As you are looking for Visvesvaraya Technological University (VTU) Industrial Engineering & Management (IEM) 6th sem syllabus , so on your demand here I am providing same for you:

PART-A
Unit-I: FOURIER SERIES
Convergence and divergence of infinite series of positive
terms, definition and illustrative examples*
Periodic functions, Dirichlet’s conditions, Fourier series of
periodic functions of period and arbitrary period, half
range Fourier series. Complex form of Fourier Series.
Practical harmonic analysis. [7 hours]
Unit-II: FOURIER TRANSFORMS
Infinite Fourier transform, Fourier Sine and Cosine
transforms, properties, Inverse transforms
[6 hours]
Unit-III: APPLICATIONS OF PDE
Various possible solutions of one dimensional wave and
heat equations, two dimensional Laplace’s equation by the
method of separation of variables, Solution of all these
equations with specified boundary conditions.
D’Alembert’s solution of one dimensional wave equation.
[6 hours]