FYSS7116 Integral Transformations (4 cr)

• Sine and Cosine series, Fourier series, formation and convergence of these series, complex number representations

• Fourier and Laplace transformations and inverse transformations

• Discrete Fourier transform and inverse transform

• Dirac delta function and Green’s function

• Solving differential equations using series and transformations 

After completing the course, student is expected to

• Compute Fourier, sine and cosine series with real and complex coefficients for different functions.

• Compute Fourier transformations and inverse Fourier transformations for different functions.

• Compute discrete Fourier transformations and inverse transformations for different functions.

• Present Dirac’s delta function in different forms and compute integrals containing delta functions.

• Use Fourier transformations and Fourier series as a method for solving linear differential equations.

• Form Laplace transformations and use these to solve linear differential equations with constant coefficients and also apply these to solve partial differential equations 

• Basic studies on Mathematics (option A or B)

• MATA114 Differential equations (recommendation)

• MATA200 Complex calculus tai FYSS7301 Complex Analysis (recommendation, especially complex numbers and complex-valued functions)

• FYSA1130 Numerical methods (recommendation)