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
, y = ax
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 Hours UNIT-7 Numerical Methods – 3 Numerical solutions of PDE – finite difference approximation to derivatives, Numerical solution of two dimensional Laplace’s equation, one dimensional heat and wave equations 7 Hours UNIT-8
Difference Equations and Z-Transorms Difference equations: Basic definition; Z-transforms – definition, standard Z-transforms, damping rule, shifting rule, initial value and final value theorems. Inverse Z-transform. Application of Z-transforms to solve difference equations. 6 Hours Note: * In the case of illustrative examples, questions are not to be set. Text Books: 1. B.S. Grewal, Higher Engineering Mathematics, Latest edition, Khanna Publishers. 2. Erwin Kreyszig, Advanced Engineering Mathematics, Latest edition, Wiley Publications. Reference Books: 1. B.V. Ramana, Higher Engineering Mathematics, Latest edition, Tata Mc. Graw Hill Publications. 2. Peter V. O’Neil, Engineering Mathematics, CENGAGE Learning India Pvt Ltd.Publishers.
MOMENTUM TRANSFER Subject Code No. of Lecture Hours/Week Total No. of Lecture Hours : 10CH32 : 04 : 52 PART – A UNIT 1: Fluid Statics and its Applications: Concept of unit operations, Concept of Momentum Transfer, Nature of fluids and pressure concept, Variation of pressure with height – hydrostatic equilibrium, Barometric equation, Measurement of fluid pressure – manometers. Continuous gravity decanter, Centrifugal decanter. 6 Hours UNIT 2: Fluid flow phenomena: Types of fluids – shear stress and velocity gradient relation, Newtonian and non – Newtonian fluids, Viscosity of gases and liquids. Types of flow – laminar and turbulent flow, Reynolds stress, Eddy viscosity. Flow in boundary layers, Reynolds number, Boundary layer separation and wake formation. 6 Hours UNIT 3: Basic equations of fluid flow: Average velocity, Mass velocity, Continuity equation, Euler and Bernoulli equations, Modified equations for real fluids with correction factors. Pump work in Bernoulli equation. Angular momentum...
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