Advanced Engineering. Mathematics
- First-Order simultaneous Partial Differential Equations, Method of grouping and multipliers
- Lagrange's first-order linear PDE
- Solvable second-order Partial Differential Equations, Canonical Forms
- The Method of Separation of Variables
- Partial differential equations governing the longitudinal vibration of a rod, torsional vibration of a shaft, vibration of a string, and one-dimensional heat conduction
- Solvability of sets of linear algebraic equations, Order and Rank of a matrix, Elementary operations
- Linear vector space, Independent vector sets, Linear equations and vector space
- Characteristic-value problems, Orthogonalization of vector sets, Quadratic forms, Equivalent matrices
- Functions of symmetric matrices, Generalized Characteristic-value problems
- Vibration of multi-degree of freedom systems, Natural frequencies, Mode shapes, Space of function
- Calculus of variations and applications
- Variational notation, Constraints and Lagrange multipliers
- Hamilton's principle, Lagrange's equations, Sturm-Liouville problems
- Dynamical systems, linear vibrations, Variational problems for deformable bodies
- Integral equations
- Relations between differential and integral equations, Green's function
- Linear equations in cause and effect, Influence function, Fredholm equations with separable kernels