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VTU syllabus 2010 [Mathematics] common to all branches [10MAT31] Engineering
ENGINEERING MATHEMATICS – III
CODE: 10 MAT 31 IA Marks: 25
Hrs/Week: 04 Exam Hrs: 03
Total Hrs: 52 Exam
Unit-I: 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-II: FOURIER TRANSFORMS
Infinite Fourier transform, Fourier Sine and Cosine transforms,
properties, Inverse transforms
Unit-III: APPLICATIONS 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.
Unit-IV: CURVE FITTING AND OPTIMIZATION
Curve fitting by the method of least squares- Fitting of curves of
the form y = ax+b, y =a x2 + b x + c, , y
y = a e = ax
Optimization: Linear programming, mathematical formulation
of linear programming problem (LPP), Graphical method and
Unit-V: 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.
Unit-VI: 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)
Unit-VII: 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
Unit-VIII: DIFFERENCE EQUATIONS AND ZTRANSFORMS
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.
Note: * In the case of illustrative examples, questions are not
to be set.
1. B.S. Grewal, Higher Engineering Mathematics, Latest
edition, Khanna Publishers
2. Erwin Kreyszig, Advanced Engineering Mathematics,
Latest edition, Wiley Publications.
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
BUILDING MATERIALS AND CONSTRUCTION TECHNOLOGY
(COMMON TO CV/TR/CTM)
Sub Code : 10 CV 32 IA Marks : 25
Hrs/ Week : 04 Exam Hours : 03
Total Hrs. : 52 Exam Marks : 100
Previous year question paperhttps://drive.google.com/file/d/0B9vIYsUygp6ETk14X0M2X3pyYUk/view
Notes from other sources
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