Mathematical Physics 2 1102282 Chapter 7 Fourier Series and Transforms Lecture 2 Basic of Fourier series Mathematical methods in the physical sciences 3rd edition Mary L. Boas Lecturer: Dr. Mai Khaleel Outline 5. Fourier coefficients 5. Fourier coefficients We want to expand a given periodic function in a series of sines and cosines. [First, we start with sin(nx) and cos(nx) instead of sin(nt) and cos(nt).] - Given a function f(x) of period 2, f ( x) 1 a0 a1 cos x a2 cos 2 x a3 cos 3x 2 b1 sin x b2 sin 2 x b3 sin 3x , We need to determine the coefficients!! Orthogonality conditions Orthogonality conditions Orthogonality conditions Orthogonality conditions Orthogonality conditions Fourier coefficients Fourier coefficients Fourier coefficients Fourier coefficients Fourier coefficients Fourier coefficients Fourier coefficients Fourier coefficients Fourier coefficients Fourier coefficients