1002: Engineering Mathematics I KL Diploma Syllabus for IT 1st Sem 2015 Revision SITTTR

Engineering Mathematics I detailed syllabus for Information Technology (IT) for 2015 revision curriculum has been taken from the SITTTRs official website and presented for the IT students. For course code, course name, number of credits for a course and other scheme related information, do visit full semester subjects post given below.

For Information Technology 1st Sem scheme and its subjects, do visit IT 1st Sem 2015 revision scheme. The detailed syllabus of engineering mathematics i is as follows.

MODULE I

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MODULE II

TRIGONOMETRY-II

1. MULTIPLE AND SUB MULTIPLE ANGLES 4
2. SUM OR DIFFERENCE FORMULAE AND CONVERSE 4
3. PROPERTIES AND SOLUTIONS OF TRIANGLES 10

MODULE III

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MODULE IV

APPLICATIONS OF DIFFERENTIATION

1. EQUATIONS OF TANGENTS AND NORMALS 4
2. RATES AND MOTION 8
3. MAXIMA AND MINIMA 4
4. TUTORIALS, TESTS, ASSIGNMENTS 10

Course Outcomes:

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SPECIFIC OUTCOME

MODULE-I TRIGONOMETRY-I

1. ANGLE
   1. Definition of an angle.
   2. Concept of an angle in trigonometry ,
   3. Different systems of measuring an angle.
   4. Definition of degree and radian.
   5. Express a right angle in different systems,
   6. Relation between degree & radian .
2. TRIGONOMETRIC RATIOS.
   1. Definition of Trigonometric ratios
   2. Trigonometric identities.(statements only)
   3. Problems based on trigonometric identities,
   4. Trigonometric ratios of standard angles like 00, 300, 450, 600 and 900.
   5. Problems.
3. TRIGONOMETRIC RATIOS OF RELATED ANGLES
   1. Angle of any magnitude and sign
   2. Give examples to differentiate positive and negative angles
   3. Trigonometric ratios in different quadrants and signs ASTC-Rule
   4. Finding all other t-functions, when a t-function in a particular quadrant is given.
   5. Complementary angles and relation between trigonometric ratios of complementary angles.
   6. Formulae of 90 0, 180 0, 270 0, 360 0 and (-0)
   7. Evaluation of sin 120, cos 330, tan 315
   8. Problems on related angles.
4. HEIGHTS AND DISTANCES
   1. Angle of elevation and angle of depression.
   2. Simple problems on height and distance.
5. COMPOUND ANGLES.
   1. Compound angles
   2. Examples for compound angles.
   3. Formulae of sin(A+B),and cos (A+B),
   4. tan(A+B) in terms of tan A and tan B
   5. Formula for sin(A-B),cos (A-B) and tan(A-B).
   6. Simple problems on compound angles.

MODULE-II TRIGONOMETRY-II

1. MULTIPLE AND SUBMULTIPLE ANGLES.
   1. Multiple and sub multiple angles with examples.
   2. Formulae for sin2A,cos2A and tan 2A (statements only)
   3. Formulae for sin 3A, cos 3A (statements only)
   4. Simple problems on multiple angles (problems involving half angle formulae are excluded)
2. SUM OR DIFFERENCE FORMULAE AND CONVERSE
   1. Expressions for sinC sinD and cosC cosD in terms of Product of trigonometric ratios.
   2. Expressions for sinAcosB, cosAsinB, cosAcosB and sinAsinB in terms of the sum and difference of trigonometric ratios.
   3. Simple problems.
3. PROPERTIES AND SOLUTION OF TRIANGLES.
   1. The relation between sides of a triangle and Sines, Cosines and Tangents of any angle
   2. Sine rule, Cosine rule and Tangent rule-(statements only) ,
   3. Projection formulae in any triangle.(no proof)
   4. Simple problems on above rules.
   5. Solution of a triangle in the following cases when
      1. All the three sides are given
      2. Two sides and included angle are given
      3. Two angles and one side is given
   6. Area of a triangle (Formulae and simple problems, no proof) when,
      1. All the three sides a, b and c are given
      2. Two sides and one included angle are given

MODULE-III DIFFERENTIAL CALCULUS

1. FUNCTIONS AND LIMITS.
   1. Variables and Constants.
   2. Dependent and independent variables.
   3. Definition of a function
   4. Explicit and implicit functions
   5. Concept of limit of a function (intuitive idea only).
   6. Need for this concept in finding instantaneous rate of change like velocity and slope.
   7. Explanation of lim 1 = and lim 1 = 0, A’^0 x x^-‘X x
   8. Simple problems on evaluation of limits of functions
      1. When x tends to a’
      2. By factorization,
      3. When x tends to
   9. Algebraic and trigonometrical limits:

   lim x >a xn – an = nan 1 for any rational number. limS!lf = 1

   • > 0

   where 0 is in radians x – a

   1. Simple problems on evaluation of limits based on direct application of the above standard limits.
2. DIFFERENTIATION-I
   1. Increment and incremental ratio.
   2. Differential coefficient or derivative of a function.
   3. Derivatives of functions of xn, sinx,and cosx with respect to x’ from method of first principles
   4. List of standard derivatives.
   5. Derivatives of ex and log x (no proof).
   6. Derivatives of inverse trigonometric functions (no derivation)
   7. Rules of differentiation: Sum, product and quotient of functions.
   8. Simple problems based on these rules.
3. DIFFERENTIATION-II
   1. Derivatives of function of a function (Chain rule).
   2. Problems based on chain rule.
   3. Differentiation of Implicit functions and Parametric functions.
   4. Simple problems on differentiation of implicit functions and parametric functions.
   5. Successive differentiation up to second order.
   6. Problems on successive differentiation.

MODULE-IV APPLICATIONS OF DIFFERENTIAL CALCULUS

1. EQUATIONS OF TANGENTS AND NORMALS
   1. Geometrical meaning of derivative
   2. Slope of a curve at a point.
   3. Equations of tangent and normal to the curve y = f
   4. at a given point.
2. RATES AND MOTION
   1. Derivative as a rate measurer
   2. Simple problems of rates occurring in engineering.
   3. Velocity and acceleration
   4. Simple problems to find velocity and acceleration of a moving body 13.5 when displacement s’ is given in terms of t’ and related problems
   5. Problems to determine the rate of change of a variable, when the rate of change of some related variable is given.
3. MAXIMA AND MINIMA
   1. Increasing and decreasing functions.
   2. Conditions for maxima and minima.(No proof)
   3. Maxima and minima of a function.
   4. Simple direct problems on maxima and minima.

MODULE – I

For the complete syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.
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MODULE – II

1. MULTIPLE AND SUBMULTIPLE ANGLES.Multiple and sub multiple angles with examples, Formulae for sin2A,cos2A,tan2A,Sin3A,Cos3A(without proof), problems on multiple angles (problems involving half angle formulae are excluded)
2. SUM OR DIFFERENCE FORMULAE AND CONVERSESum, Difference, product formulae, converse of product formulae (without proof) and simple problems based on it.
3. PROPERTIES AND SOLUTION OF TRIANGLES.Sine rule, Cosine rule and Tangent rule-(statements only), Projection formulae in any triangle.(no proof),Simple problems on above rules. Solution of a triangle when all the three sides are given ,two sides and included angle are given two angles and one side is given Area of a triangle (Formulae and simple problems, no proof) when all the three sides a, b and c are given & when two sides and one included angle are given

MODULE – III

1. FUNCTIONS AND LIMITS.Variables and Constants. Dependent and independent variables Definition of a function Explicit and implicit functions, Concept of limit of a function, Explanation of lim1 = and lim 1 = 0, Simple problems on evaluation of limits of functions
   1. x^0 x x^'<. x

   when x tends to a’

   1. by factorization,
   1. when x tends to tt’ Algebraic and trigonometrical limit( without proof) and simple problems based on it
2. DIFFERENTIATION-IIncrement and incremental ratio, derivative of a function, Derivatives of functions of xn, sinx and cosx with respect to x’ from method of first principles, List of standard derivatives. Derivatives of ex ,log x & Derivatives of inverse trigonometric functions (no derivation), Rules of differentiation: Sum, product and quotient of functions. Simple problems based on these rules.
3. DIFFERENTIATION-IIDerivatives of function of a function (Chain rule).Problems based on chain rule. Differentiation of Implicit functions and Parametric functions. Simple problems on differentiation of implicit functions and parametric functions, Successive differentiation up to second order. Problems on successive differentiation. MODULE – IV
4. EQUATIONS OF TANGENTS AND NORMALSGeometrical meaning of derivative Slope of a curve at a point. Equations of tangent and normal to the curve y = f
   1. at a given point.
5. RATES AND MOTIONDerivative as a rate measurer, Simple problems of rates occurring in engineering, Velocity and acceleration, Simple problems to find velocity and acceleration of a moving body when displacement s’ is given in terms of t’ and related problems. Problems to determine the rate of change of a variable, when the rate of change of some related variable is given.
6. MAXIMA AND MINIMAIncreasing and decreasing functions. Conditions for maxima and minima.(No proof) Maxima and minima of a function. Simple direct problems on maxima and minima NB: Emphasis is given in application oriented problems and hence proofs and derivations are not expected.

Text Books:

For the complete syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.
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Reference Books:

1. Anton – Calculus, 7 edn. – WILEY
2. Dr.M.K.Venkatraman – Engineering Mathematics – National Publishing Co, Chennai
3. Dr.P.Kandasamy & Others – Engineering Mathematics – S.Chand & Co Ltd, New Delhi

For detailed syllabus of all other subjects of Information Technology, 2015 revision curriculum do visit IT 1st Sem subject syllabuses for 2015 revision.

To see the syllabus of all other branches of diploma 2015 revision curriculum do visit all branches of SITTTR diploma 2015 revision.