Integrated Calculus
Description
This unique Calculus textbook presents a comprehensive treatment of single-variable calculus with an emphasis on applications and real-world motivation of the abstract mathematical concepts. As part of the applications, substantial content from elementary ordinary differential equations is also developed.
This textbook covers all of the topics expected in a traditional calculus course, and does so in a manner that distinguishes it from much of the existing literature. Specifically, integration and differentiation are introduced immediately and developed in parallel as a unified whole; series and sequences are introduced very early and used throughout; Leibniz notation is introduced later and with great care; pattern recognition is emphasized as a tool for finding antiderivatives, with formal substitutions deemphasized. A wide variety of exercises will aid students with varying levels of ability, motivation, and interest, to solidify understanding of the material. This book will be ideal for a range of instructing styles, as the presentation of topics is flexible, and it may be used both in the university and high school settings.
More details
Person
Christopher Goodrich is a senior lecturer and researcher in the School of Mathematics and Statistics at the University of New South Wales (UNSW), Sydney. Prior to his appointment at UNSW Sydney, he taught high school mathematics for many years in Omaha, Nebraska, and his years teaching calculus to high school students have informed many of the pedagogical choices in this book. He completed the PhD in mathematics at the University of Nebraska-Lincoln in August 2012, and he has had over 125 research papers published. His research interests include nonlocal differential and difference equations, including fractional calculus, and his research has investigated both boundary value problems and the qualitative properties of nonlocal operators. He also has an interest in regularity theory for elliptic PDEs and minimizers of variational problems, and holds particular interest in problems that involve discontinuous coefficients and how such coefficients affect the regularity of any solution or minimizer.
Content
Preface.- 1 The fundamentals.- 2 Extending the fundamentals.- 3 Qualitative analysis of the growth and decay of populations.- 4. Differentiation and antidifferentiation techniques and applications.- 5 Differential equations: analytical and numerical solution techniques with applications.- 6 Calculus on parametrized curves in the plane.- 7 Vector-valued functions.- 8 Power series and their application.- Index.