Determining Eigenvalues and Eigenvectors–Properties of Eigenvalues and Eigenvectors - Some applications of Eigenvalue problems– Eigenvalue problems arising from population models (Leslie model) – Elastic deformations – Cayley Hamilton Theorem (statement only) and its applications.
Diagonalization of a real symmetric matrix–Quadratic form– Canonical form – Nature of the quadratic form – Reduction of quadratic form to canonical form by orthogonal transformation – Some Applications: Transformation to Principal axes- Conic sections – Solving first order linear system using diagonalization.
Radius of Curvature in Cartesian co-ordinates – Centre and circle of curvature in Cartesian co-ordinates – Evolutes – Envelopes.
Partial derivatives –Total derivatives – Jacobians – Taylor’s expansion of functions of two variables – Errors and Approximations – Maximaand Minima of functions of two variables – Lagrange’s method of undetermined multipliers.
Homogeneous Linear ODEs with constant coefficients – Linear ODE with variable coefficients - Cauchy’s and Legendre’s Equations – Method of variation of parameters – Methods of undetermined coefficients - 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. James Stewart, Calculus, 7th Edition, Cengage Learning, 2012.