Subject Code:53001 L:4 T/P/D:1 Credits:4 Int. Marks:25 Ext. Marks:75 Total Marks:100
UNIT I: Linear Systems:
Matrices: Elementary row transformations � Rank � Normal form - Echelon form � Consistency � Solution of system of simultaneous linear homogeneous and non- homogeneous equations.
UNIT II: Eigen values, Eigen vectors :
Eigen values, Eigen vectors � properties � Cayley-Hamilton Theorem - 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
UNIT IV: Quadratic forms:
Quadratic forms- Reduction of quadratic form to canonical form � Rank - Positive, negative definite - semi definite - index - signature - Sylvester law. Applications of Quadratic forms
UNIT V: 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.
UNIT VI: Introduction to Partial Differential Equations
Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions � solutions of first order linear (Lagrange) equation and nonlinear (standard type) equations.
UNIT VII: Solution to Partial Differential Equations
Classification of second order linear Partial Differential Equations, solutions of one dimensional heat equation, wave equation and two-dimensional Laplace�s equation under initial and boundary conditions.
UNIT VIII: Fourier transforms:
Fourier integral theorem � Fourier sine and cosine integrals. Fourier transforms � Fourier sine and cosine transforms � properties � inverse transforms � Finite Fourier transforms.
TEXT BOOKS:
1. Engineering Mathematics - II by PB Bhaskara rao, SKVS RamaChary, MBhujanga Rao, BSP.
2. A text Book of Engineering Mathematics, C. Sankaraiah, V. G. S. Book Links.
3. A text Book of Engineering Mathematics, Shahnaz Bathul, Right Publishers.
4. A text Book of Engineering Mathematics, P. Nageshwara Rao, Y. Narasimhulu & N. Prabhakar Rao, Deepthi Publications.
REFERENCE BOOKS:
1. A text Book of Engineering Mathematics, B. V. Raman, Tata Mc Graw Hill.
2. Advanced Engineering Mathematics, Irvin Kreyszig, Wiley India Pvt. Ltd.
3. A text Book of Engineering Mathematics, Thamson Book Collection.
4. Engineering Mathematics II by TKV Iyengar, BKrishna Gandhi & Others SCHAND.