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10.linear Algebra

This document outlines a Linear Algebra course for first year Bachelor of Technology students. The course aims to teach applications of matrices to engineering problems. Over 15 weeks, topics will include vectors, matrices, vector spaces, eigenvalues, inner product spaces, and infinite series. Students will learn to apply matrix knowledge to problems in their engineering branches. Evaluation will consist of a university exam, continuous assessment, and total marks of 100. References and e-resources are provided.

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168 views2 pages

10.linear Algebra

This document outlines a Linear Algebra course for first year Bachelor of Technology students. The course aims to teach applications of matrices to engineering problems. Over 15 weeks, topics will include vectors, matrices, vector spaces, eigenvalues, inner product spaces, and infinite series. Students will learn to apply matrix knowledge to problems in their engineering branches. Evaluation will consist of a university exam, continuous assessment, and total marks of 100. References and e-resources are provided.

Uploaded by

sakilmemon
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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FACULTY OF ENGINEERING AND TECHNOLOGY

First Year Bachelor of Technology


In Effect from Academic Year 2016-17

Subject Code: 1ET1000109 Subject Title: Linear Algebra


Pre-requisite Subject Calculus

Course Objective:
To understand the applications of matrices to engineering problems. To apply knowledge of matrices in various
applications of relevant branch.

Teaching Scheme (Hours per week) Evaluation Scheme (Marks)


Theory Practical
Lecture Tutorial Practical Credit University Continuous University Continuous Total
Assessment Assessment Assessment Assessment
3 2 - 5 70 30 - - 100

Subject Contents
Sr. Total Weightage
Topic
No Hours (%)
Beta and Gamma function:
1. Gamma function, Beta function, Relation between Beta and Gamma functions and 3 7
their properties.
Vectors in 𝑹𝒏 and its properties:
2. Vectors in 𝑅 𝑛 , Dot Product, Norm and Distance, Cauchy-Schwartz Inequality, 3 7
Triangle Inequality, Pythagorean Theorem
Matrices and System of Linear Equations:
3. Revision, Rank of a matrix, Normal form of a matrix, Consistency of system of linear 5 12
equations and Examples.
Vector Spaces:
Definition, Examples of vector spaces, Vector subspace, Linear Independence and
4. dependence, Linear span of set of vectors, Basis and Dimension, Extension to basis, 10 24
Row space, Column space, Null space of a matrix, Rank and nullity of a matrix,
Dimension Theorem (Rank – Nullity theorem)
Eigenvalues and Eigenvectors:
Eigen values and Eigen vectors, Eigen space of a matrix, Algebraic and Geometric
5. 6 14
multiplicity, Diagonalization, Orthogonal Diagonalization, Power of a matrix, Cayley-
Hamilton Theorem, Application to Quadratic forms
Inner Product Spaces:
Inner Product, Dot Product on 𝑅 𝑛 , Inner Product Spaces, Orthonormal Bases,
6. 7 17
Orthogonal Complements, Projection Theorem, Gram-Schmidtz Process,
Applications to Least Squares.
Infinite Series:
Definition of a sequence, Divergence and Convergence of a sequence, Sandwich
7. Theorem for sequences, Infinite Series, Comparison test, Cauchy’s integral test, De’ 8 19
Alembert’s ratio test, Cauchy’s root test, Leibniz’s rule for alternating series, Power
series, Range of convergence, Uniform convergence.
FACULTY OF ENGINEERING AND TECHNOLOGY
First Year Bachelor of Technology
In Effect from Academic Year 2016-17

Course Outcome:
 Students will be able to apply matrices to engineering problems of their relevant branches after studying this
course.

List of References:
1. Elementary Linear Algebra, Applications version, Anton and Rorres, Wiley India Edition, Ninth Edition.
2. Calculus, Volume 2, T. M. Apostol, Wiley Eastern. Second Edition.
3. Introduction to Linear Algebra with Application, Jim Defranza, Daniel Gagliardi, Tata McGraw-Hill,
First Edition
4. Advanced Engineering Mathematics, Erwin Kreysig, Wiley Publication, 9th Edition
5. Linear Algebra and its Applications, Gilbert Strang, Cengage Learning, Fourth Edition.

E-Resources:
1. NPTEL Video Lectures. www.nptel.ac.in
2. MIT Open Course Ware
Link:http://ocw.mit.edu/courses/mathematics/18-06-linear-algebraspring2010/videolectures/
3. MIT Open Course Ware
Link:http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall- 2007/video-lectures/

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