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This paper, which is largely selfcontained with many explicit examples, is an extended written version of a series of lectures 10 h given during a short intensive c ourse organized by the Center of Theoretical Physics CPT in Marseille may 2325, 2016 under t he title Algebraic Analysis, Double Duality and Applications in Mathematical Physics .
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This note explains the following topics: classical statistical mechanics, Review of classical mechanics, Review of probability and measure, The Maxwellian distribution Probability spaces in classical mechanics, Review of thermodynamics Macro states, Macro variables, Thermal equilibrium and entropy, The Boltzmann equation, The thermodynamic arrow of time, Quantum statistical mechanics and thermodynamic ensembles.
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The intent of this note is to introduce students to many of the mathematical techniques useful in their undergraduate physics education long before they are exposed to more focused topics in physics. Topics covered includes ODEs and SHM, Linear Algebra, Harmonics Fourier Series, Function Spaces, Complex Representations, Transform Techniques, Vector Analysis and EM Waves, Oscillations in Higher Dimensions.
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