Foundations of Applied Mathematics, Volume 1

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Foundations of Applied Mathematics, Volume 1

Name: Foundations of Applied Mathematics, Volume 1
Brand: SIAM - SOCIETY FOR INDUSTRIAL AND APPLIED
SKU: 9781611974898
Price: 220.0 AUD
Availability: InStock

SIAM - SOCIETY FOR INDUSTRIAL AND APPLIEDISBN: 9781611974898

Mathematical Analysis

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By Jeffrey Humpherys, Tyler Jarvis, Emily J. Evans
Imprint: SIAM - SOCIETY FOR INDUSTRIAL AND APPLIED
Release Date: October 28, 2017
Format: HARDBACK
Dimensions: 229 x 152 mm
Weight: 1720 g
Pages: 689

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This book provides the foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. 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

"Humpherys, Jarvis, and their collaborators are in the process of achieving something extraordinary: the creation of an entire curriculum of rigorous graduate-level applied mathematics with a four-volume series of first-rate books to support it." - Lloyd N. Trefethen, University of Oxford

Foundations of Applied Mathematics, Volume 1

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