Get complete eBook Instant Download Link below https://scholarfriends.com/singlePaper/455932/ebooksingle-variable-essential-calculus-early-transcendentals2nd-edition-by-james-stewart "Single Variable Essential Calculus: Early Transcendentals" by James Stewart is
second edition is structured into several chapters, each delving into key topics of single-variable calculus. Here's a chapter-wise summary:
Chapter 1: Functions and Limits
Functions and Their Representations: Introduction to functions, including various ways to represent them—graphically, numerically, analytically, and verbally.
A Catalog of Essential Functions: Overview of fundamental functions such as polynomials, rational functions, trigonometric functions, exponential functions, and logarithms.
The Limit of a Function: Concept of limits, approaching a value, and the formal definition of a limit.
Calculating Limits: Techniques for evaluating limits, including factoring, rationalizing, and using special limit laws.
Continuity: Discussion on continuous functions, points of discontinuity, and the Intermediate Value Theorem.
Limits Involving Infinity: Exploration of limits as functions approach infinity or negative infinity, and horizontal asymptotes.
Chapter 2: Derivatives
Derivatives and Rates of Change: Definition of the derivative, interpreting it as a rate of change, and its applications to real-world problems.
The Derivative as a Function: Understanding the derivative as a function itself, and exploring higher-order derivatives.
Basic Differentiation Formulas: Introduction to fundamental differentiation rules, including the power rule, sum rule, and constant multiple rule.
The Product and Quotient Rules: Techniques for differentiating products and quotients of functions.
The Chain Rule: Method for differentiating composite functions.
Implicit Differentiation: Differentiating equations not solved for one variable in terms of another.
Related Rates: Solving problems involving rates at which related quantities change.
Linear Approximations and Differentials: Using the derivative to approximate function values and understanding differentials.
Chapter 3: Inverse Functions
Exponential Functions: Properties and graphs of exponential functions, and their applications.
Inverse Functions and Logarithms: Understanding inverse functions, the natural logarithm, and their properties.
Derivatives of Logarithmic and Exponential Functions: Techniques for differentiating logarithmic and exponential functions.
Exponential Growth and Decay: Modeling and solving problems involving exponential growth and decay.
Inverse Trigonometric Functions: Introduction to arcsine, arccosine, arctangent, and their derivatives.
Hyperbolic Functions: Definition and properties of hyperbolic functions and their derivatives.
Indeterminate Forms and L'Hôpital's Rule: Techniques for evaluating limits that result in indeterminate forms using L'Hôpital's Rule.
Chapter 4: Applications of Differentiation
Maximum and Minimum Values: Finding local and absolute extrema of functions.
The Mean Value Theorem: Understanding and applying the Mean Value Theorem.
Derivatives and the Shapes of Graphs: Analyzing how derivatives affect the shape of graphs, including concavity and inflection points.
Curve Sketching: Techniques for sketching graphs of functions using first and second derivatives.
Optimization Problems: Solving real-world problems by finding optimal values.
Newton's Method: An iterative method for approximating roots of equations.
Antiderivatives: Introduction to antiderivatives and basic integration techniques.
Chapter 5: Integrals
Areas and Distances: Understanding the definite integral as a limit of Riemann sums to calculate areas and distances.
The Definite Integral: Formal definition and properties of the definite integral.
Evaluating Definite Integrals: Techniques for calculating definite integrals, including the use of the Fundamental Theorem of Calculus.
The Fundamental Theorem of Calculus: Connecting differentiation and integration, and its significance in evaluating integrals.
The Substitution Rule: Method for simplifying integrals through substitution.
Chapter 6: Techniques of Integration
Integration by Parts: Technique derived from the product rule for integrating products of functions.
Trigonometric Integrals and Substitutions: Integrating products of trigonometric functions and using trigonometric substitutions.
Partial Fractions: Decomposing rational functions into simpler fractions for integration.
Integration with Tables and Computer Algebra Systems: Utilizing integration tables and technology to evaluate complex integrals.
Approximate Integration: Numerical methods for approximating definite integrals, including the Trapezoidal Rule and Simpson's Rule.
Improper Integrals: Evaluating integrals with infinite limits or integrands with infinite discontinuities.
Chapter 7: Applications of Integration
Areas between Curves: Calculating the area enclosed between two or more curves.
Volumes: Determining volumes of solids of revolution using the disk and washer methods.
Volumes by Cylindrical Shells: Using the shell method to find volumes of solids of revolution.
Arc Length: Computing the length of curves defined by functions.
Area of a Surface of Revolution: Finding the surface area of solids generated by revolving curves around an axis.
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