Mathematical Analysis

Notebooks to accompany the text Foundations of Applied Mathematics Volume 1: Mathematical Analysis. Topics covered include linear, spectral, multivariate, and complex analysis, which should prepare the reader for a graduate-level study of dynamical systems and differential equations.

Available Chapters

Chapter 1: Abstract Vector Spaces

Chapter 3: Inner Product Spaces

Chapter 4: Spectral Theory

Chapter 5: Metric Space Topology

Chapter 6: Differentiation

Chapter 7: Contraction Mappings and Applications

Chapter 8: Integration

Chapter 10: Calculus on Manifolds

Chapter 11: Complex Analysis

Chapter 12: Spectral Calculus