Differential CalculusNew Age International, 2007 - 416 pages Differential Calculus, An Outgrowth Of The Problems Concerned With Slope Of Curved Lines And The Areas Enclosed By Them Has Developed So Much That Texts Are Required Which May Lead The Students Directly To The Heart Of The Subject And Prepare Them For Challenges Of The Field. The Present Book Is An Attempt In This Regard. An Excellent Book On Differential Calculus This Book Has Been Meticulously Planned And Numerous Solved Examples Have Been Selected To Make The Subject Interesting; Besides Problems Are Given At The End Of Each Main Theorem Which Supplement The Text And By Solving Them The Reader Can Judge His Level Of Understanding Of The Given Facts.Exercises Have Been Framed By Arranging Questions In Such A Manner That After Doing Illustrative Examples, One Should Not Feel Difficulty In Solving Any Problem. Considerable Material Has Been Included Here That Covers A Large Number Of Courses. This Has Been Done To Make The Book More Flexible, To Provide A Useful Book Of Reference And To Stimulate Further Interest In The Topics. |
Contents
REAL NUMBERS | 1 |
CONTINUITY 27 | 27 |
DIFFERENTIABILITY | 48 |
4 | 56 |
ROLLES THEOREM MEAN VALUE | 82 |
5 | 88 |
9 | 95 |
INDETERMINATE FORMS | 106 |
8 | 152 |
13 | 167 |
TANGENTS AND NORMALS | 175 |
5 | 185 |
9 | 193 |
CURVATURE | 229 |
ENVELOPES AND EVOLUTES | 265 |
ASYMPTOTES | 286 |
Common terms and phrases
angle asymptote parallel ax² ay² closed interval co-ordinates concave conjugate point continuous cos² cosec cusp derivative differential coefficient discontinuity double point dx dy dx² dy dx ellipse equated to zero equation of curve Euler's theorem Exercise Find the asymptotes Find the envelope following curves function f(x given curve given equation Hence homogeneous function Illustrative Examples Example indeterminate forms intersection lim h→0 limit loge lowest degree terms mean value theorem negative normal origin parabola parallel to x-axis parameter perpendicular point of inflexion positive number prove radius of curvature real numbers Rolle's theorem sec² Show Similarly sin² sint Substituting subtangent tangent Taylor's theorem y-axis y₁ δε ди ди дип дх ду