Foundations of Applied Mathematics, Volume 1
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-1-61197-489-8 (ISBN)
Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell–Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, ""When am I going to use this?
Jeffrey Humpherys is a professor of mathematics at Brigham Young University, former Vice Chair of the SIAM Activity Group on Applied Mathematics Education, and a two-term member of the SIAM Education Committee. He is the recipient of a National Science Foundation CAREER award. His research spans a wide range of topics in applied and computational mathematics, from nonlinear partial differential equations to network sciences to machine learning. Tyler Jarvis is a professor of mathematics at Brigham Young University whose research has primarily been in geometric problems arising from physics. He is the recipient of a National Science Foundation CAREER award and the Mathematical Association of America's Deborah and Franklin Tepper Haimo Award for Distinguished University Teaching of Mathematics. Emily Evans is an assistant professor in the Department of Mathematics at Brigham Young University. Prior to earning her Ph.D. she spent seven years in industry as a software engineer. Her research interests include finite elements for domains with fractal boundaries, biological modeling, computational mechanics, the mathematics of computer animation, and network science.
Part I: Linear Analysis I
Chapter 1: Abstract Vector Spaces
Chapter 2: Linear Transformations and Matrices
Chapter 3: Inner Product Spaces
Chapter 4: Spectral Theory
Part II: Nonlinear Analysis I
Chapter 5: Metric Space Topology
Chapter 6: Differentiation
Chapter 7: Contraction Mappings and Applications
Part III: Nonlinear Analysis II
Chapter 8: Integration I
Chapter 9: Integration II
Chapter 10: Calculus on Manifolds
Chapter 11: Complex Analysis
Part IV: Linear Analysis II
Chapter 12: Spectral Calculus
Chapter 13: Iterative Methods
Chapter 14: Spectra and Pseudospectra
Chapter 15: Rings and Polynomials
Part V: Appendix
Appendix A: Foundations of Abstract Mathematics
Appendix B: The Complex Numbers and Other Fields
Appendix C: Topics in Matrix Analysis
Appendix D: The Greek Alphabet
| Erscheinungsdatum | 18.08.2017 |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 1720 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 1-61197-489-5 / 1611974895 |
| ISBN-13 | 978-1-61197-489-8 / 9781611974898 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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