This Book Is Designed To Be Used For Class-Room Teaching For A Course In Differential Calculus At The Undergraduate Level And Also As A Reference Book For Others Who Need The Use Of Differential Calculus. The Book Is Designed In Accordance With The Syllabus In Differential Calculus Prescribed In Most Of The Indian Universities.The Following Are Some Of The Special Features Of This Textbook: * In Addition To The Theoretical Treatment Of The Topics In Differential Calculus, Due Respect Is Given To Application-Oriented Approach Through Various Illustrations And Exercises Drawn From Practical Sciences. * The Graphical And Numerical Approach Provided In The Text Enhances The Appreciation And Understanding Of The Concepts Involved. * A Large Number Of Worked Examples And Exercises, With Answers, Drawn From Various Examination Papers Of Indian And Foreign Universities Are Included. * Biographical Notes And Historical Snippets Have Been Added With A View To Motivating And Inspiring The Students. Brief Life-Sketches And Contributions Of Great Mathematicians Like Sir Isaac Newton And Leibniz Form Part Of The Book. * The Unique And Pioneering Aspect Of The Present Book Is That A Large Number Of Computer Programs And Graphic Printouts For Various Topics Indifferential Calculus Are Included. The Fascinating Potential Of Graphics, For The Understanding Of Calculus, On A Computer Is Well Brought Out Through Computer Programs Which Can Be Readily Worked On An Ibm-Compatible Pc. Further, In Order To Make The Programs Useful To Students And Amateurs Who Have Access Only To The Popular Home-Computers Interesting Programs Which Can Be, Run On The Very Popular Bbc Microcomputer And Sinclair Spectrum Have Also Been Provided.Very Interesting Graphics Of Evolutes Of Famous Curves And Envelopes Of Families Of Curves Along With Their Ready-To-Work Programs Add To The Value Of The Book.
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Limits and Continuity
to the tangent and Pedal equations
Functions of two variables and Partial differentiation
Concavity Convexity and Inflexion
Maxima and minima
Curves and Curvesketching
30 PRINT astroid asymptotes asymptotes parallel axis calculus cardioid cartesian centre of curvature concave conjugate point Consider continuous convex coordinates corresponding cos2 cos9 cosh cusp cycloid difference quotients Differentiating double point ellipse ENVELOPE OF CIRCLES EVAL F evolute Example exists given curve GOTO graph Hence homogeneous function hyperbola increasing INPUT TAB integer interval a,b Leibniz Lemniscate lim f(x Limacon limit local maximum LOCATE lowest degree terms mathematics maximum mean value theorem MOVE XC nephroid open interval origin parabola parametric equations partial derivatives pedal equation perpendicular point of inflexion point of intersection positive PRINT TAB PROGRAM prove radius vector real numbers Rolle's theorem Show Similarly sin2 sin3 sin9 slope spiral stationary points sub-normal sub-tangent tangent Taylor's theorem variable zero ду Дх