Lectures on Differential Geometry (1版)

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【簡介】 This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry. 【目錄】

ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS ELEMENTARY

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This is a textbook that covers several selected topics in the theory of elliptic partial differential equations which can be used in an advanced undergraduate or graduate course. The book considers many important issues such as existence, regularity, qualitative properties, and all the classical topics useful in the wide world of partial differential equations. It also includes applications with interesting examples. The structure of the book is flexible enough to allow different chapters to be taught independently. The book is friendly, welcoming, and written for a newcomer to the subject. It is essentially self-contained, making it easy to read, and all the concepts are fully explained from scratch, combining intuition and rigor, and therefore it can also be read independently by students, with limited or no supervision.

Mathematics for Engineers Vol.1 Numbers and Equations, Vectors and Matrices, Functions in one Variable, Differential Calculus

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【簡介】 The Karlsruhe University of Applied Sciences started an English-language Bachelor's program in Electrical Engineering in 2021. In order to support our international students with appropriate material, this three-volume textbook was written. Taking into account that different students will attend different mathematics courses, we decided to design three volumes of a series of mathematics books, each part for a single semester. Mathematical terms are clearly motivated, systematically equated and visualized in many animations. Mathematical proofs are almost completely renounced. Instead, a lot of applications support not only the application of mathematics but also contribute to a better understanding of mathematics. Important formulas and statements are clearly highlighted in order to increase the readability of the books. More than 300 images and sketches support the character of modern textbooks. The color-coded layout provides a clear overview of the presentation of the content, e.g. by adding new terms and definitions in light grey, important statements and sentences in grey. 【目錄】 Numbers, Equations and Systems of Equations Vectors and Vector Calculus Matrices and Determinants Basic Functions Complex Numbers Limits and Continuity Differential Calculus

Fractional Partial Differential Equations

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【簡介】 This monograph offers a comprehensive exposition of the theory surrounding time-fractional partial differential equations, featuring recent advancements in fundamental techniques and results. The topics covered encompass crucial aspects of the theory, such as well-posedness, regularity, approximation, and optimal control. The book delves into the intricacies of fractional Navier–Stokes equations, fractional Rayleigh–Stokes equations, fractional Fokker–Planck equations, and fractional Schrödinger equations, providing a thorough exploration of these subjects. Numerous real-world applications associated with these equations are meticulously examined, enhancing the practical relevance of the presented concepts. The content in this monograph is based on the research works carried out by the author and other excellent experts during the past five years. Rooted in the latest advancements, it not only serves as a valuable resource for understanding the theoretical foundations but also lays the groundwork for delving deeper into the subject and navigating the extensive research landscape. Geared towards researchers, graduate students, and PhD scholars specializing in differential equations, applied analysis, and related research domains, this monograph facilitates a nuanced understanding of time-fractional partial differential equations and their broader implications. 【目錄】

A First Course in Differential Equations with Modeling Applications (Asia Edition) (12版)

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【簡介】 Straightforward and easy to read, Zill's A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 12th EDITION, gives you a thorough overview of the topics typically taught in a first course in differential equations. Your study of differential equations and its applications is supported by a bounty of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions and more. 【目錄】 Ch 1 Introduction to Differential Equations Ch 2 First-Order Differential Equations Ch 3 Modeling with First-Order Differential Equations Ch 4 Higher-Order Diffential Equations Ch 5 Modeling with Higher-Order Differential Equations Ch 6 Series Solutions of Linear Equations Ch 7 The Laplace Transform Ch 8 Systems of Lineasr Differential Equations Ch 9 Numerical Solutions of Ordinary Differential Equations