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. Co-ordinate 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, co-ordinate 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 sub-multiple angles
  • Properties of Triangle
  • Logarithm
  • Solution of Triangles and General Values
  • Inverse Circular Function
15
3. Co-Ordinate 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) Non-repeated 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 + z2 I<=I zl I + lz2 I
(ii) I zl - z2 I>=I zl I - Iz2 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 sub-multiple 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 equi-sinal and equi-cosinal Inverse Circular Functions, Solution of Equations expressed in inverse notation. 05
 
 03 - Co-ordinate Geometry
Topics Content Periods
03.01 Two Dimensional Co-ordinate Geometry.  
03.01.01 Idea of Cartesian and Polar co-ordinate 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 Co-ordinate Geometry.  
03.02.01 Co-ordinates 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.

 

 Break-up of Marks
SL Topic Percentage Marks
1. Algebra 30% 24
2. Trigonometry 20% 16
3. Co-ordinate Geometry 20% 16
4. Computer Studies 10% 08

 

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