Vector Calculus & Linear Algebra - [2110015]

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Teaching Scheme

Theory
Tutorial Practical Total
3 2 0 5

Examination Scheme

Theory Examination Practical Examination Total
ESE (E) PA (M) ESE Viva (V) PA (I)
- - - - -

    ESE = End Semester Examination, PA = Progressive Assessment


Semester   
:   
2
Course Type   
:   
-
Credit   
:   
5

Syllabus Content

Systems of Linear Equations , Matrices and Elementary Row Operations , The Inverse of a Square Matrix , Matrix Equations , Applications of Systems of Linear Equations
Vectors in R^n,Linear Combinations, Linear Independence,Definition of a Vector Space, Subspaces, Basis and Dimension, Coordinates and Change of Basis
Linear Transformations ,The Null Space and Range ,Isomorphisms ,Matrix Representation of Linear Transformations ,Similarity ,Eigen values and Eigen vectors Diagonalization
The Dot Product on R^n and Inner Product Spaces, Orthonormal Bases, Orthogonal Complements, Application: Least Squares Approximation, Diagonalization of Symmetric Matrices, Application: Quadratic Forms
Vector & Scalar Functions and Fields, Derivatives , Curve, Arc length, Curvature & Torsion , Gradient of Scalar Field, Directional Derivative , Divergence of a Vector Field , Curl of a Vector Field
Line Integrals , Path Independence of Line Integrals , Green`s Theorem in the plane , Surface Integrals , Divergence Theorem of Gauss , Stokes`s Theorem

Reference Books

SrTitleAuthorPublicationAmazon Link
1Introduction to Linear Algebra with ApplicationJim Defranza, Daniel GagliardiTata McGraw-Hill   
2Elementary Linear Algebra, Applications versionAnton and RorresWiley India Edition   
3Advanced Engineering MathematicsErwin KreysigWiley Publication   
4Elementary Linear AlgebraRon LarsonCengage Learning   
5Calculus, Volumes 2T. M. ApostolWiley Eastern

Course Outcome

1. System of linear equations in solving the problems of electrical engineering, mechanical engineering, applied mechanics etc.

2. Use of matrix in graph theory, linear combinations of quantum state in physics, computer graphics and cryptography etc.

3. Students will be able to apply vectors in higher dimensional space in experimental data, storage and warehousing, electrical circuits, graphical images, economics, mechanical systems and in physics.

4. Students will able to use eigen values and eigen vector in Control theory, vibration analysis, electric circuits, advanced dynamics and quantum mechanics.

5. Students will be able to apply linear transformation in computer graphics, cryptography, thermodynamics etc.