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Full Description
This is the brief version of Calculus and Its Applications, Thirteenth Edition, containing chapters 1-9. Calculus and Its Applications, Thirteenth Edition is a comprehensive, yet flexible, text for students majoring in business, economics, life science, or social sciences. The authors delve into greater mathematical depth than other texts while motivating students through relevant, up-to-date, applications drawn from students' major fields of study. The authors motivate key ideas geometrically and intuitively, providing a solid foundation for the more abstract treatments that follow. Every chapter includes a large quantity of exceptional exercises-a hallmark of this text--that address skills, applications, concepts, and technology. The Thirteenth Edition includes updated applications, exercises, and technology coverage. The authors have also added more study tools, including a prerequisite skills diagnostic test and a greatly improved end-of-chapter summary, and made content improvements based on user reviews.
Contents
PrefaceIntroduction0. Functions0.1 Functions and Their Graphs0.2 Some Important Functions0.3 The Algebra of Functions0.4 Zeros of Functions - The Quadratic Formula and Factoring0.5 Exponents and Power Functions0.6 Functions and Graphs in Applications1. The Derivative1.1 The Slope of a Straight Line1.2 The Slope of a Curve at a Point1.3 The Derivative1.4 Limits and the Derivative1.5 Differentiability and Continuity1.6 Some Rules for Differentiation1.7 More About Derivatives1.8 The Derivative as a Rate of Change2. Applications of the Derivative2.1 Describing Graphs of Functions2.2 The First and Second Derivative Rules2.3 The First and Section Derivative Tests and Curve Sketching2.4 Curve Sketching (Conclusion)2.5 Optimization Problems2.6 Further Optimization Problems2.7 Applications of Derivatives to Business and Economics3. Techniques of Differentiation3.1 The Product and Quotient Rules3.2 The Chain Rule and the General Power Rule3.3 Implicit Differentiation and Related Rates4. The Exponential and Natural Logarithm Functions4.1 Exponential Functions4.2 The Exponential Function ex4.3 Differentiation of Exponential Functions4.4 The Natural Logarithm Function4.5 The Derivative of ln x4.6 Properties of the Natural Logarithm Function5. Applications of the Exponential and Natural Logarithm Functions5.1 Exponential Growth and Decay5.2 Compound Interest5.3 Applications of the Natural Logarithm Function to Economics5.4 Further Exponential Models6. The Definite Integral6.1 Antidifferentiation6.2 The Definite Integral and Net Change of a Function6.3 The Definite Integral and Area Under a Graph6.4 Areas in the xy-plane6.5 Applications of the Definite Integral7. Functions of Several Variables7.1 Examples of Functions of Several Variables7.2 Partial Derivatives7.3 Maxima and Minima of Functions of Several Variables7.4 Lagrange Multipliers and Constrained Optimization7.5 The Method of Least Squares7.6 Double Integrals8. The Trigonometric Functions8.1 Radian Measure of Angles8.2 The Sine and the Cosine8.3 Differentiation and Integration of sin t and cos t8.4 The Tangent and Other Trigonometric Functions9. Techniques of Integration9.1 Integration by Substitution9.2 Integration by Parts9.3 Evaluation of Definite Integrals9.4 Approximation of Definite Integrals9.5 Some Applications of the Integral9.6 Improper Integrals
