ENGINEERING MATHEMATICS III | SYLLABUS | IOE | SECOND YEAR

ENGINEERING MATHEMATICS III

SH 501

Lecture  :   3
Year  :   II
Tutorial  :   2
Part  :   I
Practical  :   0

Course Objective:
The purpose of this course is to round out the students’ preparation for more sophisticated applications with an introduction to linear algebra, Fourier Series, Laplace Transforms, integral transformation theorems and linear programming.
1.  Determinants and Matrices       (11 hours)
1.1.  Determinant and its properties
1.2.  Solution of system of linear equations
1.3.  Algebra of matrices
1.4.  Complex matrices
1.5.  Rank of matrices
1.6.  System of linear equations
1.7.  Vector spaces
1.8.  Linear transformations
1.9.  Eigen value and Eigen vectors
1.10.  The Cayley-Hamilton theorem and its uses
1.11.  Diagonalization of matrices and its applications

Engineering Mathematics II | BE Syllabus | First Year Second Part | IOE | 2066

ENGINEERING MATHEMATICS II

SH 451

Lecture: 3

Year: 1

Tutorial: 2

Part: II

Course Objectives:

i) To develop the skill of solving differential equations and to provide knowledge of vector algebra and calculus

ii) To make students familiar with calculus of several variables and infinite series

1.  Calculus of two or more variables  (6 hours)

1.1.  Introduction: limit and continuity

1.2.  Partial derivatives 

1.2.1.  Homogeneous function, Euler’s theorem for the function of 

two and three variables 

1.2.2.  Total derivatives

1.3.  Extrema of functions of two and three variables; Lagrange’s Multiplier

2.  Multiple Integrals  (6 hours)

2.1.  Introduction

2.2.  Double integrals in Cartesian and polar form; change of order of integration

2.3.  Triple integrals in Cartesian, cylindrical and spherical coordinates;

2.4.  Area and volume by double and triple integrals

Engineering Mathematics I | BE Syllabus | Marking Scheme

ENGINEERING MATHEMATICS I

EG ……SH

Lecture:  3 
Year: I
Tutorial: 2
Part: I
Practical :

Course Objectives:     
To provide students a sound knowledge of calculus and analytic geometry to apply them in their relevant fields.

1.          Derivatives and their Applications   (14 hours)

1.1.       Introduction

1.2.       Higher order derivatives

1.3.       Mean value theorem

1.3.1.     Rolle’s Theorem

1.3.2.     Lagrange’s mean value theorem

1.3.3.     Cauchy’s mean value theorem

1.4.       Power series of single valued function

1.4.1.     Taylor’s series

1.4.2.     Maclaurin’s series

1.5.       Indeterminate forms; L’Hospital rule

1.6.       Asymptotes to Cartesian and polar curves

1.7.       Pedal equations to Cartesian and polar curves; curvature and radius of curvature