Thomas Calculas

Chapter 1 Functions
1.1 Functions and Their Graphs
1.2 Classification of Functions and Combining Functions; Shifting and Scaling Graphs
1.3 Trigonometric Functions
1.4 Miscellaneous
Questions to Guide Your Review
Practice Exercises
Single Choice Questions
Multiple Choice Questions
Passage Type Questions
Matrix Match Type Questions
Integer Type Questions
Additional and Advanced Exercises

Chapter 2 Limits and Continuity
2.1 Rates of Change and Tangents to Curves
2.2 Limit of a Function and Limit Laws
2.3 The Precise Definition of a Limit
2.4 One-Sided Limits
2.5 Continuity
2.6 Limits Involving Infinity; Asymptotes of Graphs
Questions to Guide Your Review
Practice Exercises
Single Choice Questions
Multiple Choice Questions
Passage Type Questions
Matrix Match Type Questions
Integer Type Questions
Additional and Advanced Exercises

Chapter 3 Derivatives
3.1 Tangents and the Derivative at a Point
3.2 The Derivative as a Function
3.3 Differentiation Rules
3.4 Derivatives of Trigonometric Functions
3.5 The Chain Rule
3.6 Method of Differentiation
3.7 Implicit Differentiation
3.8 Inverse Trigonometric Functions and their Derivatives
3.9 Derivative of Inverse Function
3.10 Indeterminate Forms and L'Hôpital's Rule
Questions to Guide Your Review
Practice Exercises
Single Choice Questions
Multiple Choice Questions
Passage Type Questions
Matrix Match Type Questions
Integer Type Questions
Additional and Advanced Exercises

Chapter 4 Applications of Derivatives
4.1 The Derivative as a Rate of Change
4.2 Related Rates
4.3 Linearization and Differentials
4.4 Extreme Values of Functions
4.5 The Mean Value Theorem
4.6 Monotonic Functions and the First Derivative Test
4.7 Concavity and Curve Sketching
4.8 Applied Optimization
Questions to Guide Your Review
Practice Exercises
Single Choice Questions
Multiple Choice Questions
Passage Type Questions
Matrix Match Type Questions
Integer Type Questions
Additional and Advanced Exercises

Chapter 5 Integrals
5.1 Antiderivatives
5.2 Area and Estimating with Finite Sums
5.3 Sigma Notation and Limits of Finite Sums
5.4 The Definite Integral
5.5 Indefinite Integrals and the Substitution Method
5.6 Techniques of Integration
5.7 Integration by Parts
5.8 Trigonometric Integrals
5.9 Trigonometric Substitutions
5.10 Integration of Rational Functions by Partial Fractions
5.11 Reduction Formulas
5.12 Improper Integrals
5.13 Properties of Definite Integrals
5.14 The Fundamental Theorem of Calculus
5.15 Definite Integral Substitutions
Questions to Guide Your Review
Practice Exercises
Single Choice Questions (Indefinite)
Multiple Choice Questions (Indefinite)
Passage Type Questions (Indefinite)
Matrix Match Type Questions (Indefinite)
Integer Type Questions (Indefinite)
Single Choice Questions (Definite)
Multiple Choice Questions (Definite)
Passage Type Questions (Definite)
Matrix Match Type Questions (Definite)
Integer Type Questions (Definite)
Additional and Advanced Exercises

Chapter 6 First-Order Differential Equations and Area Under Curve
6.1 Solutions, Slope Fields, and Euler's Method
6.2 First-Order Linear Equations
6.3 Applications
6.4 Area Under the Graph of a Nonnegative Function
Questions to Guide Your Review
Practice Exercises
Single Choice Questions
Multiple Choice Questions
Passage Type Questions
Matrix Match Type Questions
Integer Type Questions
Additional and Advanced Exercises

Answer Keys






Salient Features

• Topics thoughtfully synchronized to meet students' requirements
• Numerous illustrations, worked-out examples and exercises
• A research-based problem-solving approach used in solved examples
• Vast collection of objective questions as per the JEE question paper pattern
* Single Choice Questions
* Multiple Choice Questions
* Passage Type Questions
* Matrix Match Type Questions
* Integer Type Questions