In writing this book, the author has placed great emphasis on the fundamental concepts and methods of proofs of articles. I have provided sufficient number of illustrative examples on each concept. To reinforce the concepts developed in the definitions and articles, several exercises have been provided in the appropriate sections of this book.
Salient features of the present book are:
- Well explained concepts.
- Sufficient number of solved examples.
- Well graded exercises.
- Hints for selected questions.
SECTION A: DIFFERENTIAL GEOMETRY
1. Curves in Space
2. Curvature and Torsion
3. Surface in Space
SECTION B: CALCULUS OF VARIATIONS
4. Variatioal Problems with Fixed Boundaries
5. Variational Problems with Moving Boundaries
6. Sufficient Conditions for an Extremum