differential equations

MATHEMATICAL METHODS

PARTIAL DIFFERENTIAL EQUATIONS
I YEAR B.Tech

By
Mr. Y. Prabhaker Reddy
Asst. Professor of Mathematics
Guru Nanak Engineering College
Ibrahimpatnam, Hyderabad.

SYLLABUS OF MATHEMATICAL METHODS (as per JNTU Hyderabad)
Name of the Unit
Unit-I
Solution of Linear systems Unit-II
Eigen values and
Eigen vectors

Name of the Topic
Matrices and Linear system of equations: Elementary row transformations – Rank
– Echelon form, Normal form – Solution of Linear Systems – Direct Methods – LU
Decomposition from Gauss Elimination – Solution of Tridiagonal systems – Solution of Linear Systems.
Eigen values, Eigen vectors – properties – Condition number of Matrix, Cayley –
Hamilton Theorem (without proof) – Inverse and powers of a matrix by Cayley –
Hamilton theorem – Diagonalization of matrix – Calculation of powers of matrix –
Model and spectral matrices.
Real Matrices, Symmetric, skew symmetric, Orthogonal, Linear Transformation -

Unit-III
Linear
Transformations

Orthogonal Transformation. Complex Matrices, Hermition and skew Hermition matrices, Unitary Matrices - Eigen values and Eigen vectors of complex matrices and their properties. Quadratic forms - Reduction of quadratic form to canonical form,
Rank, Positive, negative and semi definite, Index, signature, Sylvester law, Singular value decomposition.
Solution of Algebraic and Transcendental Equations- Introduction: The Bisection
Method – The Method of False Position – The Iteration Method - Newton –Raphson

Unit-IV
Solution of Nonlinear Systems

Method Interpolation:Introduction-Errors in Polynomial Interpolation - Finite differences- Forward difference, 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 - Lagrange’s Interpolation formulae- B.