Elementary Differential Geometry by Andrew PressleyElementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum - nothing beyond first courses in linear algebra and multivariable calculus - and the most direct and straightforward approach is used throughout. 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. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com
You should also take a look at Appendix A. Homework Solutions Here are the solutions for the first homework assignment. Practice problems for the exam will be posted soon. Here is the assignment: Homework 3 TeX , PDF You should feel free to work together on the assignment, though everyone must write up their own solutions. Practice Problems: Space Curves Here are some practice problems on space curves.
Elementary Differential Geometry Chapter 1 1. These points correspond to the four cusps of the astroid see Exercise 1. The point P is then at the point. If b and c are parallel there are infinitely-many such planes. If all the normal lines are parallel, so are all the tangent lines. By Exercise 1. Iterating this argument gives the desired sequence.
Elementary Differential Geometry. Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques. It is a subject that contains some of the most beautiful and profound results in mathematics, yet many of them are accessible to higher level undergraduates. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum. Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times. Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there.
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