Series: Undergraduate Texts in Mathematics
Subseries: Readings in Mathematics
2012, 2012, X, 437 p. 72 illus. in color.
Hardcover, ISBN 978-3-642-29162-3
Due: May 31, 2012
Valuable tool for teaching geometry with a strong emphasis of the historical development of the subject
Includes numerous examples, applications, exercises and figures
Stimulating and enjoyable reading for students in mathematics, physics, computer science and teachers alike
In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19th century.
Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.
Preface.- Part I: Classical Geometry.- Thales and Pythagoras.- The Elements of Euclid.- Conic Sections.- Further Results on Euclidean Geometry.- Trigonometry.- Part II: Analytic Geometry.- Descartes' Geometry.- Cartesian Coordinates.- To be Constructible, or not to be.- Spatial Geometry and Vector Algebra.- Matrices and Linear Mappings.- Projective Geometry.- Solutions to Exercises.- References.- Figure Source and Copyright.- Index.
2012, 2012, XII, 330 p. 50 illus.
Hardcover, ISBN 978-0-8176-8324-5
Due: April 30, 2012
A uniquely concise, focused, and rigorous study of linear algebra for beginners
Integrates a variety of applications without distracting from the elegance and interconnectedness of theory
Offers a wealth of exercises, many using MATLAB, and a complete solutions manual
Provides many precise illustrations to enhance clarity
Notation integrates seamlessly with future courses students can expect to take
This book offers a refreshingly concise, manageable introduction to linear algebra: Whereas most treatments of the subject give an exhaustive survey supplemented with applications, this book presents a carefully selected array of the most essential topics that can be thoroughly covered in a single semester.
The exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, but notably deviates in providing an early emphasis on the geometric foundations of linear algebra. Starting with vectors, lines, and planes in two and three dimensions gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts. Two important pedagogical devices are also directed to this end: First, throughout the book, the notation is carefully selected to indicate the connections between related quantities; second, in addition to numbering, brief mnemonic titles are appended to theorems and examples, making it easier for the student to internalize and recall important concepts (e.g., it is much more satisfying to recall the Dimension Theorem than to recall Theorem 3.5.1).
The focus throughout is primarily on fundamentals, guiding readers to appreciate the elegance and interconnectedness of linear algebra. At the same time, the text presents a number of interesting, targeted applications, offering a glimpse of how the subject is used in other fields, especially in physics. A section on computer graphics and a chapter on numerical methods also provide looks at the potential uses of linear algebra, and most sections contain exercises using MATLABR to put theory into practice in a variety of contexts. Visuals and problems are included to enhance and reinforce understanding throughout the book, and both studentsf and instructorsf solutions manuals (for non-MATLAB exercises) are available online.
A Concise Introduction to Linear Algebra builds on the author's previous title on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996). With brevity, precision, and rigor, the work is an ideal choice for a standard one-semester course targeted primarily at math or physics majors. It is a valuable addition to the book collection of anyone who teaches or studies the subject.
Preface.- 1 Analytic Geometry of Euclidean Spaces.- 2 Systems of Linear Equations, Matrices.- 3 Vector Spaces and Subspaces.- 4 Linear Transformations.- 5 Orthogonal Projections and Bases.- 6 Determinants.- 7 Eigenvalues and Eigenvectors.- 8 Numerical Methods.- 9 Appendices.
2012, 2012, XV, 520 p. 10 illus.
Hardcover, ISBN 978-1-4614-3454-2
Due: April 30, 2012
Effectively examines the subject from many different angles
Uses detailed examples to drive the presentation
A useful text for researchers, professionals and practitioners ?
This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material.
Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.?
1. Introduction to Oscillation Theory.- 2. Scalar Delay Differential Equations on Semiaxes.- 3. Scalar Delay Differential Equations on Semiaxis with Positive and Negative Coefficients.- 4. Oscillation of Equations with a Distributed Delay.- 5. Scalar Advanced and Mixed Differential Equations on Semiaxes.- 6. Neutral Differential Equations.- 7. Second Order Delay Differential Equations.- 8. Second Order Delay Differential Equations with Damping Terms.- 9. Vector Delay Differential Equations.- 10. Linearized Methods for Nonlinear Equations with a Distributed Delay.- 11. Nonlinear Models - Modifications of Delay Logistic Equations.- 12. First Order Linear Delay Impulsive Differential Equation.- 13. Second Order Linear Delay Impulsive Differential Equations.- 14. Linearized Oscillation Theory for Nonlinear Delay Impulsive Equations.- 15. Maximum Principles and Nonoscillation Intervals for First Order Volterra Functional Differential Equations.- 16. Systems of Functional Differential Equations on Finite Intervals.- 17. Nonoscillation Interval for n-th Order Functional Differential Equations.- Appendix A.- Appendix B.
Series: Springer Undergraduate Mathematics Series
Original Portugese edition published by IST Press, Portugal (2010)
2012, 2012, X, 390 p. 37 illus.
Softcover, ISBN 978-1-4471-4007-8
Due: June 30, 2012
Emphasis is given to the applications of complex analysis to differential equations
Provides a rigorous approach with the right balance between theory and practice
Includes approximately 200 examples and 200 problems with detailed solutions
This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations.
The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty.
Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.
Part 1 Complex Analysis.- Basic Notions.- Holomorphic Functions.- Sequences and Series.- Analytic Functions.- Part 2 Differential Equations.- Ordinary Differential Equations.- Solving Differential Equations.- Fourier Series.- Partial Differential Equations?.
Series: Studies in Universal Logic
2012, 2012, XII, 460 p. 105 illus., 16 in color.
Softcover, ISBN 978-3-0348-0378-6
Due: May 2012
Exclusively dedicated to the square of oppositions
Presenting the topic from an interdisciplinary perspective
Of interest for mathematical logicians as well as philosophers
The theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, sociology, physics. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original Aristotelian theory.
The square of opposition is a very attractive theme which has been going through centuries without evaporating. Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection of previously unpublished papers by high level specialists of the square from all over the world.
1 Historical and Critical Aspects of the Square.- 2 Philosophical Discussions around the Square of Opposition.- 3 The Square of Opposition and Non-Classical Logics.- 4 Constructions Generalizing the Square of Opposition.- 5 Applications of the Square of Opposition.