DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS OPREA PDF

This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole, it mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors, it is also for students in engineering and the sciences. Into the mix of these ideas comes the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. Students will also see how particles move under constraints.

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The second edition has been expanded by over pages to try to take account of various useful suggestions made by users since the appearance of the first edition. The version of Maple that has been tested for all Maple work in the new edition is Maple Projects for Differential Geometry refers to 1st Ed.

The book includes many Maple procedures that allow students to view geometry and calculate things such as Euler-Lagrange equations. In particular, Chapter 5 on geodesics contains a procedure to plot geodesics on surfaces and this procedure gives beautiful illustrations of the Clairaut relation for example. The same type of procedure also allows students to visualize the motion of a particle constrained to move in bowls of various shapes under gravity. These are the kinds of connections between geometry and applications which I like and which I think are important for students to see.

Here is an example of a geodesic on the surface of revolution obtained by revolving the Witch of Agnesi about the x-axis. Notice how the geodesic is bounded between two parallels. This is the Clairaut relation in action. By the way, the following picture is only a first attempt at using Maple to create a JPEG file for the web better things will surely come later!

Here are a few other examples of geodesics on surfaces constructed from this procedure.

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DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS OPREA PDF

Geometry from Africa Paulus Gerdes. Hints and solutions to selected problems. Skip to main content. This book studies the differential geometry of surfaces with the goal of helping students make differentiak transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole, it mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and appljcations from the sciences. Search Enter search terms: Differential geometry is not just for mathematics majors, it is also for students in engineering and the sciences.

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Solutions to Oprea Differential Geometry 2e

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