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Applied Calculus Fifth Edition Download Free PDF



Applied Calculus Fifth Edition produced by The Calculus Consortium and initially funded by a National Science Foundation Grant. This is an other great mathematics book cover the following topics of CALCULAS.

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  • 1. Functions and Change
    Chapter 1 introduces the concept of a function and the idea of change, including the distinction between total change, rate of change, and relative change. All elementary functions are introduced here. Although the functions are probably familiar, the graphical, numerical, verbal, and modeling approach to them is likely to be new. We introduce exponential functions early, since they are fundamental to the understanding of real-world processes. The trigonometric functions are optional. A brief introduction to elasticity has been added to Section 1.3.

  • 2. Rate of Change: The Derivative
    Chapter 2 presents the key concept of the derivative according to the Rule of Four. The purpose of this chapter is to give the student a practical understanding of the meaning of the derivative and its interpretation as an instantaneous rate of change. Students will learn how the derivative can be used to represent relative rates of change. After finishing this chapter, a student will be able to approximate derivatives numerically by taking difference quotients, visualize derivatives graphically as the slope of the graph, and interpret the meaning of first and second derivatives in various applications. The student will also understand the concept of marginality and recognize the derivative as a function in its own right. Focus on Theory: This section discusses limits and continuity and presents the symbolic definition of the derivative.

  • 3. Short-Cuts to Differentiation The derivatives of all the functions in Chapter 1 are introduced, as well as the rules for differentiating products, quotients, and composite functions. Students learn how to find relative rates of change using logarithms. Focus on Theory: This section uses the definition of the derivative to obtain the differentiation rules. Focus on Practice: This section provides a collection of differentiation problems for skill-building.

  • 4. Using the Derivative The aim of this chapter is to enable the student to use the derivative in solving problems, including optimization and graphing. It is not necessary to cover all the sections.

  • 5. Accumulated Change: The Definite Integral
    Chapter 5 presents the key concept of the definite integral, in the same spirit as Chapter 2. The purpose of this chapter is to give the student a practical understanding of the definite integral as a limit of Riemann sums, and to bring out the connection between the derivative and the definite integral in the Fundamental Theorem of Calculus. We use the same method as in Chapter 2, introducing the fundamental concept in depth without going into technique. The student will finish the chapter with a good grasp of the definite integral as a limit of Riemann sums, and the ability to approximate a definite integral numerically and interpret it graphically. The chapter includes applications of definite integrals in a variety of contexts, including the average value of a function. Chapter 5 can be covered immediately after Chapter 2 without difficulty. The introduction to the definite integral has been streamlined. Average values, formerly in Section 6.1, are now in Section 5.6. Focus on Theory: This section presents the Second Fundamental Theorem of Calculus and the properties of the definite integral.

  • 6. Antiderivatives and Applications This chapter combines the former Chapter 6 and 7. It covers antiderivatives from a graphical, numerical, and algebraic point of view. The Fundamental Theorem of Calculus is used to evaluate definite integrals. Optional application sections are included on consumer and producer surplus and on present and future value; the integrals in these sections can be evaluated numerically or using the Fundamental Theorem. The chapter concludes with optional sctions on integration by substitution and integration by parts. Section 6.1, on graphical and numerical antiderivatives, is based on the former Section 7.5. Section 6.2, on symbolic antiderivatives, is based on the former Section 7.1. Using the Fundamental Theorem to find definite integrals is in Section 6.3, formerly Section 7.3. Sections 6.4 and 6.5 are the former Sections 6.2 and 6.3. Sections 6.6 and 6.7 are the former Sections 7.2 and 7.4. Focus on Practice: This section provides a collection of integration problems for skill-building.

  • 7. Probability
    This chapter covers probability density functions, cumulative distribution functions, the median and the mean. Chapter 7 is the former Chapter 8.

  • 8. Functions of Several Variables
    This chapter introduces functions of two variables from several points of view, using contour diagrams, formulas, and tables. It gives students the skills to read contour diagrams and think graphically, to read tables and think numerically, and to apply these skills, along with their algebraic skills, to modeling. The idea of the partial derivative is introduced from graphical, numerical, and symbolic viewpoints. Partial derivatives are then applied to optimization problems, ending with a discussion of constrained optimization using Lagrange multipliers. Chapter 8 is the former Chapter 9. Focus on Theory: This section uses optimization to derive the formula for the regression line.

  • 9. Mathematical Modeling Using Differential Equations

  • 10. Geometric Series
    This chapter covers geometric series and their applications to business, economics, and the life sciences. Chpater 10 is the former Chapter 11.

  • Appendices
    The first appendix introduces the student to fitting formulas to data; the second appendix provides further discussion of compound interest and the definition of the number e. The third appendix contains a selection of spreadsheet projects.

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