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Building on the proven success of its previous edition, Calculus and Its Applications, Second Edition helps students across the curriculum discover the excitement and relevance of applied calculus. Retaining his integrated problem-solving approach, the author engages students in the learning process by carefully discussing key questions, determining equations, and demonstrating the relation between the final solution and the original problem.
Note: Each chapter contains Key Terms and Ideas, Review Exercises, and Projects and Essays. Brief Calculus and Its Applications contains Chapters 1-9.
1. Functions
1.1. Real Numbers
1.2. Some Algebra Review
1.3. Introduction to Functions
1.4. Linear Functions
1.5. Graphs of Functions
1.6. Translations and Reflections (optional)
1.7. Functions in Economics.
2. An Introduction to Limits
2.1. Introduction to Limits
2.2. Continuity
2.3. One-Sided Limits
2.4. Limits at Infinity
2.5. Infinite Limits.
3. Derivatives
3.1 Introduction to the Derivative
3.2. Basic Rules for Differentiation
3.3. Rates of Change
3.4. Marginal Analysis
3.5. The Product and Quotient Rules
3.6. The Chain Rule
3.7. Higher-Order Derivatives
3.8. Implicit Differentiation
3.9. Related Rates
3.10. Differentials.
4. Additional Applications of the Derivative
4.1. Increasing and Decreasing, Graphs, and Critical Numbers
4.2. Relative Extrema and Curve Stretching
4.3. Concavity, the Second Derivative Test, and Curve Sketching
4.4. Absolute Extrema
4.5 Additional Applications, Applied Maximum/Minimum
4.6 Elasticity of Demand .
5. Exponential and Logarithmic Functions
5.1 Exponential Functions
5.2 Logarithmic Functions
5.3 Differentiation of Exponential Functions
5.4 Differentiation of Logarithmic Functions
5.5 Some Additional Business Applications.
6. Integration
6.1. Antidifferentiation
6.2. Some Applications of Antidifferentiation
6.3 The Definite Integral as the Area Under a Curve
6.4 The Fundamental Theorem of Calculus
6.5 Some Applications of the Definite Integral
6.6. Surplus
6.7. Area in the Plane.
7. Techniques of Integration
7.1. Integration by Substitution
7.2. Integration by Parts
7.3. Integration by Tables
7.4. Numerical Methods of Approximation
7.5. Improper Integrals.
8. Probability and Calculus
8.1. Probability and Calculus
8.2. Random Variables, Expected Value, and Variance
8.3. Uniform and Exponential Random Variables
8.4. The Normal Distribution.
9. Differential Equations
9.1. Introduction to Differential Equations
9.2. Separation of Variables
9.3. Additional Applications
9.4 A Numerical Method.
10. Multivariable Calculus
10.1. Functions of Several Variables
10.2. Partial Derivatives
10.3. Maximum and Minimum
10.4. Lagrange Multipliers
10.5. The Method of Least Squares
10.6. Total Differentials
10.7. Double Integrals.
11. Trigonometric Functions
11.1. Right Angles
11.2. Radians and the Trigonometry for Calculus
11.3. Differentiation of Trigonometric Functions
11.4. Integration of Trigonometric Functions
11.5. Integration by Parts Revisited.
12. Infinite Series and Other Advanced Topics
12.1. Some Introductory Concepts
12.2. Geometric Series
12.3. Geometric Power Series
12.4. Taylor Series
12.5. Integration of Series
12.6. Newton's Method
12.7. Indeterminate Forms: L'H"pital's Rule.
Building on the proven success of its previous edition, Calculus and Its Applications, Second Edition helps students across the curriculum discover the excitement and relevance of applied calculus. Retaining his integrated problem-solving approach, the author engages students in the learning process by carefully discussing key questions, determining equations, and demonstrating the relation between the final solution and the original problem.
Table of Contents
Note: Each chapter contains Key Terms and Ideas, Review Exercises, and Projects and Essays. Brief Calculus and Its Applications contains Chapters 1-9.
1. Functions
1.1. Real Numbers
1.2. Some Algebra Review
1.3. Introduction to Functions
1.4. Linear Functions
1.5. Graphs of Functions
1.6. Translations and Reflections (optional)
1.7. Functions in Economics.
2. An Introduction to Limits
2.1. Introduction to Limits
2.2. Continuity
2.3. One-Sided Limits
2.4. Limits at Infinity
2.5. Infinite Limits.
3. Derivatives
3.1 Introduction to the Derivative
3.2. Basic Rules for Differentiation
3.3. Rates of Change
3.4. Marginal Analysis
3.5. The Product and Quotient Rules
3.6. The Chain Rule
3.7. Higher-Order Derivatives
3.8. Implicit Differentiation
3.9. Related Rates
3.10. Differentials.
4. Additional Applications of the Derivative
4.1. Increasing and Decreasing, Graphs, and Critical Numbers
4.2. Relative Extrema and Curve Stretching
4.3. Concavity, the Second Derivative Test, and Curve Sketching
4.4. Absolute Extrema
4.5 Additional Applications, Applied Maximum/Minimum
4.6 Elasticity of Demand .
5. Exponential and Logarithmic Functions
5.1 Exponential Functions
5.2 Logarithmic Functions
5.3 Differentiation of Exponential Functions
5.4 Differentiation of Logarithmic Functions
5.5 Some Additional Business Applications.
6. Integration
6.1. Antidifferentiation
6.2. Some Applications of Antidifferentiation
6.3 The Definite Integral as the Area Under a Curve
6.4 The Fundamental Theorem of Calculus
6.5 Some Applications of the Definite Integral
6.6. Surplus
6.7. Area in the Plane.
7. Techniques of Integration
7.1. Integration by Substitution
7.2. Integration by Parts
7.3. Integration by Tables
7.4. Numerical Methods of Approximation
7.5. Improper Integrals.
8. Probability and Calculus
8.1. Probability and Calculus
8.2. Random Variables, Expected Value, and Variance
8.3. Uniform and Exponential Random Variables
8.4. The Normal Distribution.
9. Differential Equations
9.1. Introduction to Differential Equations
9.2. Separation of Variables
9.3. Additional Applications
9.4 A Numerical Method.
10. Multivariable Calculus
10.1. Functions of Several Variables
10.2. Partial Derivatives
10.3. Maximum and Minimum
10.4. Lagrange Multipliers
10.5. The Method of Least Squares
10.6. Total Differentials
10.7. Double Integrals.
11. Trigonometric Functions
11.1. Right Angles
11.2. Radians and the Trigonometry for Calculus
11.3. Differentiation of Trigonometric Functions
11.4. Integration of Trigonometric Functions
11.5. Integration by Parts Revisited.
12. Infinite Series and Other Advanced Topics
12.1. Some Introductory Concepts
12.2. Geometric Series
12.3. Geometric Power Series
12.4. Taylor Series
12.5. Integration of Series
12.6. Newton's Method
12.7. Indeterminate Forms: L'H"pital's Rule.