Mathematical Methods - JNTU Anantapur First Year Syllabus 2009 |
UNIT – I : Matrices |
Elementary row transformations Rank Echelon form, normal form Solution of Linear System of Homogenous and Non Homogeneous equations Direct Methods Gauss Elimination, Gauss Jordan methods.
Eigen Values, Eigen vectors Properties. Cayley Hamilton Theorem Inverse and powers of a matrix by CayleyHamilton theorem Diagonolization of matrix. Calculation of powers of matrix.
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UNIT II : |
Real matrices Symmetric, skew Symmetric, orthogonal matrices. Linear Transformation Orthogonal Transformation. Complex matrices: Hermitian, Skew-Hermitian,Unitary matrices and their properties. Quadratic forms Reduction of quadratic form to canonical form and their nature. |
UNIT III : |
Solution of Algebraic and Transcendental Equations: Introduction The Bisection Method The Method of False Position The Iteration Method Newton -Raphson Method.
Interpolation: Introduction Finite differences Forward Differences backward Differences Newton 's forward and backward difference formulae for interpolation Lagrange's Interpolation formula. |
UNIT IV : |
Curve fitting: Fitting a straight line Second degree curve Exponential curve-Power curve by method of least squares. Numerical Differentiation and Integration Trapezoidal rule Simpson's 1/3 Rule Simpson's 3/8 Rule.
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UNIT V : |
Numerical solution of Ordinary Differential equations: Solution by Taylor 's series-Euler's Method-Runge-Kutta Methods Milne's Predictor-Corrector Method. |
UNIT VI : |
Fourier Series: Determination of Fourier coefficients Fourier series of Even and odd functions Fourier series in an arbitrary interval Even and odd periodic continuation Half-range Fourier sine and cosine expansions. Fourier integral theorem (statement only) Fourier sine and cosine integrals. Fourier transform Fourier sine and cosine transforms Properties Inverse transforms Finite Fourier transforms. |
UNIT VII: |
Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions Method of separation of variables Solutions of one dimensional wave equation, heat equation and two-dimensional Laplace equation under initial and boundary conditions.
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UNIT VIII : |
z-transform Inverse z-transform Properties Damping rule Shifting rule Initial and final value theorems. Convolution theorem Solution of difference equations by z-transforms. |
REFERENCE |
TEXT BOOKS: |
1. Mathematical Methods, T.K.V. Iyengar, B. Krishna Gandhi and Others, S. Chand & Company.
2. Mathematical Methods, C. Sankaraiah, V.G.S. Book Links.
3. Mathematical Methods, G. Shanker Rao, E. Keshava Reddy, I. K. International Publishing House Pvt. Ltd.
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Reference Books |
1. Numerical Methods for Scientific and Engineering Computation , M.K. Jain, S.R.K. Iyengar & R.K. Jain,
New Age international Publishers.
2. Mathematical Methods Pal Oxford.
3. Introduction to Numerical Analysis S.S. Sastry Printice Hall of India
4. Mathematical Methods, S.K.V.S. Sri Ramachary, M. Bhujanga Rao, P.B. Bhaskar Rao & P.S. Subramanyam,
BS Publications.
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