Syllabus  3rd Semester Engineering Mathematics III  Subject Code  06MAT31
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Syllabus  3rd Semester Engineering Mathematics III  Subject Code  06MAT31
Engineering Mathematics III
PART – A
UNIT 1:
Fourier Series
Periodic functions, Fourier expansions, Half range expansions, Complex form of Fourier series, Practical harmonic analysis.
7 Hours
UNIT 2:
Fourier Transforms
Finite and Infinite Fourier transforms, Fourier sine and consine transforms, properties. Inverse transforms.
6 Hours
UNIT 3:
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.
6 Hours
UNIT 4:
Applications of 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).
7 Hours
PART – B
UNIT 5:
Numerical Methods
Introduction, Numerical solutions of algebraic and transcendental equations: NewtonRaphson and RegulaFalsi 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.
6 Hours
UNIT 6:
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)
7 Hours
UNIT 7:
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.
6 Hours
UNIT 8:
Difference Equations and Ztransforms
Difference equations – Basic definitions. Ztransforms – Definition, Standard Ztransforms, Linearity property, Damping rule, Shifting rule, Initial value theorem, Final value theorem, Inverse Ztransforms. Application of Ztransforms to solve difference equations.
Reference Books:
0. Text Book: Higher Engineering Mathematics by Dr. B.S. Grewal (36th Edition – Khanna Publishers
1. Higher Engineering Mathematics by B.V. Ramana (TataMacgraw Hill).
2. Advanced Modern Engineering Mathematics by Glyn James – Pearson Education.
Note:
1. One question is to be set from each unit.
2. To answer Five questions choosing atleast Two questions from each part.
PART – A
UNIT 1:
Fourier Series
Periodic functions, Fourier expansions, Half range expansions, Complex form of Fourier series, Practical harmonic analysis.
7 Hours
UNIT 2:
Fourier Transforms
Finite and Infinite Fourier transforms, Fourier sine and consine transforms, properties. Inverse transforms.
6 Hours
UNIT 3:
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.
6 Hours
UNIT 4:
Applications of 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).
7 Hours
PART – B
UNIT 5:
Numerical Methods
Introduction, Numerical solutions of algebraic and transcendental equations: NewtonRaphson and RegulaFalsi 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.
6 Hours
UNIT 6:
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)
7 Hours
UNIT 7:
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.
6 Hours
UNIT 8:
Difference Equations and Ztransforms
Difference equations – Basic definitions. Ztransforms – Definition, Standard Ztransforms, Linearity property, Damping rule, Shifting rule, Initial value theorem, Final value theorem, Inverse Ztransforms. Application of Ztransforms to solve difference equations.
Reference Books:
0. Text Book: Higher Engineering Mathematics by Dr. B.S. Grewal (36th Edition – Khanna Publishers
1. Higher Engineering Mathematics by B.V. Ramana (TataMacgraw Hill).
2. Advanced Modern Engineering Mathematics by Glyn James – Pearson Education.
Note:
1. One question is to be set from each unit.
2. To answer Five questions choosing atleast Two questions from each part.
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