eBook Single Variable Essential Calculus Early Transcendentals 2nd Edition By James Stewart

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CHAPTER WISE BOOK SUMMARY

"Single Variable Essential Calculus: Early Transcendentals," 2nd Edition by James Stewart, is a concise textbook focusing on the fundamental concepts of single-variable calculus. The book is structured into several chapters, each dedicated to specific topics within calculus. Below is a chapter-wise summary:

Chapter 1: Functions and Limits

 1.1 Functions and Their Representations: Introduction to functions, including various ways to represent them—graphically, numerically, and analytically.

 1.2 A Catalog of Essential Functions: Overview of essential functions such as polynomials, rational functions, trigonometric functions, exponential functions, and logarithms.

 1.3 The Limit of a Function: Definition and intuitive understanding of limits.

 1.4 Calculating Limits: Techniques for evaluating limits, including algebraic manipulation and limit laws.

 1.5 Continuity: Discussion on continuous functions and the implications of continuity.

 1.6 Limits Involving Infinity: Exploration of limits as the input or output approaches infinity, including asymptotic behavior.

Chapter 2: Derivatives

 2.1 Derivatives and Rates of Change: Introduction to the derivative as a measure of how a function changes, including physical interpretations.

 2.2 The Derivative as a Function: Understanding the derivative as a function in its own right.

 2.3 Basic Differentiation Formulas: Presentation of fundamental differentiation rules and formulas.

 2.4 The Product and Quotient Rules: Techniques for differentiating products and quotients of functions.

 2.5 The Chain Rule: Method for differentiating composite functions.

 2.6 Implicit Differentiation: Techniques for differentiating implicitly defined functions.

 2.7 Related Rates: Application of derivatives to problems involving rates of change in related quantities.

 2.8 Linear Approximations and Differentials: Using derivatives to approximate function values and understand differentials.

Chapter 3: Inverse Functions

 3.1 Exponential Functions: Properties and applications of exponential functions.

 3.2 Inverse Functions and Logarithms: Introduction to inverse functions, focusing on logarithmic functions as inverses of exponentials.

 3.3 Derivatives of Logarithmic and Exponential Functions: Differentiation techniques for logarithmic and exponential functions.

 3.4 Exponential Growth and Decay: Modeling and analysis of exponential growth and decay phenomena.

 3.5 Inverse Trigonometric Functions: Definition and properties of inverse trigonometric functions.

 3.6 Hyperbolic Functions: Introduction to hyperbolic functions and their properties.

 3.7 Indeterminate Forms and L'Hôpital's Rule: Techniques for resolving indeterminate forms using L'Hôpital's Rule.

Chapter 4: Applications of Differentiation

 4.1 Maximum and Minimum Values: Techniques for finding local and global extrema of functions.

 4.2 The Mean Value Theorem: Statement and implications of the Mean Value Theorem.

 4.3 Derivatives and the Shapes of Graphs: Using derivatives to analyze and sketch the graphs of functions.

 4.4 Curve Sketching: Comprehensive approach to graphing functions based on derivative information.

 4.5 Optimization Problems: Applying differentiation to solve real-world optimization problems.

 4.6 Newton's Method: Iterative technique for finding roots of functions.

 4.7 Antiderivatives: Introduction to antiderivatives and basic integration techniques.

Chapter 5: Integrals

 5.1 Areas and Distances: Conceptual foundation of integration through area and distance problems.

 5.2 The Definite Integral: Definition and properties of the definite integral.

 5.3 Evaluating Definite Integrals: Techniques for computing definite integrals.

 5.4 The Fundamental Theorem of Calculus: Connection between differentiation and integration.

 5.5 The Substitution Rule: Method for simplifying integrals via substitution.

Chapter 6: Techniques of Integration

 6.1 Integration by Parts: Technique for integrating products of functions.

 6.2 Trigonometric Integrals and Substitutions: Strategies for integrating trigonometric functions.

 6.3 Partial Fractions: Decomposition method for integrating rational functions.

 6.4 Integration with Tables and Computer Algebra Systems: Utilizing resources to assist in integration.

 6.5 Approximate Integration: Numerical methods for approximating integrals.

 6.6 Improper Integrals: Handling integrals with infinite limits or integrands.

Chapter 7: Applications of Integration

 7.1 Areas between Curves: Calculating the area enclosed by multiple curves.

 7.2 Volumes: Determining volumes of solids of revolution and other solids.

 7.3 Volumes by Cylindrical Shells: Alternative method for finding volumes of solids.

 7.4 Arc Length: Computing the length of curves.

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"We have all the books, eBooks, test banks, and solution manuals available at a cheap price for instant download. If you need any book other than this, feel free to contact us for instant access and downloads, please contact us via email or WhatsApp.

 Whatsapp link: https://wa.me/+447507735190

 Email: etutorsource@gmail.com



 ("And we also provide academic writing services.")



 Do you need the best quality, organic,and plagiarismfree assignments, and dissertation help without using AI tools? I am a UK-based professional researcher and tutor. I have been consulting and tutoring for more than 14 years in dissertations, essay help, reports, and other assignments.

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