Mathematical Modeling and Applied Calculus

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.

• 1: Functions for Modeling Data1.1: Functions1.2: Multivariable Functions1.3: Linear Functions1.4: Exponential Functions1.5: Inverse Functions1.6: Logarithmic Functions1.7: Trigonometric Functions2: Mathematical Modeling2.1: Modeling with Linear Functions2.2: Modeling with Exponential Functions2.3: Modeling with Power Functions2.4: Modeling with Sine Functions2.5: Modeling with Sigmoidal Functions2.6: Single Variable Modeling2.7: Dimensional Analysis3: The Method of Least Squares3.1: Vectors and Vector Operations3.2: Linear Combinations of Vectors3.3: Existence of Linear Combinations3.4: Vector Projection3.5: The Method of Least Squares4: Derivatives4.1: Rates of Change4.2: The Derivative as a Function4.3: Derivatives of Modeling Functions4.4: Product and Quotient Rules4.5: The Chain Rule4.6: Partial Derivatives4.7: Limits and the Derivative5: Optimization5.1: Global Extreme Values5.2: Local Extreme Values5.3: Concavity and Extreme Values5.4: Newton's Method and Optimization5.5: Multivariable Optimization5.6: Constrained Optimization6: Accumulation and Integration6.1: Accumulation6.2: The Definite Integral6.3: First Fundamental Theorem6.4: Second Fundamental Theorem6.5: The Method of Substitution6.6: Integration by Parts

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.