UNIT I MATRICES AND EIGENVALUE PROBLEMS
Eigenvalues and Eigenvectors of real matrix-Properties of Eigenvalues and Eigenvectors- Cayley Hamilton Theorem (statement only) and its applications. Diagonalization of a real symmetric matrix- Quadratic forms - Reduction of quadratic form to canonical form by orthogonal transformation- Nature of the quadratic form.
UNIT II SEQUENCES AND SERIES
Sequences: Definition and examples – Series: Types and Convergence – Series of positive terms – Tests of convergence: Comparison test, Integral test and D’Alembert’s ratio test – Alternating series – Leibnitz’s test.
UNIT III APPLICATIONS OF DIFFERENTIAL CALCULUS
Basics-Radius of Curvature in Cartesian co-ordinates – Centre and circle of curvature in Cartesian co- ordinates – Evolutes – Envelopes.
UNIT IV FUNCTIONS OF SEVERAL VARIABLES
Partial derivatives –Total derivatives – Jacobians – Taylor’s series of functions of two variables – Errors and Approximations – Maxima and Minima of functions of two variables – Lagrange’s method of undetermined multipliers
UNIT V SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS
Homogeneous Linear ODEs with constant coefficients – Linear ODE with variable coefficients - Cauchy’s and Legendre’s Equations – Method of variation of parameters –- Applications: Modelling of Free Oscillations of a Mass-Spring system.
Reference Book:
1. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley & Sons, 2018.
2. Howard Anton, Elementary Linear Algebra, 11th Edition, Wiley, 2013.
3. David C Lay, Linear Algebra and its applications, Pearson, 2018.
4. G.B.Thomas, Calculus, 12th Edition, Pearson Education India, 2015.
5. T. Veerarajan, Engineering Mathematics, 3rd Edition, Tata McGraw-Hill, New Delhi, 2011.
Text Book:
1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 43rd Edition, 2015.
2. Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi Publications Pvt Ltd., (2011)
