Linear Algebra and Differential Equations Detailed Syllabus for B.Tech first year first sem is covered here. This gives the details about credits, number of hours and other details along with reference books for the course.<\/p>\n
The detailed syllabus for Linear Algebra and Differential Equations B.Tech 2016-2017 (R16) \u00a0first year fristsem is as follows.<\/p>\n
B.Tech. I Year I Sem. L T\/P\/D C
\nCourse Code: MA101BS 3 1\/0\/0 3
\nPrerequisites: Foundation course (No prerequisites).<\/p>\n
Course Objectives:<\/strong><\/p>\n Course Outcomes:<\/strong> UNIT\u2013I : Initial Value Problems and Applications<\/strong><\/p>\n Exact differential equations – Reducible to exact. Applications: Newton\u2019s law of cooling, law of natural growth and decay, orthogonal trajectories, Electrical circuits.<\/p>\n UNIT\u2013II : Linear Systems of Equations<\/strong><\/p>\n Types of real matrices and complex matrices, rank, echelon form, normal form, consistency and solution of linear systems (homogeneous and Non-homogeneous) – Gauss elimination, Gauss Jordon and LU decomposition methods- Applications: Finding current in the electrical circuits.<\/p>\n UNIT\u2013III : Eigen values, Eigen Vectors and Quadratic Forms<\/strong><\/p>\n Eigen values, Eigen vectors and their properties, Cayley – Hamilton theorem (without proof), Inverse and powers of a matrix using Cayley – Hamilton theorem, Diagonalization, Quadratic forms, Reduction of Quadratic forms into their canonical form, rank and nature of the Quadratic forms \u2013 Index and signature.<\/p>\n\n
\nAfter learning the contents of this paper the student must be able to<\/p>\n\n
\nLinear differential equations of higher order with constant coefficients: Non homogeneous terms with RHS term of the type ax e , sin ax, cos ax, polynomials in x, ax e V(x), xV(x)- Operator form of the differential equation, finding particular integral using inverse operator, Wronskian of functions, method of variation of parameters.<\/p>\n