Download Linear Algebra, Differential Equations and

MEHRAN UNIVERSITY OF ENGINEERING & TECHNOLOGY
Form-001/00/qsp-004
Dec. 01, 2001
TENTATIVE TEACHING PLAN
DEPARTMENT / INSTITUTE / DIRECTORATE: BSRS
Name of the Teacher: Prof. Dr. Muhammad Anwar Solangi
Subject: Linear Algebra Differential Equations & Analytical Geometry
Batch: 16IN Year: 1st Term: 2nd
Code: MTH 103 (03+00)
Term Starting Date: 21-07-2016
Term Suspension Date: 09-11-2016
S.#
CONTENTS
No. of
Lectures
hrs
01
Introduction to Linear Algebra and Matrix Theory
02
02
Elementary row operations, Echelon form and Reduced echelon form
01
03
Rank of matrix and Inverse of a matrix
01
04
System of linear equations. System of non-homogeneous and homogeneous linear
equations. Gaussian elimination method Gauss Jordon method.
02
05
Consistency criterion for solution of homogeneous and non-homogeneous system of
linear equation and Case Study Problems
02
06
Determinants. Introduction to determinants. Properties of determinants of order n.
02
07
Applications of determinants (Cramer’s Rule)
01
08
Differential equations of first order:
Differential equations and their classification. Formation of differential equations.
02
09
Solution of differential equations, Separable equations.
01
10
Homogeneous equations
01
11
Equations reducible to homogeneous
01
12
Exact and Non-Exact differential equations
02
13
Linear and Bernoulli differential equations
01
14
Orthogonal trajectories
01
15
01
17
Application of first order differential equations
Higher order linear differential equation:
Homogeneous linear equations of order n with constant coefficients,
auxiliary/characteristic equations. Solution of higher order differential equation
according to the roots of auxiliary equation.
Non-homogeneous linear equations. Working rules for finding particular integral.
18
Cauchy Euler equation
01
19
Method of variation of parameters for solving y” + p(x)y1 +q(x)y = f(x).
01
20
Applications of higher order linear differential equations.
01
21
Analytical Geometry of 3-Dimenssions. Introduction. Coordinates of a point dividing
a line segment in a given ration.
01
22
Straight line in R3
01
23
Direction ratios and direction cosines, Angle between two straight lines.
01
16
01
02
24
Distance of point from a line.
01
25
Planes: Equation of a plane.
01
26
Angle between two planers, intersection of two planes.
01
27
A plane and a straight line, skew lines.
01
28
Cylindrical and spherical coordinates: Introduction to cylindrical and spherical
coordinates.
02
29
Sphere: General equation of sphere, great circle.
01
30
Multiple integrals. Definition, double integral as volume, evaluation of double
integral, change of order of integration.
01
31
Application of double integrates area, mass of an element, moment of inertia, and
center of gravity.
01
32
Triple integrals, evaluation of triple integrals, Triple integration in cylindrical and
spherical coordinates.
01
33
Application of triple integrals, volume, mass of an element.
01
34
Center of Gravity, movement of inertia by triple integral
01
Total Lectures Hours:
Signature of Teacher:
Date:
Remarks of DMRC:
Signature of Chairman:
Date:
42