Mathematical Modeling and Applied Calculus

• 1: Functions for Modeling Data


• 1.1: Functions


• 1.2: Multivariable Functions


• 1.3: Linear Functions


• 1.4: Exponential Functions


• 1.5: Inverse Functions


• 1.6: Logarithmic Functions


• 1.7: Trigonometric Functions


• 2: Mathematical Modeling


• 2.1: Modeling with Linear Functions


• 2.2: Modeling with Exponential Functions


• 2.3: Modeling with Power Functions


• 2.4: Modeling with Sine Functions


• 2.5: Modeling with Sigmoidal Functions


• 2.6: Single Variable Modeling


• 2.7: Dimensional Analysis


• 3: The Method of Least Squares


• 3.1: Vectors and Vector Operations


• 3.2: Linear Combinations of Vectors


• 3.3: Existence of Linear Combinations


• 3.4: Vector Projection


• 3.5: The Method of Least Squares


• 4: Derivatives


• 4.1: Rates of Change


• 4.2: The Derivative as a Function


• 4.3: Derivatives of Modeling Functions


• 4.4: Product and Quotient Rules


• 4.5: The Chain Rule


• 4.6: Partial Derivatives


• 4.7: Limits and the Derivative


• 5: Optimization


• 5.1: Global Extreme Values


• 5.2: Local Extreme Values


• 5.3: Concavity and Extreme Values


• 5.4: Newton's Method and Optimization


• 5.5: Multivariable Optimization


• 5.6: Constrained Optimization


• 6: Accumulation and Integration


• 6.1: Accumulation


• 6.2: The Definite Integral


• 6.3: First Fundamental Theorem


• 6.4: Second Fundamental Theorem


• 6.5: The Method of Substitution


• 6.6: Integration by Parts

Joel M. Kilty joined the faculty of Centre College, a US News Top 50 Liberal Arts College, as an Assistant Professor of Mathematics in 2009, receiving tenure and promotion to the rank of Associate Professor in 2015. In 2017 he was named the Elizabeth Molloy Dowling Associate Professor of Mathematics. He received his Ph.D. and M.A. degrees in mathematics from the University of Kentucky in 2009 and 2006 respectively, and his B.A. degree in mathematics from Asbury College in 2004. He has published several research articles in the field of differential equations is an active member of the Mathematical Association of America.

Alex M. McAllister joined the Centre College faculty in 1999, and he has taught mathematics to undergraduates at the University of Notre Dame, Dartmouth College, and Centre College. He was awarded the H.W. Stodghill Jr. and Adele H. Stodghill Professorship in Mathematics in 2015 and the Mathematical Association of America's Kentucky Section Teaching Award in 2015. His scholarly interests include mathematical logic and foundations, computability theory, and the history of mathematics. McAllister earned a B.S. from Virginia Polytechnic Institute and State University, and a Ph.D. from the University of Notre Dame.

There is an excellent balance of theory and application. Furthermore, most of the theoretical concepts covered in the textbook are essential for gaining facility in basic mathematical modelling. The book contains a high number of practice exercises. These extensive exercise sets give diverse opportunities to practice and deepen comprehension. The reviewer warmly recommends this book for consideration as a textbook for a course on calculus and/or mathematical modeling. Teodora-Liliana Radulescu, Zentralblatt MATH