MATH 2020 - Mathematics IV

• Laplace transform (introduction, standard function, properties, convolution theorem, inverse Laplace transform, solving differential equations using Laplace transform)
• Special functions (beta and gamma functions, properties, relations, application to definite integration)
• Fourier series (definition and example, periodic functions, Fourier series of even and odd functions, half-range Fourier series) 
• Linear differential equations of second order with variable coefficients (solving equations by different methods, like changing independent variable, changing dependent variable, and variation of parameters)
• Partial differential equations (formation, equations of first order, Lagrange’s linear equation, solutions of second order partial differential equations)
• Matrices (Elementary row and column transformation, row-reduced echelon form, rank of a matrix, consistency of linear equations, eigenvalues and eigenvectors, Cayley-Hamilton theorem)

• Kreyszig, E. (2011). Advanced engineering mathematics. Wiley.