3 Review(s)

Differential Calculus is a comprehensive theory cum practice book that aims to acquaint aspirants with all aspects of the topic. It helps sharpen the problem solving skills in Calculus through solved and unsolved problems. The solutions to the problems are supported by time saving strategies and tips to avoid mistakes while applying the laws of Calculus. Table of Contents 1. Limit Introduction Concept of Infinity Theorems on Limits One-sided limits determinate and Indeterminate Forms Factorisation and Cancellation of Common Factors Rationalization Limit Using Exapnasion Series of Functions Standard of Limits Algebra of limits Limits when (Some function) Asymptotes Limits of a Sequence Limits of Forms Sandwich Theorem / Squeeze Play Theorem L'Hospital's Rule Geometerical Limits Miscellaneous Limits Target Problems Things to Remember Exercises Answers 2. Continuity of Functions Definition of Continuity Continuity in an Interval Classification of Discontinuity Algebra of Continous Functions Properties of Functions Continous on a Closed Interval Intermediate Value Theorem Target Problems Things to Remember Exercises Answers 3. Differentiability Introduction Differentiability Reasons of Non-differentiability Relation between Continuity and Differentiability Derivability at Endpoints Differentiability over an interval Alternative limit form of the Derivative Derivatives of Higher Order Algebra of Differentiable Functions Functional Equations Target Problems Things to Remember Exercises Answers 4. Methods of Differentiation Introduction Derivative using First principle (ab initio) Method Derivative of Standard Functions Rules of Differentiation The Chain Rule Logarithmic Differentiation Derivative of Inverse Functions Parametric Differentiation Differentiation of Implicit Functions Differentiation by Trigonometric Substitution Derivatives of Higher Order Successive Differentiation Derivative of a Determinant Properties of Derivative L'Hospital Rule Target Problems Things to Remember Exercises Answers 5. Tangent and Normal Introduction Rate Measurement Approximation Error Tangent and Normal Angle of Intersection Common Tangents Length of Tangent Target Problems Things to Remember Exercises Answers 6. Monotonicity Definitions Monotonicity over an interval Critical Point Intervals of Monotonicity Monotonicity in Parametric Functions Algebra of Monotonous Functions Proving Inequalities Concavity and Point of Inflection Target Problems Things to Remember Exercises Answers 7. Maxima and Minima Introduction Concept of Local Maxima and Local Minima Fermat Theorem The First Derivative Test The First Derivative Procedure for Sketching the Graph of a Continous Function Second Derivative Test Higher Order Derivative Test Extrema of Parametric Functions Operations on Functions having points of Extrema Global Maximum and Minimum Boundedness Algebra of Global Extrema Miscellaneous Methods Optimisation Problems Asymptotes Points of Inflection Curve Sketching Isolation of Roots Rolle's Theorem Deductions of Rolle's Theorem Lagrange's mean Value Theorem Corollaries of LMVT Related Inequalities Cauchy's Mean Value Theorem Target Problems Things to Remember Exercises Answers