The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.
Stumped trying to understand calculus? Calculus Demystified, Second Edition, will help you master this essential mathematical subject.
Written in a step-by-step format, this practical guide begins by covering the basics--number systems, coordinates, sets, and functions. You'll move on to limits, derivatives, integrals, and indeterminate forms. Transcendental functions, methods of integration, and applications of the integral are also covered. Clear examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key concepts.
It's a no-brainer! You'll get:Applications of the derivative and the integral Rules of integration Coverage of improper integrals An explanation of calculus with logarithmic and exponential functions Details on calculation of work, averages, arc length, and surface area
Simple enough for a beginner, but challenging enough for an advanced student, Calculus Demystified, Second Edition, is one book you won't want to function without!
The text begins with an introductory chapter on the concept of an automorphism group in which the theory in one complex variable is presented, emphasizing the classical ideas of Schwarz, Jobe, and others. Also examined is the theory of planar domains of multiple but finite connectivity, principally develped by Heins in the 1940s and 1950s. The authors treatment progresses to the theory in several complex variables with the so-called "classical domains" of E. Cartan, the Siegel domains of type I, II, and III, and the more modern theory of automorphism groups of smoothly bounded domains.
Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories.
After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in a number of areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems. The appendices offer background material on logic, set theory, the properties of real numbers, the axiom of choice, and basic algebraic structures.
Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond.
The author has written this book in an enticing, rich manner that will engage students and introduce new paradigms of thought. Careful readers will develop critical thinking skills which will help them compete in today’s world.
The book explains:
What goes behind a Google search algorithm
How to calculate the odds in a lottery
The value of Big Data
How the nefarious Ponzi scheme operates
Instructors will treasure the book for its ability to make the field of mathematics more accessible and alluring with relevant topics and helpful graphics. The author also encourages readers to see the beauty of mathematics and how it relates to their lives in meaningful ways.