Differential Equations
An Introduction with Mathematica®
Seiten
2010
|
Softcover reprint of hardcover 2nd ed. 2004
Springer-Verlag New York Inc.
978-1-4419-1941-0 (ISBN)
Springer-Verlag New York Inc.
978-1-4419-1941-0 (ISBN)
Goals and Emphasis of the Book Mathematicians have begun to find productive ways to incorporate computing power into the mathematics curriculum. I believe that if a student's first exposure to a subject is pleasant and exciting, then that student will seek out ways to continue the study of the subject.
Goals and Emphasis of the Book Mathematicians have begun to find productive ways to incorporate computing power into the mathematics curriculum. There is no attempt here to use computing to avoid doing differential equations and linear algebra. The goal is to make some first ex plorations in the subject accessible to students who have had one year of calculus. Some of the sciences are now using the symbol-manipulative power of Mathemat ica to make more of their subject accessible. This book is one way of doing so for differential equations and linear algebra. I believe that if a student's first exposure to a subject is pleasant and exciting, then that student will seek out ways to continue the study of the subject. The theory of differential equations and of linear algebra permeates the discussion. Every topic is supported by a statement of the theory. But the primary thrust here is obtaining solutions and information about solutions, rather than proving theorems. There are other courses where proving theorems is central. The goals of this text are to establish a solid understanding of the notion of solution, and an appreciation for the confidence that the theory gives during a search for solutions. Later the student can have the same confidence while personally developing the theory.
Goals and Emphasis of the Book Mathematicians have begun to find productive ways to incorporate computing power into the mathematics curriculum. There is no attempt here to use computing to avoid doing differential equations and linear algebra. The goal is to make some first ex plorations in the subject accessible to students who have had one year of calculus. Some of the sciences are now using the symbol-manipulative power of Mathemat ica to make more of their subject accessible. This book is one way of doing so for differential equations and linear algebra. I believe that if a student's first exposure to a subject is pleasant and exciting, then that student will seek out ways to continue the study of the subject. The theory of differential equations and of linear algebra permeates the discussion. Every topic is supported by a statement of the theory. But the primary thrust here is obtaining solutions and information about solutions, rather than proving theorems. There are other courses where proving theorems is central. The goals of this text are to establish a solid understanding of the notion of solution, and an appreciation for the confidence that the theory gives during a search for solutions. Later the student can have the same confidence while personally developing the theory.
1 About Differential Equations.- 2 Linear Algebra.- 3 First-Order Differential Equations.- 4 Applications of First-Order Equations.- 5 Higher-Order Linear Differential Equations.- 6 Applications of Second-Order Equations.- 7 The Laplace Transform.- 8 Higher-Order Differential Equations with Variable Coefficients.- 9 Differential Systems: Theory.- 10 Differential Systems: Applications.- References.
| Erscheint lt. Verlag | 25.11.2010 |
|---|---|
| Reihe/Serie | Undergraduate Texts in Mathematics |
| Zusatzinfo | XIV, 434 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4419-1941-4 / 1441919414 |
| ISBN-13 | 978-1-4419-1941-0 / 9781441919410 |
| Zustand | Neuware |
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