
Engineering Mathematics I  00101 


Periods/Week 

Periods in one
Session 

Full
Marks 

Annual
Exam 

Internal
Exam 
L 
T 
P/S 

3 
0 
0 

60 

100 

80 

20 
Rationale
The Subject Engineering Mathematics is being introduced into the Diploma Course to provide mathematical background to the students so that they can be able to grasp the engineering subjects properly. This course will enable them to analyze and understand the engineering problems scientifically based on Mathematics.
The subject is divided into two papers, viz. Engineering Mathematics  I and Engineering Mathematics  II. The curriculum of Engineering Mathematics  I consists of the following:
1. Algebra
2. Trigonometry
3. Coordinate Geometry
4. Computer Studies
The details are given in the curriculum.
Objectives
By covering the course in Engineering Mathematics  I, the students will be able to:

Know Sequence and Series, Permutations and Combinations, Binomial Theorem, Determinates and Matrices, Properties of Triangles, Solution of Trigonometrical equations, Inverse Circular functions, complex quantities, coordinate systems, equations of lines, circles, equations of lines in three dimensions, equation of plane, about the organization of computers, how to write algorithms, how to prepare flow charts and how to write programmes in BASIC to solve simple problems.

Understand their engineering applications.

Solve related simple numerical problems which will enable them to understand the subject.

CONTENTS 
SL 
Topics 
Periods 
1. 
Algebra
 Sequence and Series
 Partial Fraction
 Permutation and Combination
 Binomial Theorem
 Determinants and their properties
 Matrix Algebra
 Complex Quantities

22 
2. 
Trigonometry
 Trigonometrical Function up to trigonometrical ratio of submultiple angles
 Properties of Triangle
 Logarithm
 Solution of Triangles and General Values
 Inverse Circular Function

15 
3. 
CoOrdinate Geometry
 Two Dimensional: up to equation of circles
 Three Dimensional: up to straight line

15 
4. 
Computer Studies
 Components of a Computer System
 Number System
 Programming

08 
01  Algebra 
Topics 
Content 
Periods 
01.01 
Sequence & Series: Arithmetic Progression (A.P.), Simple examples of A.P., Geometrical Progression (G.P.), Sum to infinity of a G.P., Sum of Squares and cubes of a naturals, idea of Harmonic Progression (H.P.), Relation between Arithmetic mean, Geometrical Mean and Harmonic mean. Insertions of AMs, GMs & HMs between two numbers. 
04 
01.02 
Partial Fraction: Resolution into partial fraction of simple form  (i) Nonrepeated linear factors and (ii) Repeated linear factors. 
02 
01.03 
Permutations & Combinations: Introduction, Fundamental Principle of counting; The Factorial; Permutations, Simple practical problems on permutation; Combinations; simple practical problems on combinations. 
02 
01.04 
Binomial Theorem: Binomial Theorem for positive Index, Some applications of Binomial Theorem for any Index, Idea of Exponential and Logarithmic Series. (Simple Problem). 
04 
01.05 
Determinants: Determinants and their fundamental properties, simple problem, Difference between Determinants and a Matrix. 
02 
01.06 
Matrices:
 Different types of Matrices
 Algebra of Matrices
 Transpose, Adjoint and Inverse of Matrices
 Solution of Linear simultaneous equations by Matrix method

04 
01.07 
Complex Quantities: Idea of a complex number, its geometrical representation, Modulus and Amplitude, Conjugate of a Complex number, Addition and Substraction of a complex number with geometric notation, geometric notation. Derive the relations:
(i) I zl + z^{2} I<=I zl I + lz^{2} I
(ii) I zl  z^{2} I>=I zl I  Iz^{2} I
Multiplication and Division of one complex number by another with geometric representation. Idea of DeMoivre's Theorem, Roots of a Complex and Cube root of unity. 
04 



02  Trigonometry 
Topics 
Content 
Periods 
02.01 
Trigonometrical Functions, Trigonometrical Functions of angles of arbitrary magnitude, Trigonometrical ratios of Compound angles. Trigonometrical ratios of Multiple and submultiple angles and transformation formulae. 
04 
02.02 
Properties of Triangle: Relations between the side and angles of a triangle. Simple problems based on it. 
04 
02.03 
Logarithm: Definition, Fundamental Rules and properties of Logarithms. 
02 
02.04 
General Values and Inverse Function: Formulae for all angles which have a given Sine, Cosine and Tangent. Formulae for angles both equisinal and equicosinal Inverse Circular Functions, Solution of Equations expressed in inverse notation. 
05 



03  Coordinate Geometry 
Topics 
Content 
Periods 
03.01 
Two Dimensional Coordinate Geometry. 

03.01.01 
Idea of Cartesian and Polar coordinate systems. Relations between them. 
01 
03.01.02 
Distance between two points, section formula and Area of Triangle. Intelligent questions based on these (Cartesian system only), Centroid and Incentre of a triangle. 
02 
03.01.03 
Equations of Locus: Equation of a straight line in different forms. Angle between two straight lines and their deduction, equation of circle, simple problem. 
04 
03.02 
Three Dimensional Coordinate Geometry. 

03.02.01 
Coordinates of a point, Distance between two points, Section formula (Cartesian system only). 
01 
03.02.02 
Direction Cosines, Angle between two lines, Important deductions. 
02 
03.02.03 
Plane, Projection of the join of two points on a plane, Equation of plane, Angle between two planes, Important deductions. 
02 
03.02.04 
Equation of a straight line as intersection of two planes, Symmetric form of a straight line, simple problem. 
03 



04  Computer Studies 
Topics 
Content 
Periods 
04.01 
Components of a Computer System: Input/Output devices, Memory unit, Central processing unit. 
01 
04.02 
Number System: Binary, Octal, Decimal & Hexadecimal System Radix conversion. 
02 
04.03 
Computer Arithmetic's: Binary, addition & substraction, Boolean Algebra & Karnaugh Map, ASCII Code. 
02 
04.04 
Programming: Algorithm, Flow Chart: Elements of BASIC programming. Typical examples on (i) Sum & Product of a number (ii) Finding the maximum or minimum of three given numbers. 
03 
Recommended Books  Mathematics  I & II 
SL 
Title 
Author/Publisher 
1. 
Mathematics for Class XI Part I. 
NCERT 
2. 
Mathematics for Class XI Part II 
NCERT 
3. 
Mathematics for Class XII Part I 
NCERT 
4. 
Mathematics for Class XII Part II 
NCERT 
5. 
Dynamics via Calculus 
Dr. H.N.Sharma, Dr. K.C.Sinha 
6. 
Statics via Vector 
 



Reference Books  Mathematics  I & II 
SL 
Title 
Author/Publisher 
1. 
Engineering Mathematics  Part I & II. 
H.K.Dass, S.Chand & Co. 
2. 
Polytechnic Mathematics for Diploma Level 
H.K.Dass, S.Chand & Co. 
3. 
Solid Geometry 
Lal Jee Prasad 
Scheme of Examination 
SL 
Scheme of Examination 
Percentage 
Marks 
Types of Questions 
1. 
To test the knowledge of the subject. 
20% 
16 
Objective type questions covering the entire syllabus. 
2. 
To test the understanding and application of the subject. 
80% 
64 
Short and/or Long answer type. 
Breakup of Marks 
SL 
Topic 
Percentage 
Marks 
1. 
Algebra 
30% 
24 
2. 
Trigonometry 
20% 
16 
3. 
Coordinate Geometry 
20% 
16 
4. 
Computer Studies 
10% 
08 

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