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Now in its third edition, this outstanding textbook explains everything you need to get started using MATLAB®. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB's programming features, graphical capabilities, simulation models, and rich desktop interface. MATLAB 8 and its new user interface is treated extensively in the book. New features in this edition include: a complete treatment of MATLAB's publish feature; new material on MATLAB graphics, enabling the user to master quickly the various symbolic and numerical plotting routines; and a robust presentation of MuPAD® and how to use it as a stand-alone platform. The authors have also updated the text throughout, reworking examples and exploring new applications. The book is essential reading for beginners, occasional users and experienced users wishing to brush up their skills. Further resources are available from the authors' website at www-math.umd.edu/schol/a-guide-to-matlab.html.
Now in its third edition, this outstanding textbook explains everything you need to get started using MATLAB®. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB's programming features, graphical capabilities, simulation models, and rich desktop interface. MATLAB 8 and its new user interface is treated extensively in the book. New features in this edition include: a complete treatment of MATLAB's publish feature; new material on MATLAB graphics, enabling the user to master quickly the various symbolic and numerical plotting routines; and a robust presentation of MuPAD® and how to use it as a stand-alone platform. The authors have also updated the text throughout, reworking examples and exploring new applications. The book is essential reading for beginners, occasional users and experienced users wishing to brush up their skills. Further resources are available from the authors' website at www-math.umd.edu/schol/a-guide-to-matlab.html.
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.
The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.
This accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the topics required to prove the Hilbert–Schmidt theorem, including orthonormal bases, the Riesz representation theorem, and the basics of spectral theory. The material on Banach spaces and their duals includes the Hahn–Banach theorem, the Krein–Milman theorem, and results based on the Baire category theorem, before culminating in a proof of sequential weak compactness in reflexive spaces. Arguments are presented in detail, and more than 200 fully-worked exercises are included to provide practice applying techniques and ideas beyond the major theorems. Familiarity with the basic theory of vector spaces and point-set topology is assumed, but knowledge of measure theory is not required, making this book ideal for upper undergraduate-level and beginning graduate-level courses.
This accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the topics required to prove the Hilbert–Schmidt theorem, including orthonormal bases, the Riesz representation theorem, and the basics of spectral theory. The material on Banach spaces and their duals includes the Hahn–Banach theorem, the Krein–Milman theorem, and results based on the Baire category theorem, before culminating in a proof of sequential weak compactness in reflexive spaces. Arguments are presented in detail, and more than 200 fully-worked exercises are included to provide practice applying techniques and ideas beyond the major theorems. Familiarity with the basic theory of vector spaces and point-set topology is assumed, but knowledge of measure theory is not required, making this book ideal for upper undergraduate-level and beginning graduate-level courses.
Since its inception in the early 20th century, Functional Analysis has become a core part of modern mathematics. This accessible and lucid textbook will guide students through the basics of Functional Analysis and the theory of Operator Algebras. The text begins with a review of Linear Algebra and Measure Theory. It progresses to concepts like Banach spaces, Hilbert spaces, Dual spaces and Weak Topologies. Subsequent chapters introduce the theory of operator algebras as a guide to study linear operators on a Hilbert space and cover topics such as Spectral Theory and C*-algebras. Theorems have been introduced and explained through proofs and examples, and historical background to the mathematical concepts have been provided wherever appropriate. At the end of chapters, practice exercises have been segregated in a topic-wise manner for targeted practice, making the book ideal both for classroom teaching as well as self-study.
Since its inception in the early 20th century, Functional Analysis has become a core part of modern mathematics. This accessible and lucid textbook will guide students through the basics of Functional Analysis and the theory of Operator Algebras. The text begins with a review of Linear Algebra and Measure Theory. It progresses to concepts like Banach spaces, Hilbert spaces, Dual spaces and Weak Topologies. Subsequent chapters introduce the theory of operator algebras as a guide to study linear operators on a Hilbert space and cover topics such as Spectral Theory and C*-algebras. Theorems have been introduced and explained through proofs and examples, and historical background to the mathematical concepts have been provided wherever appropriate. At the end of chapters, practice exercises have been segregated in a topic-wise manner for targeted practice, making the book ideal both for classroom teaching as well as self-study.
