BS - Mathematical Methods - JNTU Hyderabad First Year Syllabus 2009 |
UNIT – I : Solution for linear systems |
Matrices and Linear systems of equations: Elementary row transformations-Rank-Echelon form, Normal
form – Solution of Linear Systems – Direct Methods- LU Decomposition- LU Decomposition from Gauss
Elimination –Solution of Tridiagonal Systems-Solution of Linear Systems |
UNIT – II : Eigen Values & Eigen Vectors |
Eigen values, eigen vectors – properties – Condition number of rank, Cayley-Hamilton Theorem (without
Proof) - Inverse and powers of a matrix by Cayley-Hamilton theorem – Diagonolization of matrix. Calculation
of powers of matrix – Modal and spectral matrices. |
UNIT – III : Linear Transformations |
Real matrices – Symmetric, skew - symmetric, orthogonal, Linear Transformation – Orthogonal
Transformation. Complex matrices: Hermitian, Skew-Hermitian and Unitary – Eigen values and eigen
vectors of complex matrices and their properties. Quadratic forms- Reduction of quadratic form to canonical
form – Rank - Positive, negative definite - semi definite - index - signature - Sylvester law, Singular value
decomposition.
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UNIT – IV : Solution of Non- linear Systems |
Solution of Algebraic and Transcendental Equations: Introduction – The Bisection Method – The Method of
False Position – The Iteration Method – Newton-Raphson Method.
Interpolation: Introduction- Errors in Polynomial Interpolation – Finite differences- Forward Differences-
Backward differences –Central differences – Symbolic relations and separation of symbols- Difference
Equations - Differences of a polynomial-Newton’s formulae for interpolation – Central difference interpolation
Formulae – Gauss Central Difference Formulae –Interpolation with unevenly spaced points-Lagrange’s
Interpolation formula. B. Spline interpolation - Cubic spline.
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UNIT – V : Curve fitting & Numerical Integration |
Curve fitting: Fitting a straight line –Second degree curve-exponentional curve-power curve by method of
least squares. Numerical Differentiation – Simpson’s 3/8 Rule , Gaussian Integration, Evaluation of principal
value integrals, Generalized Quadrature. |
UNIT – VI : Numerical solution of IVP’s in ODE |
Numerical solution of Ordinary Differential equations: Solution by Taylor’s series-Picard’s Method of
successive Approximations-Euler’s Method-Runge-Kutta Methods –Predictor-Corrector Methods- Adams-
Bashforth Method.
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UNIT – VII Fourier Series |
Fourier Series: Determination of Fourier coefficients – Fourier series – even and odd functions – Fourier
series in an arbitrary interval – even and odd periodic continuation – Half-range Fourier sine and cosine
expansions.
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UNIT – VIII Partial differential equations |
Introduction and Formation of partial differential equation by elimination of arbitrary constants and arbitrary
functions, solutions of first order linear (Lagrange) equation and nonlinear (Standard type) equations,
Method of separation of variables for second order equations -Two dimensional wave equation.
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REFERENCE |
TEXT BOOKS: |
1. Mathematical Methods by P.B.Bhaskara Rao, S.K.V.S. Rama Chary, M.Bhujanga Rao,
B.S.Publications.
2. Mathematical Methods by K.V.Suryanarayana Rao by Scitech Publications. |
Reference Books |
1. Mathematical Methods by T.K.V. Iyengar, B.Krishna Gandhi & Others, S. Chand.
2. Introductory Methods by Numerical Analysis by S.S. Sastry, PHI Learning Pvt. Ltd.
3. Mathematical Methods by G.Shankar Rao, I.K. International Publications, N.Delhi
4. Higher Engineering Mathematics by B.S. Grewal, Khanna Publications.
5. Mathematical Methods by V. Ravindranath, Etl, Himalaya Publications.
6.A text Book of KREYSZIG’S Mathematical Methods, Dr .A. Ramakrishna Prasad. WILEY
publications. |