**II Year - I Sem
MATHEMATICS -IV
Course Objectives:
* Able to solve higher order differential equations.
* Learn the concept of vectors and vector space.
* Introduce to the concept of eigen values and eigen vectors.
UNIT – I: Differential Equations of Second and Higher Order (10 Periods)
Linear differential equations of second and higher order with constant coefficients, Non- homogeneous terms of the type ex, sinx, cosx, x, x2. Method of variation of parameters.
UNIT – II: Vectors (10 Periods)
Vectors in two and three dimensions, scalar (dot) product and vector(cross) product of two vectors, Scalar triple product and vector triple product. Application to find the areas of triangles and parallelograms, volume of parallelopipeds.
UNIT – III: Vector spaces (10 Periods)
Vector space, Linear dependence and independence of vectors. Subspaces. Basis and dimension of a vector space. Applications to find the dimension and basis of subspaces.
UNIT – IV: Eigen values and Eigen Vectors (10 Periods)
Eigen values and eigenvectors of a matrix. Algebraic and geometric multiplicity.
UNIT - V: Linear Transformations (10 Periods)
Linear transformations. Range and kernel of a linear transformation. Rank- Nullity theorem. Matrix representation of a linear transformation. Change of basis.
Course outcomes:
* Students will be able to solve differential equations using techniques such as variation of parameters.
* Understand and apply the concepts of vectors and vector operations in two and three dimensions.
* Understand the concept of vector spaces, subspaces, basis and dimension, and apply these concepts to analyze linear systems.
* Find eigenvalues and eigenvectors of matrices and apply them in various applications.
* Analyze linear transformations, determine their range, kernel, rank and nullity, and represent linear transformations using matrices.
References:
1. Advanced Engineering Mathematics by: E. Kreyszig, 9th Edition, John Wiley & Sons.
2. Higher Engineering Mathematics by: B. S. Grewal, 42nd Edition, Khanna Publications.
3. Engineering Mathematics by: N. P. Bali and Manish Goyal, 7th Edition, Laxmi Publications.