Advanced Engineering Mathematics
- Defining the course title and getting acquainted with the basic concepts and overview of the basic mathematical concepts.
- Orthogonal sets (perpendicular functions and vectors)
- Fourier series and special modes (even and odd functions)
- Fourier integrals and special cases (even and odd functions) and Fourier transform.
- Linear Algebra (matrices, matrices types and corresponding mathematical bonds e.g. equals, addition, subtract and multiplication of matrices).
- Linear Algebra (transpose matrix, symmetric and antisymmetric matrix, determinant of a square matrix, singular matrix and adjoint or adjugate matrix)
- Linear Algebra (eigen value and eigen vector of a matrix, Hamilton theorem, diagonalization of matrices, Gaussian elimination method, the matrix inverse method and Cramers Rule)
- Ordinary Differential Equations (O.D.E)
- Partial Differential Equations (P.D.E)
- Complex analysis (complex numbers, polar form of complex numbers and preliminary mappings)
- Complex analysis (differentiability conditions, analytical functions, entire and harmonic functions and Cauchy-Riemann equations)
- Variational Calculus (calculus of variations) and special cases
- Functional optimization under constraints
- Sturm-Liouville theory and its applications.
- Legendres Equation, Gamma Function, Bassels and modified Bassels Equation, Error Function and Laplace Transform.