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Content : 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