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.
The 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.
Durhuus and Jan Philip Solovej
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,
book is intended primarily as a class-book 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
This 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.