Integrated Calculus

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.

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.