After completion of this course each student would be able to:
The Linear Algebra, Differential Equations and Analytical Geometry is a compulsory course and has been offered by the Department of Basic Sciences and Related Studies.
|
CLO |
Description |
Taxonomy Level |
PLOs |
|
1 |
DETERMINE the basic operation of matrix algebra and solution of system of linear equations. Apply the concepts of two and three dimensional geometry. |
C2 |
1 |
|
2 |
APPLY first and higher order and differential equations methods. |
C2 |
1 |
|
3 |
ANALYZE area and volume of bounded regions by using multiple integrals |
C3 |
1 |
Contents
Introductions to matrices and elementary row operations. Brief introduction of matrices. Types of
matrices. Introduction to elementary row operations. Echelon and reduced echelon forms. Rank of a matrix. Inverse of a matrix using elementary row operations.
System of linear equations. System of non-homogeneous and homogeneous linear equations. Gaussian elimination method, Gauss Jordan method. Consistence criterion for solution of homogeneous and non-homogeneous system of linear equations. Application of system of linear equations.
Determinants. Introduction to determinants. Properties of determinants of order n. Rank of a matrix by using determinants.
Analytic geometry of 3-dimensions.Introduction; Coordinates in R3.
Line: Coordination of a point dividing a line segment in a given ratio. Straight line, in R3. Vector form of a straight line, parametric equations of a straight line, equation of a straight line in symmetric form, direction ratios and direction cosines, angle between two straight lines; distance of a point from a line.
Plane: Equation of a plane, angle between two planes, intersection of two planes, a plane and a straight line; skew lines. Cylindrical and spherical coordinates.
Sphere: General equation of sphere.
Differential equations of first order: Ordinary differential equations and their classification, formation of differential equations, solution of differential equations; initial and boundary conditions. Methods of solution of differential equation of first order and first degree; geometrical and physical applications.
Higher order linear differential equations: Homogeneous and non-homogeneous linear equations of order n with constants coefficients. Cauchy Euler equation. Method of variation of parameters. Application of higher order linear differential equations.
Multiple Integrals: Evaluation of double and triple integrals in Cartesian and polar coordinates.
