General concepts; laws of thermodynamics (review). Exergy analysis for closed and open systems; reversible work, irreversibility, exergy. The third law of thermodynamics, Chemical reactions; combustion stoichiometry (review), thermochemistry (review), second law analysis, work production from chemical reactions, fuel cells, reaction equilibrium. Chemical exergy.

Classifications of PDEs; Finite Difference Method; Matrix set up in 1D and Boundary Condition, Formulation for 2D and Matrix Setup, Higher Order Approximations, 2D Axisymmetric. Coordinate transformation to body-fitted coordinates; Advanced methods for solution of system of algebraic equations: Incomplete Decomposition, Strongly Implicit Procedure, Conjugate Gradient Methods. Multigrid Methods (Geometric/Algebraic) Advanced methods for solution of system of algebraic equations: Incomplete Decomposition, Strongly Implicit Procedure, Conjugate Gradient Methods. Multigrid Methods (Geometric/Algebraic); Stability and convergence of iterative methods, Fourier decomposition of errors, Spectral radius of convergence. Preconditioning; Treatment of time-dependent PDEs: Parabolic PDEs, Hyperbolic PDEs. Method of lines

Review of ordinary differential equations; linear differential equation of the first order; linear differential equations with constant coefficients; particular solutions by variations of parameters. Power series solutions; method of Frobenius; Legendre's equation; Fourier-Legendre Series; Bessel's equation; modified Bessel equation. Fourier methods; Fourier series; Sturm-Liouville theory; Fourier integral; Fourier transformation. Partial differential equations; heat conduction equation; separation of variables; waves and vibrations in strings; wave equation; D'Alembert's solution; longitudinal vibrations in an elastic rod; two dimensional stress systems; solution of Navier's equations by the application of Fourier transforms; Laplace equation.