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This accessible, and reader-friendly introduction to applied calculus prepares readers to deal with calculus topics when they are encountered in a variety of areas. The emphasis throughout is on computational skills, ideas, and problem solving--rather than on mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept, and general concepts and results are usually presented only after particular cases have been discussed. There are over 370 numbered worked examples, and most sections contain applied exercises from business and economics, life sciences, and social sciences. A Beginning Library of Elementary Functions. Additional Elementary Functions. The Derivative. Graphing and Optimization. Additional Derivative Topics. Integration. Additional Integration. Multivariable Calculus. Differential Equations. Taylor Polynomials and Infinite Series. Probability and Calculus. Trigonometric Functions Review. For anyone who needs a proficiency in calculus in their work in business, economics, social sciences, or life sciences.
Mathematical reform is the driving force behind the organization and development of this new college algebra text. The use of technology, primarily graphing utilities, is assumed throughout the text. The development of each topic proceeds from the concrete to the abstract and takes full advantage of technology, wherever appropriate. The first major objective of this book is to encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically. Proceeding in this way, students gain a broader, deeper,and more useful understanding of a concept or process. Even though concept development and technology are emphasized, manipulative skills are not ignored, and plenty of opportunities to practice basic skills are present. A brief look at the table of contents will reveal the importance of the function concept as a unifying theme. The second major objective of this book is the development of a library of elementary functions, includingtheir important properties and uses. Having this library of elementary functions as a basic working tool in their mathematical tool boxes, students will be able to move into calculus with greater confidence and understanding. In addition, a concise review of basic algebraic concepts is included in Appendix A for easy reference, or systematic review. The third major objective of this book is to give the student substantial experience in solving and modeling real world problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful. Most of the applications are simplified versions of actual real-world problems taken from professional journals and professional books. No specialized experience is required to solve any of the applications.
Featuring topics from finance, linear algebra, linear programming and probability, this text emphasizes computational skills, ideas and problem solving. The use of graphing calculators is integrated in optional examples, and the book includes exercises related to technology, illustrations of applications of spreadsheets and sample computer code. Linear programming is tested thoroughly, including applications of simplex, dual, big M, and two-phase methods for utilizing slack, surplus and artificial variables.