The exhaustive list of topics in Advanced Mathematical Techniques in Chemical Engineering in which we provide **Help with Homework Assignment** and **Help with Project** is as follows:

- Vector space Metric, Norm
- Inner Product space Examples
- Onto, into, one to one function, completeness of space
- Vectors

- Linear combination of vectors, dependent/independent vectors
- Orthogonal and orthonormal vectors
- Gram-Schmidt orthogonalization
- Examples
- Contraction Mapping
- Definition
- Applications in Chemical Engineering
- Gram-Schmidt orthogonalization
- Examples

- Matrix, determinants and properties
- Eigenvalue Problem
- Various theorems
- Solution of a set of algebraic equations
- Solution of a set of ordinary differential equations
- Solution of a set of non-homogeneous first order ordinary differential equation
- (IVPs)
- Applications of eigenvalue problems
- Stability analysis
- Bifurcation theory
- Examples
- Partial Differential equations
- Classification of equations
- Boundary conditions
- Principle of Linear superposition
- Special ODEs and Adjoint operators
- Properties of adjoint operator
- Theorem for eigenvalues and eigenfunctions
- Solution of linear, homogeneous PDEs by separation of variables
- Cartesian coordinate system & different classes of PDEs
- Cylindrical coordinate system
- Spherical Coordinate system
- Solution of non-homogeneous PDEs by Green's theorem
- Solution of PDEs by Similarity solution method
- Solution of PDEs by Integral method
- Solution of PDEs by Laplace transformation
- Solution of PDEs by Fourier transformation