06MAT31 - ENGINEERING MATHEMATICS – III |
PART – A |
UNIT I:Fourier Series |
Periodic functions, Fourier expansions, Half range expansions, Complex
form of Fourier series, Practical harmonic analysis.
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UNIT II:Fourier Transforms |
Finite and Infinite Fourier transforms, Fourier sine and consine transforms,
properties. Inverse transforms.
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UNIT III:Partial Differential Equations (P.D.E) |
Formation of P.D.E Solution of non homogeneous P.D.E by direct
integration, Solution of homogeneous P.D.E involving derivative with
respect to one independent variable only (Both types with given set of
conditions) Method of separation of variables. (First and second order
equations) Solution of Lagrange’s linear P.D.E. of the type P p + Q q = R.
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UNIT IV:Partial Differential Equations (P.D.E) |
Derivation of one dimensional wave and heat equations. Various possible
solutions of these by the method of separation of variables. D’Alembert’s
solution of wave equation. Two dimensional Laplace’s equation – various
possible solutions. Solution of all these equations with specified boundary
conditions. (Boundary value problems).
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PART – B |
UNIT V:Numerical Methods |
Introduction, Numerical solutions of algebraic and transcendental equations:-
Newton-Raphson and Regula-Falsi methods. Solution of linear simultaneous
equations : - Gauss elimination and Gauss Jordon methods. Gauss - Seidel
iterative method. Definition of eigen values and eigen vectors of a square
matrix. Computation of largest eigen value and the corresponding eigen
vector by Rayleigh’s power method.
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UNIT VI: |
Finite differences (Forward and Backward differences) Interpolation,
Newton’s forward and backward interpolation formulae. Divided differences
– Newton’s divided difference formula. Lagrange’s interpolation and inverse
interpolation formulae. Numerical differentiation using Newton’s forward
and backward interpolation formulae. Numerical Integration – Simpson’s
one third and three eighth’s value, Weddle’s rule.
(All formulae / rules without proof)
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UNIT VII:Calculus of Variations |
Variation of a function and a functional Extremal of a functional, Variational
problems, Euler’s equation, Standard variational problems including
geodesics, minimal surface of revolution, hanging chain and Brachistochrone
problems.
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UNIT VIII:Difference Equations and Z-transforms |
Difference equations – Basic definitions. Z-transforms – Definition,
Standard Z-transforms, Linearity property, Damping rule, Shifting rule,
Initial value theorem, Final value theorem, Inverse Z-transforms.
Application of Z-transforms to solve difference equations.
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REFERENCE |
TEXT BOOKS: |
Higher Engineering Mathematics by Dr. B.S. Grewal (36th
Edition – Khanna Publishers)
Unit No. |
Chapter No. |
Article Numbers |
Page Nos. |
I |
10 |
10.1 to 10.7, 10.10 and 10.11 |
375 – 400 |
II |
22 |
22.4, 22.5 |
716 – 722 |
III |
17, 18 |
17.1 to 17.5, 18.2 |
541 – 547
562 – 564 |
IV |
18 |
18.4, 18.5, 18.7 |
564 – 578
580 – 582 |
V |
24 |
24.1, 24.2, 24.4 to 24.6, 24.8 |
820 – 826
829 – 840
843 – 845 |
VI |
25 |
25.1, 25.5, 25.12 to 25.14, 25.16 |
846, 847
857 – 862
871 – 878
881 – 887 |
VII |
30 |
30.1 to 30.5 |
1018 – 1025 |
VIII |
26 |
26.1, 26.2, 26.9 to 26.15, 26.20,
26.21 |
888, 889
899 – 913 |
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Reference Books |
1. Higher Engineering Mathematics by B.V. Ramana (Tata-Macgraw
Hill).
2. Advanced Modern Engineering Mathematics by Glyn James –
Pearson Education |