Advanced Calculus: An Introduction to Linear Analysis
Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra Advanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis.
Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics)
Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane
Taking a practical approach that draws on the authors’ extensive teaching, consulting, and research experiences, Applied Survey Data Analysis provides an intermediate-level statistical overview of the analysis of complex sample survey data. It emphasizes methods and worked examples using available software procedures while reinforcing the principles and theory that underlie those methods.
This new textbook in Signals and Systems provides a pedagogically-rich approach to what can oftentimes be a mathematically 'dry' subject. Chaparro introduces both continuous and discrete time systems, then covers each separately in depth. Careful explanations of each concept are paired with a large number of step by step worked examples. With features like historical notes, highlighted 'common mistakes,' and applications in controls, communications, and signal processing, Chaparro helps students appreciate the usefulness of the techniques described in the book. Each chapter contains a section with Matlab applications.
Noncommutative Functional Calculus: Theory and Applications of Slice Hyperholomorphic Functions (2011)
This book presents a functional calculus for n-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions.
