Mathematical Physics by Bergfinnur Durhuus and Jan Philip SolovejBergfinnur
Durhuus and Jan Philip SolovejPDF  177 Pages  EnglishThe main focus of this note is on theoretical
developments rather than elaborating on concrete physical systems, which the
students are supposed to encounter in regular physics courses. Topics covered
includes: Newtonian Mechanics, Lagrangian Mechanics, Hamiltonian Mechanics,
Hilbert Spaces, Operators on Hilbert spaces and Quantum mechanics.

Mathematical Structures in PhysicsChristoph SchweigertPDF  210 Pages  EnglishMain goal of this
note is to show the appropriate mathematics to a student of physics, roughly
familiar with all classes of theoretical physics except for quantum field
theory. Topics covered includes: Newtonian mechanics, Lagrangian mechanics,
Classical field theories, Hamiltonian mechanics, Quantum mechanics.

Funky Mathematical Physics ConceptsEric L. MichelsenPDF  273 Pages  EnglishThe purpose of the
“Funky” series of documents is to help develop an accurate physical, conceptual,geometric, and pictorial understanding of important physics topics. We focus on
areas that don’t seem to be covered well in most texts. Topics covered includes: Vectors, Green’s
Functions, Complex Analytic Function, Conceptual Linear Algebra, Probability,
Statistics, and Data Analysis, Practical Considerations for Data Analysis,
Numerical Analysis, Fourier Transforms and Digital Signal Processing, Tensors,
Without the Tension, Differential Geometry.

Mathematical Preparation Course Before Studying PhysicsKlaus HefPDF  279 Pages  EnglishThis note
covers the following topics: Measuring: Measured Value and Measuring Unit, Signs
and Numbers and Their Linkages, Sequences and Series and Their Limits,
Functions, Differentiation, Taylor Series, Integration, Complex Numbers,
Vectors.

Mathematical Methods for PhysicsNiels WaletPDF  90 Pages  EnglishThis note describes the following topics: Notation for scalar product, Linear
vector spaces, Operators, Eigenvectors and Eigenvalues, Green’s functions,
Integral Equations, Variational calculus.

History Topics Mathematical Physics IndexSchool
of Mathematics and Statistics, University of St Andrews, ScotlandOnline  NA Pages  EnglishThis note
covers the following topics: General relativity, History of Quantum mechanics,
Orbits and gravitation, Special relativity, Topology and Scottish mathematical
physics, Light: Ancient Greece to Maxwell, Light in the relativistic and quantum
era, History of Time: Classic time, History of Time: 20th Century time,
Gravitation, Newton's bucket, Wave versus matrix mechanics, Kepler's planetary
laws and Kinematic planetary motion.

An introduction to mathematical physicsRobert Alexander HoustounOnline  224 Pages  EnglishThis
book is intended primarily as a classbook for mathematical students and
as an introduction to the advanced treatises dealing with the subjects of the
different chapters, but since the analysis is kept as simple as possible, It
will be useful for chemists and others who wish to learn the principles of these
subjects.

Mathematical Physics Lecture NotesDr.
R. L. HermanOnline  NA Pages  EnglishThis note covers the following topics: Prologue, Free Fall and Harmonic Oscillators, ODEs and SHM, Linear Algebra,
Harmonics  Fourier Series, Function Spaces, Complex Representations, Transform
Techniques, Vector Analysis and EM Waves, Oscillations in Higher Dimensions.

Partial Differential Equations of Mathematical Physics (PDF 105p)William W. SymesPDF  107 Pages  EnglishThis note aims to make students
aware of the physical origins of the main partial differential equations of
classical mathematical physics, including the fundamental equations of fluid and
solid mechanics, thermodynamics, and classical electrodynamics. Topics covered
includes: Kinematics and Conservation, Strain, Stress, Ideal Fluids and the
Euler Equations, Elastic Fluids and Acoustic Waves, Newtonian Fluids and the
NavierStokes Equations, Linear Elasticity, Thermodynamics and the Heat
Equation, Porous Flow, Electrodynamics and Maxwell’s Equations.

Lecture Notes in Mathematical Physics [PDF 70p] 
Ordinary Differential Equations and Dynamical Systems 
Calculus Based Physics 
Differential Geometry and Physics 
Calculus Based Physics VolumeI [PDF 1.7 Mb] 
Physical Applications of Geometric Algebra 
Algebraic Quantum Field Theory [PDF 202p] 
Basic Bundle Theory and K Cohomology Invariants [PDF 356p] 
Geometry in Physics (PDF 79P) 
Lecture notes for Mathematical Methods 
Lecture notes for Engineering Mathematics 
Topology and Geometry for Physics 
Mathematical Tools for Physics [PDF 459p] 
COMPLEX GEOMETRY OF NATURE AND GENERAL RELATIVITY [PDF 229p] 
Five Lectures on Soliton Equations [PDF 42] 
Holomorphic Methods in Mathematical Physics [PDF 59p] 
Homological Methods in Equations of Mathematical Physics[PDF 150p] 
An Introduction to Noncommutative Geometry [PDF 18p] 
Lectures on Orientifolds and Duality [PDF 64p] 
Differential Geometry (and Relativity) 
Mathematical Tools for Physics [PDF 591p] 
Mathematical Tools for Physics (PDF 448) 
Lecture Notes Methods of Mathematical Physics I 