DIFFERENTIAL CALCULUS

This book is prepared with a view to be used as a textbook for B.A and B.Sc students of the Indian Universities. We have tried to make the expositions of the fundamental principles clear as well as concise without going into unnecessary details: and at the same time an attempt has been made to make the treatment as much rigorous and up-to-date as possible within the scope of the elementary work. Proofs of certain important fundamental results and theorems which are assumed in the earlier chapters of the book for the convenience of the beginners and average students have been given in the appendix. A brief account of the theory of infinite series, especially the power series, is given in the appendix in order to emphasize their peculiarity in the application of the principles of calculus. Important formulae of this book are given in the beginning for ready reference. A good number of typical examples have been worked out by way of illustrations. Many varied types of examples have been given for exercise in order that the students might acquire a good grasp of the applications of the principles of calculus. B.C.D & B.N.M [authors] 1.List of Important formulae 2. A brief history of development 3. Introduction (numbers) 4. Functions 5. Limit 6. Continuity 7. Differentiation 8. Successive Differentiation 9. Expansion of functions 10. Maxima and Minima 11. Indeterminate forms 12. Partial Differentiation (functions of two or more variables) 13. Maxima and Minima of functions two variables 14. Tangent and Normal 15. Curvature 16. Asymptotes 17. Envelopes and straight lines and curves 18. Associated Loci 19. Concavity and Convexity 20. On some well known curves 21. APPENDIX