Sciences, Technology & Medicine

## Topics in Differential Geometry and Calculus of Variations

In writing this book, the author has placed great emphasis on the fundamental concepts and methods of proofs of articles. He has provided sufficient number of illustrative examples on each concept. To reinforce the concepts developed in the definitions and articles, several exercises have been given at proper places. This book has been written according to new guidelines and syllabus issued by UGC for various universities of India and all over the world.
• Publisher: Laxmi Publications
• Language: English
• ISBN : 978-93-80298-81-8
Total Price: 17.94
• Chapter 1

### Curves in Space Price 2.99  |  2.99 Rewards Points

Differential geometry is that branch of geometry which is treated using the methods of calculus. In particular, we investigate curves and surfaces in space in differential geometry. Differential geometry plays an important role in engineering designs, geodesy, geograph and space travel. Formulae regarding vector algebra and vector calculus are frequently used in the study of differential geometry.
• Chapter 2

### Curvature and Torsion Price 2.99  |  2.99 Rewards Points

For curves in space, the concepts of curvature and torsion are of fundamental importance. We know that line segments are uniquely determined by their lengths, circles by their radii, triangles by side-angle-side etc. In geometry, we look for geometric quantities which distinguish one figure from another. The importance of curvature and torsion can easily be estimated from the fact that it can be proved that a curve is uniquely determined (except for its position in space) if its curvature and torsion are given as continuous functions of arc length ‘s’.
• Chapter 3

### Surfaces in Space Price 2.99  |  2.99 Rewards Points

A sphere, a portion of a cylinder are examples of surfaces in space. Till now we have been discussing the differential geometry of curves in space. In the present chapter , we shall learn few quantities regarding surfaces in space.
• Chapter 4

### Variational Problems with Fixed Boundaries Price 2.99  |  2.99 Rewards Points

By a function we mean a correspondence between the elements of sets A and B such that to each element of A there correspond exactly one element of the set B. We have also studied the methods of finding maximum and minimum values of real functions of one or more variables. In calculus of variations, we shall deal with functionals and their maximum and minimum values. A functional associates a unique real number to each function belonging to a certain class of functions.
• Chapter 5

### Variational Problems with Moving Boundaries Price 2.99  |  2.99 Rewards Points

We know that a functional associates a unique number to each function belonging to a certain class of functions.
• Chapter 6

### Sufficient Conditions for an Extremum Price 2.99  |  2.99 Rewards Points

At an extremum, a functional may have either maximum value or minimum value. In the preceding two chapters, we have studied the necessary conditions for an extremum. At a stationary function, a functional may or may not have an extremum. In the present chapter, we shall confine ourselves to the study of sufficient conditions for extremums of variational problems with fixed boundaries only.