Engineering Mathematics I

Engineering Mathematics I

EG 1103 SH

                                                                                  Total:   5 hour /week

Year:  I           Lecture:   4 hours/week  Semester:  I         Tutorial:  1 hours/week

Practical:   hours/week

Lab:   hours/week

Course Description: 

This subject consists of four units related to trigonometry; coordinate geometry; algebra; and calculus necessary to develop mathematical background helpful for the understanding and practicing the related engineering works.

Course Objectives: 

After the completion of this course, students will be able to: 

1.     Explain the concepts of the followings terminologies:

2.     Apply them in the field of related engineering area:

•       Trigonometric ratios and equations, 

•       inverse circular functions and properties of triangles

•       Straight lines, angle between lines, circle and parabola

•       The progressions, permutations and combinations, binomial theorem, exponential and   logarithmic series as well as the quadratic and polygonal equations.

•       Sets, limit and continuity, derivatives, integration and integrals.

Course Contents:

Unit 1.      Trigonometry:                                                                    [12]

                      1.1.      Review of trigonometric ratios:

§ Basic trigonometric formulae § Identities and conditional   identities.

                      1.2.      Trigonometric equations:

§  Periodicity of trigonometric functions

§  General solutions of the following equations:

                                                      Sin x = k ,  cos x = k and Tan x = k and using trigonometric equations.

                      1.3.      Inverse circular functions:

§  Domain and their graphs

§  Formulae involving inverse circular functions

§  Simple identities and equations involving circular functions

1.4.  Properties of triangles:  § The sin law

§  The cosine law 

§  The projection law

§  The half angle formulae 

§  The area of a triangle 

§  The encircles and ex-circles of a triangle

Unit 2.	Coordinate Geometry:                                                                                               [12]
	2.1	Straight lines: §  The three standard forms of equations of a line. §  The linear equation: ax + by + c = 0. §  Any line through the intersection of two lines. §  Concurrency of lines.
	2.2	Pair of straight lines: §  Angle between two lines §  Bisectors of angles between two lines  §  Pair of lines  §  Homogeneous equation of second degree  §  General equation of second degree representing two lines  §  Angle between a pair of lines  §  Bisectors of the angles for a line pair  §  Lines joining the origin to the points of intersection of a curve and a line
	2.3.	Circle: §  Standard equation §  General form §  Tangents and normal
	2.4.	Parabola:  §  Standard equation §  Tangents and normal
Unit 3.	Algebra:  3.1.      Progressions:  §  A.P., G.P. and H.P. 3.2.      Permutations and combinations 3.3.             The binomial theorem for any index  3.4.      Series:  §  Exponential & logarithmic  3.4.      Equations:  §  Quadratic & polynomial		[12]
Unit 4.	Set relation and function:  4.1       Idea of set, set notations, set operations, 4.2.      Venn diagram,  4.3.      The set of real members and its subsets.  4.4.      The absolute value of a real number. 4.5.      Functions- algebraic and transcendental.  4.6.      Graphs of simple function.		[8]
Unit 5.	Calculus:  5.1.      Limit of community.  5.2.      Derivatives from definition of simple functions like: § xn, (ax+b)n, sin (ax +b), eax, ax , and log x.		[16]

5.3.            Derivatives of sum, difference, product and quotient of functions, chain rule, parametric and    implicit functions 5.4.        Integration, Rules for finding integrals.

5.5.         Standard integrals and their uses.

5.6.         Definite integrals- definition and evaluation.

5.7.         Definite integral as limit of sum.

 

Learning materials:

1.     A Textbook on Engineering mathematics (for Diploma Engineering) part I, Bhim Prasad kafle,  Makalu Publicartion House, Dillibazar, Kathmandu

2.     A Text book of Statistics – B.C. Bajracharya

3.     Elementary Statistics – H. C. Saxena

4.     Statistical Methods – Mrigendralal Singh

5.     Engineering Mathematics I, Hari Nandan Nath, Parishowar Acharya, Vudhyarthi Publisher and distributors, Bhotahity, Kathmandu

6.     References to be selected by the related lecturer(s) from among the texts available in the   market that meet the content needs of this subject.

7.     The related institute may develop its own textbook and approve from the related authority so as to have a prescribed textbook of this subject