IIT JEE Super Course in Mathematics: Calculus

Cover
Contents
Preface
Chapter 1: Functions and Graphs
	Study Material
		Set Theory
			Representation of sets
			Universal set
			Finite and Infinite sets
			Subset
			Power set of a set
			Equal sets
			Venn diagrams
			Algebra of sets
		Cartesian Product of Two Sets
		Relations
			Reflexive relations
			Symmetric relations
			Transitive relations
			Antisymmetric relations
			Equivalence relations
		Functions
		Composition of Functions
			Identity function
		Inverse of a Function
		Even and Odd Functions
		Periodic Functions
		Some Real Valued Functions
			Constant functions
			Graphs of a quadratic polynomial
			Graph of a cubic polynomial
			Modulus function
			Signum function
			Exponential function
			Logarithmic function
			Greatest integer function
			Catenary function
		Parametric form of Representation of a Function
		Graphs of Conic Sections
			Parabola
			Ellipse
			Hyperbola
		Graphs of a Few Composite Functions
		Transformation of Functions
		Some Special Curves
	Topic Grip
		Subjective Questions
		Straight Objective Type Questions
		Assertion–Reason Type Questions
		Linked Comprehension Type Questions
		Multiple Correct Objective Type Questions
		Matrix-Match Type Questions
	IIT Assignment Exercise
		Straight Objective Type Questions
		Assertion–Reason Type Questions
		Linked Comprehension Type Questions
		Multiple Correct Objective Type Questions
		Matrix-Match Type Questions
	Additional practice Exercise
		Subjective Questions
		Straight Objective Type Questions
		Assertion Reason Type Questions
		Linked Comprehension Type Questions
		Multiple Correct Objective Type Questions
		Matrix-Match Type Questions
	Solutions
		Answer Keys
		Hints and Explanations
Chapter 2: Differential Calculus
	Study Material
		Introduction
		Limit of a Function
		Laws on Limits
		Standard Limits
		Continuity of a Function
		Types of Discontinuities of a Function
		Concept of Derivative—Differentiation
		Differentiability of Functions
		Derivatives of Elementary Functions
		Differentiation Rules
		Concept of Differential
		Successive Differentiation
		Higher Order Derivatives
		Tangents and Normals
		Mean Value Theorem and its Applications
		Rolle’s Theorem
			Mean Value Theorem [or Lagrange’s theorem]
		L’ Hospital’s Rule
			Cauchy’s theorem
		Extension of the Mean Value Theorem
		Increasing and Decreasing Functions
		Maxima and Minima of Functions
		Convexity and Concavity of a Curve
		Summary
	Topic Grip
		Subjective Questions
		Straight Objective Type Questions
		Assertion–Reason Type Questions
		Linked Comprehension Type Questions
		Multiple Correct Objective Type Questions
		Matrix-Match Type Question
	IIT Assignment Exercise
		Straight Objective Type Questions
		Assertion–Reason Type Questions
		Linked Comprehension Type Questions
		Multiple Correct Objective Type Questions
		Matrix-Match Type Question
	Additional Practice Exercise
		Subjective Questions
		Straight Objective Type Questions
		Assertion–Reason Type Questions
		Linked Comprehension Type Questions
		Multiple Correct Objective Type Questions
		Matrix-Match Type Questions
	Solutions
		Answer Keys
		Hints and Explanations
Chapter 3: Integral Calculus
	Study Material
		Introduction
		Definite Integral as the Limit of a Sum
			Definition
		Anti-Derivatives
			Definition
			Observations
		Indefinite Integrals of Rational Functions
			Observation
		Integrals of the Form
		Integration By Parts Method
			Results
		Integrals of the form
		Evaluation of Definite Integrals
		Properties of Definite Integrals
			Results
		Improper Integrals
			Definition
			Observations
		Differential Equations
			Definition
		Formation of a Differential Equation
		Solutions of First Order First Degree Differential Equations
		Summary
	Topic Grip
		Subjective Questions
		Straight Objective Type Questions
		Assertion–Reason Type Questions
		Linked Comprehension Type Questuion
		Multiple Correct Objective Type Questions
		Matrix-Match Type Question
	IIT Assignment Exercise
		Straight Objective Type Questions
		Assertion–Reason Type Questions
		Linked Comprehension Type Questions
		Multiple Correct Objective Type Questions
		Matrix-Match Type Question
	Additional Practice Exercise
		Subjective Questions
		Straight Objective Type Questions
		Assertion–Reason Type Questions
		Linked Comprehension Type Questions
		Multiple Correct Objective Type Questions
		Matrix-Match Type Questions
	Solutions
		Answer Keys
		Hints and Explanations