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APPLIED MATHEMATICS - II L
T P 5 - - RATIONALE
Applied mathematics forms the backbone of engineering students. Basic elements of Differential calculus and integral calculus and statistics have been included in this course. This will develop analytical abilities to apply in engineering field and will provide continuing educational base to the students. DETAILED CONTENTS1. Algebra (10 hrs)
1.1 Determinants: Elementary properties of
determinants up to 3rd order, consistency of equations, Crammer’s
rule.
1.2
Matrix: Algebra of matrices, Inverse
of a matrix, matrix inverse method to solve a system of linear equations in 3
variables.
2. Differential Calculus (26 hrs) 2.1 Definition of function; Concept of limits. Lt xn - an, Four standard limits x ® a ---------- x - a Lt
Sin x Lt
ax
- 1
Lt (1+x)1/x x ® 0 -------- , x ® 0 ------- x® 0 x x
2.2 Differentiation by definition of xn , sin x, cos x, tan x, ex, logax 2.3 Differentiation of sum, product and quotient of functions. Differentiation of function of a function. 2.4 Differentiation of trigonometric inverse functions. Logarithmic differentiation. Exponential differentiation Successive differentiation (excluding nth order). 2.5 Applications: (a) Rate Measures (b) Errors and increments (c) Maxima and minima (d) Equation of tangent and normal to a curve (for explicit functions only) 3. Integral Calculus (28 hrs) 3.1 Integration as inverse operation of differentiation 3.2 Simple integration by substitution, by parts and by partial fractions (for linear factors only) 3.3 Evaluation of definite integrals (simple problems)- π/2 π /2 π/2 Evaluation of ∫ Sinn x. dx, ∫ Cosn x dx , ∫ Sinm x Cosn x dx 0 0 0 using formulae without proof (m and n being positive integers only) 3.4 Applications of integration for : (a) Simple problem on evaluation of area bounded by a curve and axes. (b) Calculation of Volume of a solid formed by revolution of an area about axes. (Simple problems). (c) To calculate average and root mean square value of a function and (d) Area by Trapezoidal Rule and Simpson Rule 4. Statistics and Probability (10 hrs) 4.1 Measures of Central Tendency: Mean, Median, Mode 4.2 Measures of Dispersion: Mean deviation, Standard deviation 4.3 Probability definition and addition law of probability, theorem and simple numerical problems, normal probability curve 5. Differential Equations (6 hrs) Solution of first order and first degree differential equation by variable separation method (simple problems) INSTRUCTIONAL
STRATEGY Basic elements of Differential Calculus, Integral Calculus and Statistics can be taught in the light of their applications in the field of engineering and technology. By laying more stress on applied part, teachers can also help in providing continuing education base to the students. RECOMMENDED
BOOKS
1. Elementary Engineering Mathematics by BS Grewal, Khanna Publishers, New Delhi. 2. Engineering Mathematics by Vol. I & II by S Kohli, IPH, Jalandhar 3. Applied Mathematics by Dr. RD Sharma 4. Applied Mathematics, Vol. I & II by SS Sabharwal & Sunita Jain, Eagle Parkashan, Jalandhar 5. Comprehensive Mathematics, Vol. I & II by Laxmi Publications 6. Engineering Mathematics by Dass Gupta 7. Engineering Mathematics by C Dass Chawla, Asian Publishers, New Delhi 8. Engineering Mathematics, Vol I, II & III by V Sundaram et.al, Vikas Publishing House (P) Ltd., New Delhi 9. Engineering Mathematics by N.Ch.S.N Iyengar et.al, Vikas Publishing House (P) Ltd., New Delhi SUGGESTED DISTRIBUTION OF MARKS
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