Syllabus
14 MECHANICAL ENGINEERING
Duration :03 Year
Eligibility :10thwith Science and Mathematics
Intake :25/40/60 (as approved by AICTE/State Govt.)
Pattern of Examination :Semester System
Assessment Type :The assessment will we carry out through credit point sytem/ learning Based Out comes
Theory and Practical Ratio :50:50
Industrial Training :Included after IInd Semester
Ecology & Environment :As pe Govenment Directions a subject named Environmen science & Energy Management has been included
General Proficiency :A provision of 6 periods per week has been made. It included of various
co-curricular activities like games, hobby clubs, seminars, declamationcontests, extension lectures, NCC, NSS, cultural activities and disclipine etc.
Syllabus              
Paper Code :991002
Paper Name :APPLIED MATHEMATICS-I
  • Unit – I (Algebra) [ 25 Periods ]
    • 1.1- Value of nP & nC (Without proof), Binomial theorem-(without proof) for r r

      positive integral index (expansion, general term, middle term) and for any index (expansion).

      1.2-Partial fractions- (linear factors, repeated linear factors, non reducible quadratic factors only).

      1.3-Determinants-Definition, Properties of determinants, Expansion of determinants (of order 2 and 3), Solution of simultaneous equations using Cramer’s rule ( in 2 and 3 unknowns ).

      1.4-Matrices- Definition of matrix, addition, subtraction, multiplication of matrices ( upto 3 order), singular and non singular matrices, Adjoint of a matrix, Inverse of a matrix by adjoint method (up to 3x 3 only).

      1.5-Sets: Sets and their representation, Empty set, finite and infinite sets, equal sets, subsets, power set, universal set, operation on sets, complement of set.
    		•
  • Unit – II (Trigonometry [15 Periods]
    • 1.1-Review of ratios of some standard angles (0,30,45,60,90 degrees), T-Ratios of Allied angles (without proof), Sum, difference formulae and their applications (without proof). Product formulae (Transformation of product to sum, difference and vice versa). T-Ratios of multiple angles, sub-multiple angles (2A, 3A, A/2).
    		•
        
  • Unit – III (Complex Number) [ 10 Periods ]
    • 1.1 Definition of complex numbers,Real and imaginary parts,Polar and Cartesian form and their conversion,Conjugate,Modulus and argument of a complex Number,Addition,Subtraction,Multiplication,division of complex numbers.

      1.2 De-Moiver's Theorem(Statement Only) related simple problems,rth root of unity.
  • Unit – IV (Differential Calculus) [ 30 Periods ]
    • 1.1- Function: Definitions of variables, constants, open & closed intervals.
      1.2- Definitions & types of functions-simple examples.

      1.3- Concept & definition of Limit.

      1.4- Standard limits of algebraic, trigonometric, exponential & logarithmic functions- simple problems. Examine the Continuity of a function at any point (simple problem only).

      1.5 Examine the continuity of a function at any point(Simple Problam Only) 1.6-Differentiation by (first principal) or by definition of differention xn, sin x, cos x, tan x, ex, log x only . a

      1.7-Differentiation of sum, product and quotient of functions. Differentiation of function of a function.

      1.8-Differentiation of trigonometric inverse functions. Logarithmic differentiation. Exponential differentiation, Successive differentiation (up to third term only).

      1.9-Application (a) Maxima and minima (b) Equation of tangent and normal to a curve (for explicit functions only) (c) L’ Hospital rule for solving in in determinate form ( 0/0, )
  • REFRENCE BOOK/ TEXT BOOK
    • 1-HIGHER ALGEBRA BY HALL & KNIGHT
      2-PLANE TRIGNOMETRY BY S L LONEY
      3-ENGINEERING MATHEMATICS BY SASTRY (PHI Learning)
      4-ENGINEERING MATHEMATICS BY B S GREWAL (Khanna Publishers)
      5-ENGINEERING MATHEMATICS BY A.B MATHUR (Khanna Publishers)
      6-APPLIED MATHMATICS , BY M K KANYAL (Khanna Publishers, New Delhi)
      7-APPLIED MATHEMATICS-I ,BY DR A.K.SINHA,Satya Prakashan,New Delhi.
      8-ENGINEERING MATHEMATICS,BY C.B.GUPTA,S.R.SINGH,MUKESH KUMAR,Mc GRAW HILL EDUCATION.
      9-APPLIED MATHEMATICS BY R.D.SHARMA,DHANPAT RAI PUBLICATIONS,NEW DELHI.
      10-ENGINEERING MATHEMATICS,VOL-I & II,BY S.S.SABRWAL AND SUNITA JAIN,EAGLE PRAKASHAN,JALANDHER.
      11-BASIC ENGINEERING MATHEMATICS,BY JHON BIRD,NEWNES PUBLICATIONS.
      12-A TEXT BOOK OF ENGINEERING MATHEMATICS,BY A.GANESH,G.BALASUBRAMNIUM.
      13-POLYTECHNIC MATHEMATICS,BY DR. D.S.PRAKASH,S.CHAND,PUBLICATIONS,NEW DELHI.
      14-A TEXT BOOK OF ENGINEERING MATHEMATICS,BY N.P.BALI & DR. MANISH GOYAL,KINDLY PUBLICATION.
      15-ENGINEERING MATHEMATICS,BY C.B.GUTA,S.R.SINGH & MUKESH KUMAR,Mc GRAW-HILL PUBLICATIONS,DELHI.
      16-APPLIED MATHEMATICS, BY KAPOOR,NAV DISTRIBUTOR,MEERUT.