Mathematics I

This course provides the "logical" foundation for "instructional materials" by covering calculus of one variable, including limits, differentiation, and integration. It focuses on the "technical clarity" needed to formulate real-world problems into mathematical statements and demonstrate solutions numerically or graphically.

Linear Algebra

Course Title: Linear Algebra

Course No: CSIT.123

Nature of the Course: THEORY

Semester: 2

Full Marks: 60 + 40

Pass Marks: 24 + 20

Credit Hours: 3

Course Description

The course intends to enable the students to understand the basics of linear algebra. In this course students will be able to study linear equation and matrices, linear transformation, vector space. At the same time students get much idea about matrix algebra, Eigen values and Eigen vectors.

Course Objectives

To acquaint the students with basics of linear algebra. To enable the students, to understand the concept of linear equation, and its solution. To know the basic concept of Eigen values and Eigen vectors and its further application.

Course Contents

1. Linear equation & Matrices

8 hrs

1.1. System of linear equations

1.2. Row reduction and Echelon form

1.3. vector equation

1.4. The matrix equations Ax = b

1.5. Solution set of linear system

1.6. Linear independence

2. Matrix Algebra

6 hrs

2.1. Matrix operation

2.2. The inverse of a matrix

2.3. Characterization of invertible matrices

2.4. Partitioned matrices

2.5. The Leontief input output model

2.6. Application to computer graphics

3. Vector Spaces

8 hrs

3.1. Definition and examples

3.2. Vector subspaces

3.3. Linear combination, linear dependence independence

3.4. Basis and dimension of a vector space.

3.5. Row and Column space of a matrix.

3.6. Row rank and column rank.

4. Linear Transformation

8 hrs

4.1. Linear transformation, representation by a matrix.

4.2. Kernel and image of linear transformation.

4.3. Rank nullity theorem

4.4. Linear isomorphism

4.5. L(V, W) is a vector space dimension of L(V, W) (statement only)

4.6. The matrix of liner transformation.

5. Inner Product Space

7 hrs

5.1. The Eucledian space & dot product.

5.2. General Inner product spaces

5.3. Orthogonality, orthogonal projection onto a line, orthogonal basis.

5.4. Gram-schmidt orthogonalization.

5.5. Orthogonal transformation.

6. Eigen Values and Eigen Vectors

8 hrs

6.1. Eigen values and Eigen vectors

6.2. The characteristic equation,

6.3. Diagonalization

6.4. Eigen vectors and linear transformation.

6.5. Complex Eigen values

6.6. Caley Hammiton theorem (statement only)

Text Books

1.David C. Lay: Linear Algebra and its applications. 3rd Edition, Pearson Edition
2.S. Lang: Introduction to Linear Algebra, second Edition. Springer verlag, New York (1986)

Reference Books

1.I. Kolman, Bernard: Introductory Linear Algebra, with application, 7th Edition. Pearson Ed.
2.G. Strang: Linear Algebra and its application 3rd Ed. Harcourt Brace Jovanovich Orlando (1986)

Notes:

This syllabus follows the official CSIT curriculum of Far Western University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative. https://cdc.fwu.edu.np/faculties.html

Mathematics I

Mathematics I

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TabFlux . Linear Algebra . FWU . BSc. CSIT

Linear Algebra

Course Description

Course Objectives

Course Contents

Text Books

Reference Books

Notes: