Differential Analysis Lecture notes by Richard B. Melrose
Differential Analysis Lecture notes by Richard B. Melrose
Differential Analysis Lecture notes by Richard B. Melrose
This
note covers the following topics: Measure and Integration, Hilbert spaces and
operators, Distributions, Elliptic Regularity, Coordinate invariance and
manifolds, Invertibility of elliptic operators, Suspended families and the
resolvent, Manifolds with boundary, Electromagnetism and Monopoles.
This
PDF book covers the following topics related to Differential and Integral
Analysis : Differentiation, The Mean Value Theorem, The Exponential
Function, Inverse Functions, Higher Order Derivatives, Definition of the
Riemann Integral, Properties of the Riemann Integral, The Fundamental
Theorem of Calculus, Sequences and Series of Functions, Power Series.
This lecture note covers the following topics: fundamental
solutions for elliptic, hyperbolic and parabolic differential operators, method
of characteristics, review of Lebesgue integration, distributions, fourier
transform, homogeneous distributions, asymptotic methods.
This lecture note covers the following topics: Analysis In Banach
Spaces, The Method of Lyapunov Schmidt, Degree Theory, Global Solution Theorems,
Existence and Uniqueness Theorems, Linear Ordinary Differential Equations,
Periodic Solutions, Stability Theory, Invariant Sets, Hopf Bifurcation and
Sturm-Liouville Boundary Value Problems.