dilations also takes geodesics to geodesics.F fixes l, m and the interior of the semicircle m. Next, either F, I0,1. Similarly, G fixes each point of l. Hence, G is the identity by (i). (iii) Let F be any isometry of H. By the proof of Proposition 11.2.3, there is an isometry G that is a composite of elementary isometries and which takes F (i) to i and F (l) to l. Then, G ? F is an isometry that fixes l and i. As m is the unique hyperbolic line intersecting l perpendicularly at i, G ? F fixes m. By (iii), G ? F is one of four composites of elementary isometries. It follows that F is a composite of elementary isometries. (iv) By (iii) it suffices to prove that every elementary isometry is a composite of reflections and inversions in lines and circles perpendicular to the real axis. For reflections and inversions there is nothing to prove, so we need only consider translations and dilations. I, where I is inversion in the circle with centre the origin and radius a. 11.2.5 (i) This is obvious from the proof of Proposition A.1.2(ii). ad?bc If (ii) If a, b, c, d. Let C and C ? be the hyperbolic circles with centres a and b, respectively, which pass through c (Exercise 11.1.4). These are Euclidean circles with centres on the imaginary axis. By Exercise 11.1.5, the equidistant curves are then a pair of Euclidean half-lines l1, l2 passing through the origin. The isometry F ?1 of H, being a composite of reflections and inversions (Exercise 11.2.4), takes Euclidean lines and circles to Euclidean lines and circles (Appendix 2). Since the real axis is the only Euclidean straight line passing through a and b, F ?1 must take l1, l2 to a pair of circular arcs passing through a and b. We observed in Exercise 11.1.5 that these are not geodesics. 11.2.8 By applying a suitable isometry, we can assume that a and d are on the imaginary axis. The calculation is similar to that already given. 11.3.4 By Exercise 11.2.5(iii), the isometries of H are of the form M or M. The case in which the hyperbolic line through a vertex meets 116 the hyperbolic line through the other two vertices in a point outside the triangle is similar. 11.3.7 (i) This was established in the solution of the preceding exercise.If at least one of l and m is a semicircle, then l and m are parallel if they intersect at a point of the real axis, and ultra-parallel otherwise. 11.4.2 We work in H and assume that l is the imaginary axis (by applying a suitable isometry). This is the equation of a pair of lines passing through the origin.The set of points c for which the triangle with vertices a, b, c has area A is the union of this line together with its reflection in the real axis. These lines are not hyperbolic lines as they do not pass through the origin. 11.4.4 In the first two parts of this exercise it is slightly easier to work in H (by applying P ?1 ). (i) By applying a suitable isometry of H, we can assume that one of the sides of the triangle is the imaginary axis. Then the other sides must be a semicircle passing through the origin and some point a. Hence, it suffices to establish Eq. 11.11 when M is of this form. This argument is only valid provided none of a, b, c, d is 0 or ?, but a similar argument works in the other cases.R, and let M be as above. Then, M (d) ? R and 0, 1, ?, M (d) lie on a Circle C, namely the real axis. But then a, b, c, d lie on the Circle M ?1 (C). 11.5.9 Let M be the M?obius transformation taking ?, 0, 1 to a, b, c, respectively. It therefore suffices to check that the six stated values are the values of the cross-ratios of the points ?, 0, 1, ? taken in any order. This is straightforward.Part (ii) is now obvious. For (iii), assume that S is not minimal. Then, there is a point p. Let R be a rotation of R3 about the origin that takes G(p to the south pole of S 2 (or any point other than the north pole). There is an open subset O of S containing p such that G(O) does not contain the north pole. By Example 6.3.5, ? ? R ? G is a conformal diffeomorphism from O to an open subset U of R2. R, the identity ? au ? i? a a is a constant vector. Hence, ? is obtained from ? by applying the dilation Da followed by the translation Ta (Appendix 1). (ii) If f and g are the functions in the Weierstrass representation of ? (Proposition 12.5.4), those in the Weierstrass representation of.This gives u v sinh ), 2 2 v u.To compute the total curvature after smoothing, we apply Theorem 13.1.2 to the smoothed cone with.This is not obvious since we must show that 0. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Libros Todavia no tienes ningun libro. Studylists Todavia no tienes ninguna Studylists. Geografia Fisica Guyton e Hall - Fisiologia medica 13 ed. Bioquimica Ilustrada Michael Porter Tratado de anatomia Humana Principios de medicina interna, 19 ed. Guyton y Hall: Tratado de fisiologia medica. Otros estudiantes tambien vieron Spivak - Calculo En Variedades Casos mas comunes de factorizacion Matlab notes For Professionals FIsiologia Primer Examen Parcial psicologia Tema-analisis dimensional Otros documentos relacionados derecho internacional publico Jorgeeduardosalazartrujillo 2007 1 conversion unidades Salud publica norma que regula las vacunas Estadistica Inferencial Facultad de Medicina UNAM Vista previa del texto Solutions to the Exercises in Elementary Differential Geometry Chapter 1 1.1.1 It is a parametrization of the part of the parabola withx?0. These points correspond to the four cusps of the This implies The curve???is a parametrization because If these vectors. Hence, the But this is clear: if we take the fixed Since ?dnnn For the circular helix in So it is enough to prove that?The second pair In that case?and?must be Esta pagina no esta disponible en la vista previa. Esta pagina no esta disponible en la vista previa. Necesitas una cuenta premium para poder ver el documento completo. Opcion 1 Comparte tus documentos para obtener acceso a Premium gratis Subir Opcion 2 Hazte Premium para leer el documento entero Obten acceso gratuito durante 30 dias ?Ya tienes una cuenta. Inicia sesion aqui Ayuda. I need a student solution manual in English with book name and authors. Can you recommend any that includes the introduction to differential geometry, tensors and Christoffel symbols. Applied Mathematics Differential Geometry Tensor Analysis Mathematics Share Facebook Twitter LinkedIn Reddit Get help with your research Join ResearchGate to ask questions, get input, and advance your work. Join for free Log in Most recent answer 2nd Aug, 2020 Omar arturo Cevallos Universidad Tecnica Estatal de Quevedo Excelente aporte a la comunidad universitaria de latinoamerica, abrazos a la distancia Cite Popular Answers (1) 10th Mar, 2014 Valentina Christova-Bagdassarian National Centre of Public Health Protection Dear Artur Sergyeyev, Thanks for the book in Russian. I also purchased one from Amazon. Unfortunately I can not download anything from the provided links to Dovnor. Thanks to all who have helped with links and information. Valentina Cite 18 Recommendations All Answers (27) 8th Mar, 2014 Artur Sergyeyev Silesian University in Opava There is a book Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers by Gadea and Munoz Masque which probably comes closest to your request for the solution manual (although it's fairly advanced, you can pick quite a few elementary problems from there): Next, while it's not exactly a solution manual, there is Schaum's Outline of Differential Geometry by Lipshutz: It is quite elementary and contains a lot of worked out examples. Finally, there is a problem book in English (but again it's not exactly a solution manual): Mishchenko, A. S.; Solovyev, Yu. P.; Fomenko, A. T. Problems in differential geometry and topology. Maybe it is nos exaxtly what you want, but it can help. Cite 1 Recommendation Deleted profile You might also find David Kay's 'Tensor Calculus', also in the Schaum's Outline Series useful. As with the 'Differential Geometry' volume (and, indeed, all the other books in the series) there is a wealth of completely worked examples in this book. Hope it will help! Regarrs Cite 6 Recommendations 9th Mar, 2014 Valentina Christova-Bagdassarian National Centre of Public Health Protection Thanks, Artur Sergyeyev. These are useful textbooks. Unfortunately, it is probably impossible to find a Russian book, you talk about, regardless of Russian or English, which for me is no difference. Thank you, Ljubomir, Always links available:) There should be more examples. Thank you all. I will consider all proposals at this moment each response is important to me. Valentina Cite 13 Recommendations 9th Mar, 2014 Artur Sergyeyev Silesian University in Opava Dear Valentina, thank you. If the books in Russian are also of interest, here is another small problem book (unfortunately without a solution manual) in Russian available online for free: A. Skopenkov, Basic differential geometry as a sequence of interesting problems, Cite 3 Recommendations 10th Mar, 2014 Valentina Christova-Bagdassarian National Centre of Public Health Protection Dear Artur Sergyeyev, Thanks for the book in Russian. Valentina Cite 18 Recommendations 10th Mar, 2014 Ljubomir Jacic Technical College Pozarevac My dear Valentina, please find a book on differential geometry. Clean 100! It contains Christo?el symbols,pp 96, 130. Cite 8 Recommendations 10th Mar, 2014 Valentina Christova-Bagdassarian National Centre of Public Health Protection Dear Ljubomir, This is a very very nice link. Thank you! Your links are always great. With a lot of corrected exercices included. A nice student solution manual in differential geometry is the following: P.M. Gadea, J. Munoz Masque, Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers You can find them in: Cite 4 Recommendations 25th Apr, 2014 Valentina Christova-Bagdassarian National Centre of Public Health Protection Dear Mohamed Behayou, Thank you very much. This book can really be taken from that site. A very useful book. I found all three books. Valentina Cite 7 Recommendations 26th Apr, 2014 Mohamed Amine Bahayou Universite Kasdi Merbah Ouargla You are welcome. Cite 1 Recommendation 14th Jul, 2014 James F Peters University of Manitoba Here is an entire book on differential geometry (complete with solutions): T. Shifrin, Differential Geometry: A First Course in Curves and Surfaces, 2014: In addition to many problems and solutions, this book has a high comfort level for beginners with its generous provision of drawings (see, e.g., p. 50). Cite 9 Recommendations 15th Jul, 2014 Valentina Christova-Bagdassarian National Centre of Public Health Protection Thank you, Professor Peters for the usseful link. Cite 5 Recommendations 13th Jun, 2019 Cristiano Mascarenhas Universidade Estadual de Feira de Santana i am taking a course in riamannian geometry and i would like to get acess a some issues about exercises solved in conexion, geodesics and curvature.Cite 14th Jun, 2019 Cristiano Mascarenhas Universidade Estadual de Feira de Santana thank you Irving, but i need material about Riemannian Geometry in manifolds. About Connection, geodesics, curvature and on. Have a little about what i need in Christian Baer. Thank you and best wishes. It treats those topics.Cite 8th Jul, 2020 Anton Vrdoljak University of Mostar Thanks a lot to all colleagues for links which their provided here. Cite Can you help by adding an answer. Answer Add your answer Similar questions and discussions Can anyone recommend a good book on manifolds or differential geometry of curves and surfaces. Question 7 answers Asked 26th Apr, 2014 Shakeel Ahmed Khan I have an interest in differential geometry. Question 33 answers Asked 5th Dec, 2019 Mohamed Amine Bahayou Dear colleagues, Could you please recommend conferences and Schools in 2020-2021 having Geometry (Symplectic, Lie theory) and topology (differential, low dimensional) as their main topics. View What are the most active research areas in mathematics today.Discussion 77 replies Asked 19th Oct, 2018 Mahfouz Rostamzadeh Mathematics has been always one of the most active field for researchers but the most attentions has gone to one or few subjects in one time for several years or decades. I'd like to know what are the most active research areas in mathematics today. View What is a mathematical way to calculate the Earth's position on its orbit in terms of time. Question 26 answers Asked 4th Jun, 2017 Ada Chen So I firstly got the formula of the Earth's elliptical orbit on an x-y axis (The inclination was ignored) with sun being the origin (0,0). The sun-earth distance can be easily obtained. Then I sunstitued the values into the orbit speed formula to get the instantaneous velocity f(v) of the Earth. However, the formula got way to complicated and I just couldn't integrate it anymore (a fraction with the denominator being a square root inside of another square root). If anyone is willing to check my workout I am happy to upload it: ) Could someone please kindly offer me a way of doing it. But nothing too complicated though. A graphic calculator is all I have got. P.S. English is not my first language so please tell me if I am not making any sense. Thank you so much! Ada View How do I find Killing vectors of any space time. Question 9 answers Asked 19th Aug, 2015 Ashok Patel In mathematics, a Killing vector field (often just Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow generates a symmetry, in the sense that moving each point on an object the same distance in the direction of the Killing vector field will not distort distances on the object. View Is there any method to know the number of topologies defined on a set. Question 33 answers Asked 21st Jul, 2013 Gauree Shanker How many topologies can one define on a particular set. View How do I calculate SPI from NetCDF files using CMIP6 monthly data. Question 7 answers Asked 13th Nov, 2020 Chloe Spraggs I want calculate SPI from CMIP6 monthly precipitation climate data using Rstudio but have only seen methods of doing this when txt files or csv files are used. I have tried CLIMPACT2 but had no luck and can't see to find another way of doing it. Iam worry of generation of Africans not able to speak African languages and ignorant of their culture. It looks strange? What's your view on the issue. View Latex Table for covering both column for IEEE two-column format. Question 4 answers Asked 9th Sep, 2020 Md Abdus Samad In the survey paper, I would like to put a table to compare works on the basis of specific parameters or features. For this purpose, I would like to use a table covering both columns in LaTeX. Can someone help me by giving a code that is compatible with the IEEE template, preferably overleaf. Well, thank you in advance. Geometria algebraica. Geometria diferencial. Matematicas aplicadas. View Tensor Analysis and Differential Geometry Article Jan 1962 C. E. Springer T. Y. Thomas View Tensor Analysis of Networks Article Jan 1965 G. Kron View Got a technical question. Get high-quality answers from experts. Keep me logged in Log in or Continue with LinkedIn Continue with Google Welcome back. Keep me logged in Log in or Continue with LinkedIn Continue with Google No account. All rights reserved. Terms Privacy Copyright Imprint. We also use these cookies to understand how customers use our services (for example, by measuring site visits) so we can make improvements. This includes using third party cookies for the purpose of displaying and measuring interest-based ads. Sorry, there was a problem saving your cookie preferences. Try again. Accept Cookies Customise Cookies Used: Very GoodThe book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged.Please try again.Please try your request again later. Prerequisites are kept to an absolute minimum.New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com Create a free account Buy this product and stream 90 days of Amazon Music Unlimited for free. E-mail after purchase. Conditions apply. Learn more Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required. Don't have a free Kindle app. Get yours here Differential geometry is concerned with the precise mathematical formulation of some of these questions. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyses reviews to verify trustworthiness. Please try again later. D. Siska 4.0 out of 5 stars It is well written and fairly well structured, providing a consistently flowing and logical exposition of the material. There are a plenty of diagrams and worked out examples, so one can easily see whether he's on the ball or not. Apart from worked out exaples directly in the text, there is a wealth of exercies, with solutions (or major hints) at the back. The exercies are almost worth the price of the book by themself, starting from basic ones, checking that one understands definitions, followed by more difficult ones outlining the subtler points of the subject and a couple of rather involved ones; ones which it is easy to spend a whole afternoon with. The author does a good job at pointing the diffucult parts of proofs and constructions. The style is very enthusiastic, which might help motivating the reader. The proofs are sometimes a bit too fast paced for someone who might not be as quick witted as the author when it comes to differetial calculus. I did find certain steps not obvious the first time round. A second or third reading (plus trying to work out the steps on a paper) helps a lot. What is rather important to know, before buying, is that the book is only concerned with curves and surfaces in 3 dimensional euclidean space. The approaches taken here would not, very often, generalise to higher dimensional cases. This means that the material is easily accesible to begginers. At the same time, it is not for people who are after an introduction to coordinate free geometry and manifolds. By the time Gauus-Bonnet theorems are discussed, I had the feeling that the proofs are not as detailed and rigorous as they could be. On the other hand this makes them easier to follow and one is not overwhelmed by techicalities. So why not give it 5? I don't know, maybe there are other better books out there, maybe I'm just not too keen on differential geometry in general. I guess I might have given it 5, but then maybe Prof. Pressley won't feel like improving this great book and that would be a shame.There are many graphs for reader to build better understanding, and this is quite helpful if one feel so tricky to the formulas.My only criticism would be that it is perhaps a bit too slow-paced if you are impatient. The same ground could have been covered, probably just as well, in half as many pages.In particular, I realized that geodesic equations are non-linear and usually difficult or impossible to solve explicitly. I recommend this book. Shed the societal and cultural narratives holding you back and let step-by-step Elementary Differential Geometry textbook solutions reorient your old paradigms. NOW is the time to make today the first day of the rest of your life. Unlock your Elementary Differential Geometry PDF (Profound Dynamic Fulfillment) today. YOU are the protagonist of your own life. Let Slader cultivate you that you are meant to be! Please reload the page. Please try again.Please try again.Please try again. Please try your request again later. New features of this revised and expanded second edition include:a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required. Differential geometry is concerned with the precise mathematical formulation of some of these questions. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.Full content visible, double tap to read brief content. Videos Help others learn more about this product by uploading a video. Upload video To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. It also analyzes reviews to verify trustworthiness. Please try again later. Bruce Gould 5.0 out of 5 stars The book DOES say clearly in the introduction what it's scope is: mostly differential geometry in low dimensions and with methods that do NOT generalize to higher dimensions - so if you're looking for something else this isn't the book you want.This is the difference between classical and modern treatments of differential geometry.Most of the good ones are fairly pricey, or require the reader to have a deep knowledge of mathematics. This fits in neither category.The first five chapters are pretty good, after that it starts to go downhill. Chapter 6 on normal and geodesic curvature, is very heavy on linear algebra, and the geometry seems to be put off until the very end of the chapter. Chapter 7 is somewhat better about this. Chapter 8 is boring and I found the problems to be overly challenging simply because a lot of explicitly refer to results from exercises in chapter 5 and 6. I am still in the process of reading this book.The book has a typo almost every other page. Don't get me wrong, typos are generally not a big deal, however if they're in the middle of equations it is just incorrect and useless. I don't recommend this book to anyone. I can only imagine how much worse the first one was.I used this book for a course in differential geometry which was not intended for math majors (so yes, it is sort of my fault), but thought I would mention this here just in case there are math students who are considering it. Like the author mentions, some of the methods he uses don't generalize and so they keep the requirements to a minimum and parts of the book cover topics that a math major would already know and not as rigorously. A math student should be able to tackle the classic in the genre by do Carmo.