Foundations of Applied Mathematics, Volume 1

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 IChapter 1: Abstract Vector SpacesChapter 2: Linear Transformations and MatricesChapter 3: Inner Product SpacesChapter 4: Spectral TheoryPart II: Nonlinear Analysis IChapter 5: Metric Space TopologyChapter 6: DifferentiationChapter 7: Contraction Mappings and ApplicationsPart III: Nonlinear Analysis IIChapter 8: Integration IChapter 9: Integration IIChapter 10: Calculus on ManifoldsChapter 11: Complex AnalysisPart IV: Linear Analysis IIChapter 12: Spectral CalculusChapter 13: Iterative MethodsChapter 14: Spectra and PseudospectraChapter 15: Rings and PolynomialsPart V: AppendixAppendix A: Foundations of Abstract MathematicsAppendix B: The Complex Numbers and Other FieldsAppendix C: Topics in Matrix AnalysisAppendix 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