Text Book of Differential Calculus for IIT-JEE

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The book “Textbook of Differential Calculus for IIT-JEE” is the first book of the Super Success Series in Mathematics for IIT-JEE. This book on Differential Calculus is the first attempt towards providing a logical and conceptual approach to solving problems for Engineering Entrance Examinations especially the IIT-JEE. The book is an attempt to provide the right mix of theoretical concepts, problem discussions through solved examples and exercises in the new IIT-JEE flavour. Some of Salient features of the new book : Best theory points needed for IIT-JEE preparation. Techniques to Problem Solving much needed for IIT-JEE Best collection of problems on the latest trends of IIT-JEE Covers all new pattern problems with detailed solution to every question. Previous year IIT-JEE questions Table Of Contents 1. Functions Symbols of Some Sets of Specific Type Numbers Intervals as Sets Ordered Pairs Cartesian Product of Two Sets Relations Functions Representation of Function Vertical Line Test to Identify whether a Given Relation is a Function or Not Types of Functions Based on Mapping (A) One -One Function or Injective (B) Many-One Function (C) Onto Function or Surjective (D) Into Function (E) One-One Onto Function or Bijection (F) One-One Into Function (G) Many One-Onto Function (H) Many One-Into Function Number of Functions Domain, Co-domain and Range of a Function Rules for Finding the Domain of a Function Rules for Solving Problems on Domain of a Function Rules for Finding the Range of a Function Equal or Identical Functions Arithmetic Combinations of Functions Composition of Functions Common Functions (A) Real Value Functions (B) Even and Odd Functions (C) Continuous and Discontinuous Functions (D) Homogenous functions (E) Bounded Functions (F) Implicit and Explicit Functions (G) Periodic Functions (H) Invertible Functions (I) Inverse Functions Special Type Functions (A) Algebraic Functions (B) Transcendental Functions Domains and Ranges of Common Functions Graphing New Functions Graphing Made Easy ViaTransformations Reflections of the Basic Curves X-axis Reflection : Y-axis Reflection : Reading Graphs Useful Tips Miscellaneous Solved Examples Exercise 1, 2, 3 & 4 2. Limits Limit of a Function Neighbourhood of a Point General Definition of the Limit of a Function Bounded and Unbounded Functions Comparison between the Value of a Function at a Point and The Limit of a Function at the Same Point Properties of Limits Limit in Case of Composite Functions Sandwich Theorem The Limit of as x ? Some Standard Results on Limits Expansion of Some Standard Functions L-Hospital’s Rule Standard Methods of Evaluation of Limits (A) When x ? ? (B) When x ? a , a R Limit of Miscellaneous Forms (A) ? 0 form (B) Use of Newton-Leibnitz’s formula in evaluating the limits (C) Summation of series using definite integral as the limit Miscellaneous Solved Examples Exercise 1, 2, 3 & 4 3. Continuity of Functions Continuity and Discontinuity of a Function Continuity of a Function at a point Continuity of a Function in an Interval Single Point Continuity Examining the Continuity of a Function in a Given Domain Basic Elementary Functions Which are Everywhere Continuous Basic Elementary Functions Which are Continuous in their Domain Basic Results on Continuous Functions Types of Discontinuity at a Point Discontinuity of Special Types of Functions Discontinuity of Some More Functions Intermediate Value Theorem Miscellaneous Solved Examples Exercise 1, 2, 3 & 4 4. Differentiability Differentiability of a Function at a Point Differentiability of a Function in a Set Differentiability in an open interval : Differentiability on a closed interval : Some Standard Results on Differentiability Useful Tips Miscellaneous Solved Examples Exercise 1, 2, 3 & 4 5. Differentiation Introduction Derivative of a Function Derivative of a Power Function Derivative of a Constant Function Derivative of a Sum of Functions Derivative of a Product of Functions (Product Rule) Derivative of a Quotient of two Functions (Quotient Rule) Derivative of Trigonometric Functions Derive of Composite Functions (Chain Rule) Derivative of an Inverse Functions Derivative of Logarithmic Function Derivative of an Exponential Function Derivative of Inverse Trigonometric Functions Derivative of a Function Represented Parametrically Differentiation of One Function w.r.t. other Function Derivative of an Implicit Function Logarithmic Differentiation Differentiation of a Determinant Differentiation by Trigonometrical Substitution Differentiation of Infinite Series Successive Differentiation nth Derivatives of Some Standard Functions Leibnitz’s Theorem [nth Derivative of Product of Two Specific Type Functions] Partial Derivatives List of Differentiation of Some Standard Functions List of Important Theorems Miscellaneous Solved Examples Exercise 1, 2, 3 & 4 6. Mean values theorems and applications of derivatives Introduction Rolle’s Theorem Langrange’s Mean Value Theorem Useful Results, While Applying Rolle’s and Lagrange’s Mean Value Theorems Monotonicity (Strictly Increasing / Strictly Decreasing Function) Differentials Approximation of Error(s) Derivative as a Rate Measurer Slopes of the Tangent & The Normal Equations of Tangent and Normal Length of Intercepts made on Axes by the Tangent Length of Perpendicular from Origin to the Tangent Angle of Intersection of Two Curves Orthogonal Curves Length of Tangent, Normal, Sub Tangent & Sub Normal L’ Hospital’s Rule Application of Derivative In Determining The Nature of Roots of a Cubic Polynomial Useful Tips Miscellaneous Solved Examples Exercise 1, 2, 3 & 4