# basic mathematics for physics pdf

### mathematics for physics pdf ### basic book of mathematics for physics pdf

These notes were prepared for the first semester of a year-long mathematical methods course for begining graduate students in physics. The emphasis is on linear operators and stresses the analogy between such operators acting on function spaces and matrices acting on finite dimensional spaces. The op-erator language then provides a unified framework for investigating ordinary and partial differential equations, and integral equations.
The mathematical prerequisites for the course are a sound grasp of un-dergraduate calculus (including the vector calculus needed for electricity and magnetism courses), linear algebra (the more the better), and competence
at complex arithmetic. Fourier sums and integrals, as well as basic ordinary differential equation theory receive a quick review, but it would help if the reader had some prior experience to build on. Contour integration is not required.
Calculus of Variations 1
1.1 What is it good for.
1.2 Functionals
1.2.1 The functional derivative
1.2.2 The Euler-Lagrange equation
1.2.3 Some applications
1.2.4 First integral
1.3 Lagrangian Mechanics
1.3.1 One degree of freedom
1.3.2 Noether’s theorem
1.3.3 Many degrees of freedom
1.3.4 Continuous systems
1.4 Variable End Points
1.5 Lagrange Multipliers
1.6 Maximum or Minimum?
1.7 Further Exercises and Problems
2 Function Spaces 55
2.1 Motivation
2.1.1 Functions as vectors
2.2 Norms and Inner Products
2.2.1 Norms and convergence
2.2.2 Norms from integrals
2.2.3 Hilbert space
2.2.4 Orthogonal polynomials
2.3 Linear Operators and Distributions