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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

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