This book is ideal for one- or two-semester or two- or three-quarter courses covering topics in college algebra, finite mathematics, and calculus for students in business, economics, and the life and social sciences.
Haeussler, Paul, and Wood establish a strong algebraic foundation that sets this text apart from other applied mathematics texts, paving the way for students to solve real-world problems that use calculus. Emphasis on developing algebraic skills is extended to the exercises–including both drill problems and applications. The authors work through examples and explanations with a blend of rigor and accessibility. In addition, they have refined the flow, transitions, organisation, and portioning of the content over many editions to optimise manageability for teachers and learning for students. The table of contents covers a wide range of topics efficiently, enabling instructors to tailor their courses to meet student needs.
Applications: An abundance and variety of applications for the intended audience appear throughout the book so that students see frequently how the mathematics they are learning can be used. These applications cover such diverse areas as business, economics, biology, medicine, sociology, psychology, ecology, statistics, earth science, and archaeology.
Now Work Problem N: Throughout the text we have retained the popular Now Work Problem N feature. The idea is that after a worked example, students are directed toan end of section problem (labelled with a coloured exercise number) that reinforces theideas of the worked example. This gives students an opportunity to practice what theyhave just learned.
Cautions: Cautionary warnings are presented in very much the same way an instructor would warn students in class of commonly-made errors. These appear in the margin, along with other explanatory notes and emphases.
Definitions, key concepts, and important rules and formulas: These are clearly stated and displayed as a way to make the navigation of the book that much easier for the student.
Review material: Each chapter has a review section that contains a list of important terms and symbols, a chapter summary, and numerous review problems. In addition, key examples are referenced along with each group of important terms and symbols.
Early treatment of summation notation: This topic is necessary for study of the definite integral in Chapter 14 but it is useful long before that. Since it is a notation that is new to most students at this level, but no more than a notation, we get it out of the way in Chapter 1. By using it when convenient, before coverage of the definite integral, it is not a distraction from that challenging concept.
Section 1.6 on sequences: This section provides several pedagogical advantages. The very definition is stated in a fashion that paves the way for the more important and more basic definition of function in Chapter 2. In summing the terms of a sequence we are able to practice the use of summation notation introduced in the preceding section. The most obvious benefit though is that “sequences” allows us a better organization in the annuities section of Chapter 5. Both the present and the future values of an annuity are obtained by summing (finite) geometric sequences. Later in the text, sequences arise in the definition of the number e in Chapter 4, in Markov chains in Chapter 9, and in Newton’s method in Chapter 12, so that a helpful unifying reference is obtained.
Sum of an infinite sequence: In the course of summing the terms of a finite sequence, it is natural to raise the possibility of summing the terms of an infinite sequence. This is a nonthreatening environment in which to provide a first foray into the world of limits. We simply explain how certain infinite geometric sequences have well-defined sums and phrase the results in a way that creates a toehold for the introduction of limits in Chapter 10. These particular infinite sums enable us to introduce the idea of a perpetuity, first informally in the sequence section, and then again in more detail in a separate section in Chapter 5.
Leontief’s input-output analysis in Section 6.7: In this section we have separated various aspects of the total problem. We begin by describing what we call the Leontief matrix A as an encoding of the input and output relationships between sectors of an economy.
Birthday probability in Section 8.4: This is a treatment of the classic problem of determining the probability that at least 2 of n people have their birthday on the same day. While this problem is given as an example in many texts, the recursive formula that we give for calculating the probability as a function of n is not a common feature. It is reasonable to include it in this book because recursively defined sequences appear explicitly in Section 1.6.
Sign Charts for a function in Chapter 10: The sign charts that we introduced in the 12th edition now make their appearance in Chapter 10. Our point is that these charts can be made for any real-valued function of a real variable and their help in graphing a function begins prior to the introduction of derivatives.