Calculus Concepts – An Applied Approach to the Mathematics
This book presents a fresh, intuitive approach to the concepts of calculus for students in fields such as business, economics, liberal arts, management, and the social and life sciences. It is appropriate for courses generally known as “brief calculus” or “applied calculus.”
Our overall goal is to improve learning of basic calculus concepts by involving students with new material in a way that is different from traditional practice. The development of conceptual understanding coupled with a commitment to make calculus meaningful to the student are guiding forces. The material in this book involves many applications of real situations through its data-driven, technology-based modeling approach. It considers the ability to correctly interpret the mathematics of reallife situations of equal importance to the understanding of the concepts of calculus in the context of change.
Fourfold Viewpoint Complete understanding of the concepts is enhanced and emphasized by the continual use of the fourfold viewpoint: numeric, algebraic, verbal, and graphical.
Data-Driven Many everyday, real-life situations involving change are discrete in nature and manifest themselves through data. Such situations often can be represented by continuous or piecewise continuous mathematical models so that the concepts, methods, and techniques of calculus can be utilized to solve problems. Thus we seek, when appropriate, to make real-life data a starting point for our investigations.
The use of real data and the search for appropriate models also expose students to the reality of uncertainty. We emphasize that sometimes there can be more than one appropriate model and that answers derived from models are only approximations.
We believe that exposure to the possibility of more than one correct approach or answer is valuable.
Modeling Approach We consider modeling to be an important tool and introduce it at the outset. Both linear and nonlinear models of discrete data are used to obtain functional relationships between variables of interest. The functions given by the models are the ones used by students to conduct their investigations of calculus concepts.
It is the connection to real-life data that most students feel shows the relevance of the mathematics in this course to their lives and adds reality to the topics studied. Interpretation Emphasis This book differs from traditional texts not only in its philosophy but also in its overall focus, level of activities, development of topics, and attention to detail. Interpretation of results is a key feature of this text that allows students to make sense of the mathematical concepts and appreciate the usefulness of those concepts in their future careers and in their lives.
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