Syllabus of Vtu Chem Engg
B.E Chemical Engineering Syllabus
ENGINEERING MATHEMATICS – III Sub Code Hrs/ Week Total Hrs. : : : 10MAT31 04 52 IA Marks Exam Hours Exam Marks PART-A UNIT-1 Fourier series Convergence and divergence of infinite series of positive terms, definition and illustrative examples* Periodic functions, Dirichlet’s conditions, Fourier series of periodic functions of period and arbitrary period, half range Fourier series. Complex form of Fourier Series. Practical harmonic analysis. 7 Hours UNIT-2 Fourier Transforms Infinite Fourier transform, Fourier Sine and Cosine transforms, properties, Inverse transforms 6 Hours UNIT-3 Application of PDE Various possible solutions of one dimensional wave and heat equations, two dimensional Laplace’s equation by the method of separation of variables, Solution of all these equations with specified boundary conditions. D’Alembert’s solution of one dimensional wave equation. 6 Hours UNIT-4 Curve Fitting and Optimisation Curve fitting by the method : : : 25 03 100
y = ax + b, y = a x 2 + b x + c,
y = ae
bx
of
least
, y = ax
b
squares-
Fitting
of
curves
of
the
form
Optimization: Linear programming, mathematical formulation of linear programming problem (LPP), Graphical method and simplex method. 7 Hours PART-B UNIT-5 Numerical Methods - 1 Numerical Solution of algebraic and transcendental equations: Regula-falsi method, Newton - Raphson method. Iterative methods of solution of a system of equations: Gauss-seidel and Relaxation methods. Largest eigen value and the corresponding eigen vector by Rayleigh’s power method. 6 Hours
UNIT-6 Numerical Methods – 2 Finite differences: Forward and backward differences, Newton’s forward and backward interpolation formulae. Divided differences - Newton’s divided difference formula, Lagrange’s interpolation formula and inverse interpolation formula. Numerical integration: Simpson’s one-third, three-eighth and Weddle’s rules (All formulae/rules without proof) 7
ENGINEERING MATHEMATICS – III Sub Code Hrs/ Week Total Hrs. : : : 10MAT31 04 52 IA Marks Exam Hours Exam Marks PART-A UNIT-1 Fourier series Convergence and divergence of infinite series of positive terms, definition and illustrative examples* Periodic functions, Dirichlet’s conditions, Fourier series of periodic functions of period and arbitrary period, half range Fourier series. Complex form of Fourier Series. Practical harmonic analysis. 7 Hours UNIT-2 Fourier Transforms Infinite Fourier transform, Fourier Sine and Cosine transforms, properties, Inverse transforms 6 Hours UNIT-3 Application of PDE Various possible solutions of one dimensional wave and heat equations, two dimensional Laplace’s equation by the method of separation of variables, Solution of all these equations with specified boundary conditions. D’Alembert’s solution of one dimensional wave equation. 6 Hours UNIT-4 Curve Fitting and Optimisation Curve fitting by the method : : : 25 03 100
y = ax + b, y = a x 2 + b x + c,
y = ae
bx
of
least
, y = ax
b
squares-
Fitting
of
curves
of
the
form
Optimization: Linear programming, mathematical formulation of linear programming problem (LPP), Graphical method and simplex method. 7 Hours PART-B UNIT-5 Numerical Methods - 1 Numerical Solution of algebraic and transcendental equations: Regula-falsi method, Newton - Raphson method. Iterative methods of solution of a system of equations: Gauss-seidel and Relaxation methods. Largest eigen value and the corresponding eigen vector by Rayleigh’s power method. 6 Hours
UNIT-6 Numerical Methods – 2 Finite differences: Forward and backward differences, Newton’s forward and backward interpolation formulae. Divided differences - Newton’s divided difference formula, Lagrange’s interpolation formula and inverse interpolation formula. Numerical integration: Simpson’s one-third, three-eighth and Weddle’s rules (All formulae/rules without proof) 7