# Vector Calculus and Linear Algebra (2110015) Old Code : 110015

5
Credit
3 + 2 + 0
Lect + Tuto + Pract
Teaching Scheme
70 + 30 + 0
ESE + PA + ALA
Theory Marks
30 + 0 + 20
ESE + OEP + PA
Practical Marks
###### ESE - End Semester Examination, PA - Progress Assessment, ALA - Active Learning Assignments, OEP -Open Ended Problem

Prerequisite
Determinants and their Properties. Matrices, Types of Matrices, Algebraic Operations on Matrices, Transpose of a Matrix, Symmetric and Skew Symmetric Matrices, Elementary Operation (Transformation) of a Matrix, Minors and Cofactors of matrices, Adjoint and Inverse of a Matrix. Vector Algebra, Types of Vectors, Addition of Vectors, Multiplication of a Vector by a Scalar, Scalar and Vector Products of Vectors, Three Dimensional Geometry, Equation of a Line in Space, Angle between Two Lines, Shortest Distance between Two Lines, Plane, Co planarity of Two Lines, Angle between Two Planes, Distance of a Point from a Plane, Angle between a Line and a Plane.
Rationale

Mathematics is a language of Science and Engineering.

Course Outcome

On successful completion of the course, students will be able following points:

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.
6. Students will able to use the techniques and theory of linear algebra to model various real world problems. (Possible applications include: curve fitting, computer graphics, networks, discrete dynamical systems, systems of differential equations, and least squares solutions.
7. Modeling of heat flow, heat equation
8. Understand fluid mechanics problem such as conservation of momentum, conservation of mass etc.

Active Learning

Preparation of power-point slides, which include videos, animations, pictures, graphics for better understanding the applications of Linear Algebra and Vector Calculus to engineering applications – The faculty will allocate chapters/ parts of chapters to groups of students so that the entire syllabus of Linear Algebra and Vector Calculus is covered. The power-point slides should be put up on the web-site of the College/ Institute, along with the names of the students of the group, the name of the faculty, Department and College on the first slide. The best three works should be sent to achievements@gtu.edu.in.

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