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 Learn about linear transformation and its corresponding matrix.

THEORY (45 Hours)

UNIT – I: Euclidean Space and Matrices (18 Hours)

Fundamental operations with vectors in Euclidean space , Linear combinations of vectors, Dot
product and their properties, Cauchy-Schwarz inequality, Triangle inequality, Solving system of
linear equations using Gaussian elimination, Application: Curve Fitting, Gauss-Jordan row
reduction, Reduced row echelon form, Application: Solving several systems simultaneously,
Equivalent systems, Rank and row space of a matrix, Eigenvalues, Eigenvectors, Eigenspace,
Diagonalization, Characteristic polynomial of a matrix.

UNIT – II: Introduction to Vector Spaces (12 Hours)
Definition, Examples and some elementary properties of vector spaces, Subspaces, Span, Linear
independence and linear dependence of vectors, Basis and dimension of a vector space, Maximal
linearly independent sets, Minimal spanning sets.
UNIT – II: Linear Transformations (15 Hours)
Linear transformations: Definition, Examples and elementary properties, The matrix of a linear
transformation, Kernel and range of a linear transformation, The dimension theorem, one-to-one
and onto linear transformations, Invertible linear transformations, Isomorphic vector spaces.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGUESTED READINGS:

1. Andrilli, S., & Hecker, D. (2016). Elementary Linear Algebra (5th ed.). Elsevier India.
2. Lay, David C., Lay, Steven R., & McDonald, Judi J. (2016). Linear Algebra and its
Applications (5th ed.). Pearson Education.
3. Kolman, Bernard, & Hill, David R. (2001). Introductory Linear Algebra with Applications
(7th ed.). Pearson Education, Delhi. First Indian Reprint 2003.
4. Spectrum- Linear Algebra, Sharma Publications, Jalandhar
5. A Text Book of Linear Algebra, S. Dinesh & Co, Jalandhar

Maths.321 Numerical Analysis 3+1*

LEARNING OBJECTIVES:

The learning objectives of this course are as follows:

 To acquaint students with the techniques that uses algorithms for approximation problems.
 Develop the students‘ ability to use various numerical method techniques
 To make the students formulate and apply appropriate strategy to solve real world
problems.

Learning outcomes

On successful completion of the course, students will be able to:
 Know the basic elements of numerical methods and error analysis
 Learn Iterative methods for finding the roots of the algebraic and transcendental equations
 Apply the numerical methods to solve system of linear equations and understand the
methods
convergence analysis.

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