Learning Outcomes:

Understand all basic fundamentals of Matrices and Vectors.

Prepare him/herself for solving a Linear equation.

Prepare him/herself for Learning Advance Mathematics in coming semester.

Apply knowledge of matrices and vectors in various applications of his/her branch.

Syllabus:

Unit No | Topics |
---|---|

1 | Matrix Algebra :Review of algebra of matrices & elementary transformations, Rank of a matrix, inverse of a matrix by Gauss-Jordan method, normal form of a matrix, Solution of system of algebraic simultaneous equations, Linear dependent and Linear independent vectors. Eigen values and Eigen vectors, Eigen values and Eigen vectors of: Symmetric, Skewsymmetric, Hermitian, Skewhermitian, Unitary and Normal matrix, Algebraic and Geometric multiplicity, Diagonalization, Spectral theorem for real symmetric matrices, Application of Quadratic forms. |

2 | Vector Space :Vectors in Rn and its properties, Dot product, Norm and Distance properties in Rn , Pythagorean theorem in Rn , Definition and Examples of vector spaces, Vector subspace, Linear Independence and dependence , Linear span of set of vectors, Basis of subspaces, Extension to basis. |

3 | Linear Transformation :Definition and basic properties, Types of linear transformation (Rotation, reflection, expansion, contraction, shear, projection), Matrix of linear transformations, Change of basis and similarity, Rank nullity theorem |

4 | Infinite Series :Definition, Comparison test, Cauchy’s integral test, ratio test, root test, Leibniz’s rule for alternating series, power series, range of convergence, uniform convergence. |

Text Books:

Name :

Higher Engineering Mathematics

Author:

Dr. B. S. Grewal

Name :

Vector Calculus and Linear Algebra

Author:

Dr. A.R.Patel

Dr.H.C.Patel

Reference Books:

Name:

Higher Engineering Mathematics Vol. I & II

Name:

Advanced Engineering Mathematics

Edition:

5th

Name:

Applied mathematics for engineering

Syllabus PDF:

Attachment | Size |
---|---|

Linear Algebra.pdf | 186.07 KB |

branch:

CBA

BDA

MA

Course:

2016

Stream:

B.Tech