Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition - Laurence Hoffmann,Gerald Bradley,David Sobecki,Michael Price

About the book

Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. Students achieve success using this text as a result of the author's applied and real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets. More than 100,000 students worldwide have studied from this text!

Key features

Learning Objectives: Learning objectives, listed at the opening of each section, help to organize knowledge and topics for both instructors and students. They allow instructors to link assessment to the items covered in the book, prepare students for what they will learn, aid in review, and reinforce the important ideas in each section.

Revised and Reorganized Application Exercises : Application exercises have been revised and expanded. They are now organized by subject, making it easy for instructors and students to find the questions that relate to their area of interest. The exercise sets have been expanded to ensure full and proper coverage of all topics and to make it easy for students to relate the material they just learned to real-world problems that interest them.

Reorganized and Updated Contents: As technology advances, trigonometric functions are becoming more and more important for all applied topics. For this reason, the chapter on Trigonometric Functions has been moved from Chapter 11 to Chapter 9. This allows classes who cover this topic to do so earlier in the term, following the syllabi of most applied calculus classes and making it clear that trigonometric functions are important for future study. Trig functions are identified and integrated throughout the later chapters, allowing those professors who cover trig functions to assign items that relate to what they have covered while making it simple for students who have not seen trigonometric functions before to skip this material.

Material on the Extreme Value Property for functions of two variables and finding extreme values on closed, bounded regions has been added to Section 7.3. This completes the analogy with the one-variable case and better prepares students for future study of statistics and finite mathematics.

Connect: The online homework, eBook, videos, applets, and other electronic supplements will all be housed within McGraw-Hill's Connect platform. This allows for seamless integration of the eBook with the online homework, videos, applets, and other assets. The material is fully vetted by the digital coauthor, Mike Price, to ensure that the online content matches the pedagogy, tone, level, and style of the text. With the aid of subject matter experts who teach applied calculus and are familiar with how the online content is used by students, the questions have been improved to ensure that they are clear, correct, and easy for students to understand and use. We have addressed common errors and improved the quality and level of the online homework, including greater consistency and better feedback in the form of hints and guided solutions.

Example Titles: Titles have been added to each example in the text. This allows both students and instructors to quickly find items of interest to them. In combination with the new learning objectives, these titles make the topics clear and comprehensible for all students, help to organize ideas, and aid both students and professors with review and evaluation.

Just-in-Time Reviews : This hallmark feature serves as a hand reference that quickly reminds students of important concepts from college algebra or precalculus as they are being used in examples and discussions. Each review is placed in the margin adjacent to the location where the reviewed topic material is used. This allows for immediate reinforcement without distracting from the material under discussion

A Vast Assortment of Applications: Hoffmann/Bradley contains over 400 different applications of problems in business, economics, finance & investment, the life & environmental sciences, the physical sciences, and the social sciences. Great effort is made to ensure that topics are applied to these practical problems soon after their introduction. Many new problems have been added, as well as obsolete or outdated data has been removed. An index of applications, included in the end papers, helps students and instructors find those items most relevant to them.

Procedural Examples & Boxes: Each new topic is approached with careful clarity by providing step-by-step problem-solving techniques. These techniques are demonstrated in the numerous procedural examples and in the frequent procedural summary boxes highlighting the techniques demonstrated.

Explore! Technology: For those choosing to include a graphing focus in their course, the Explore! boxes guide students in the use of graphing calculators and challenge their understanding of the topics presented through explorations tied to specific examples. Each chapter concludes with an Explore! Update section that provides solutions and hints to selected boxes throughout the chapter.

About the author

Dave Sobecki
Dave Sobecki is an associate professor in the Department of Mathematics at Miami University in Hamilton, Ohio. He earned a B.A. in math education from Bowling Green State University before continuing on to earn an M.A. and a Ph.D. in mathematics from Bowling Green State University. He has written or coauthored five journal articles, eleven books, and five interactive CD-ROMs. Dave lives in Fairfield, Ohio, with his wife (Cat) and dogs (Macleod and Tessa).

Table of contents

Chapter 1: Functions, Graphs, and Limits
1.1 Functions
1.2 The Graph of a Function
1.3 Lines and Linear Functions
1.4 Functional Models
1.5 Limits
1.6 One-Sided Limits and Continuity
Chapter 2: Differentiation: Basic Concepts
2.1 The Derivative
2.2 Techniques of Differentiation
2.3 Product and Quotient Rules; Higher-Order Derivatives
2.4 The Chain Rule
2.5 Marginal Analysis and Approximations Using Increments
2.6 Implicit Differentiation and Related Rates
Chapter 3: Additional Applications of the Derivative
3.1 Increasing and Decreasing Functions; Relative Extrema
3.2 Concavity and Points of Inflection
3.3 Curve Sketching
3.4 Optimization; Elasticity of Demand
3.5 Additional Applied Optimization
Chapter 4: Exponential and Logarithmic Functions
4.1 Exponential Functions; Continuous Compounding
4.2 Logarithmic Functions
4.3 Differentiation of Exponential and Logarithmic Functions
4.4 Additional Applications; Exponential Models
Chapter 5: Integration
5.1 Indefinite Integration and Differential Equations
5.2 Integration by Substitution
5.3 The Definite Integral and the Fundamental Theorem of Calculus
5.4 Applying Definite Integration: Distribution of Wealth and Average Value
5.5 Additional Applications to Business and Economics
5.6 Additional Applications to the Life and Social Sciences
Chapter 6: Additional Topics in Integration
6.1 Integration by Parts; Integral Tables
6.2 Numerical Integration
6.3 Improper Integrals
Chapter 7: Calculus of Several Variables
7.1 Functions of Several Variables
7.2 Partial Derivatives
7.3 Optimizing Functions of Two Variables
7.4 The Method of Least-Squares
7.5 Constrained Optimization: The Method of Lagrange Multipliers
7.6 Double Integrals
Chapter 8: Trigonometric Functions
8.1 Angle Measurement; Trigonometric Functions
8.2 Trigonometric Applications Involving Differentiation
8.3 Trigonometric Applications Involving Integration
Chapter 9: Differential Equations
9.1 Modeling with Differential Equations
9.2 First-Order Linear Differential Equations
9.3 Additional Applications of Differential Equations
9.4 Approximate Solutions of Differential Equations
9.5 Difference Equations; The Cobweb Model
Chapter 10: Infinite Series and Taylor Series Approximations
10.1 Infinite Series; Geometric Series
10.2 Tests for Convergence
10.3 Functions as Power Series; Taylor Series
Chapter 11: Probability and Calculus
11.1 Introduction to Probability; Discrete Random Variables
11.2 Continuous Probability Distributions
11.3 Expected Value and Variance of Continuous Random Variables
10.4 Normal and Poisson Probability Distributions
Appendix A: Algebra Review
A.1 A Brief Review of Algebra
A.2 Factoring Polynomials and Solving Systems of Equations
A.3 Evaluating Limits with L'Hopital's Rule
A.4 The Summation Notation