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ENGINEERING MATHEMATICS AND APPLIED SCIENCE
(COMMON TO ALL BRANCHES)
ENGINEERING MATHEMATICS Max Marks : 40 Marks
LINEAR ALGEBRA
Unit-1: MATRICES &DETERMINANTS: 06 Mark Basic concepts of Matrices(Addition, Subtraction and Multiplication) ,Determinants: Problems on finding unknown quantity in a 2nd^ and 3rd^ order determinants using expansion. Solving simultaneous linear equations using determinant method (Cramerโs rule up to 3rd^ order).
Matrices: Minors, Cofactors, Adjoint and Inverse of matrices of 2nd^ order. Characteristic equation and roots of a square matrix.
ALGEBRA
Unit-2: VECTORS: 03 Marks
Magnitude of a vector. Position vector. Expression of vector in terms of position vectors. Vector in plane and in space in terms of unit vectors i, j and k respectively. Product of vectors. Scalar and vector product. Applications of dot and cross products i.e., Projection of vector on another vector, Area of parallelogram and area of triangle. Work done by a force and moment of force.
Unit-3: PROBABILITY: 01 Marks
Random Experiments, Sample Space, Events, Types of Events, Algebra of Events, Complementary event, the events A or B, A and B,A but not B, Mutually Exclusive Events, Exhaustive events, Simple problems.
TRIGONOMETRY
Unit-4: ALLIED ANGLES AND COMPOUND ANGLES: 06 Marks Signs of Trigonometric ratios, Trigonometric ratios of Allied Angles in terms of ฮธ. Formulae for Sin(AยฑB), Cos(AยฑB) & tan(AยฑB) and problems on them. Multiple and sub multiple angle formulae for 2A & 3A and simple problems. Transformation formulae on sum or difference into products & products into sum or difference and problems on them.
Unit-5: Complex numbers: 01 Mark Definition of complex number in the form of ๐ + ๐๐. Conjugate of complex number. Algebra of complex numbers, modulus and principal value of argument of complex number. Polar form ๐ = ๐ ๐ถ๐๐ ๐ + ๐๐๐๐๐.
INTRODUCTION TO CALCULUS
Unit-6: Limits: 03 Marks Evaluation of limit of functions by factorization, rationalization, limits when n๏ โ. Problems on
algebraic limits based on formula lim๐ฅโ๐ ๐ฅ๐^ โ๐๐ ๐ฅโ๐ =^ ๐.^ ๐
๐โ (^1). Problems on trigonometric limits
based on formula lim๐โ 0 sin ๐ ๐ = 1
CO-ORDINATE GEOMETRY
Unit-7: Straight Lines:- 02 Marks Problems on different forms of equations of straight lines such as: y = mx+c, (y-y 1 ) = m(x-x 1 ), (y-y 1 ) =
๐ฆ 2 โ๐ฆ 1 ๐ฅ 2 โ๐ฅ 1
. (x โ x1)
Problems on equation of lines through a point and parallel or perpendicular to a given line.
Finding Slope ,X-intercept and Y- intercept of general equation ๐๐ฅ + ๐๐ฆ + ๐ = 0.
DIFFERENTIATION
Unit-8: 06 Marks Problems on rules of differentiation: (Sum rule, product rule and quotient rule). Problems on
function of a function and inverse trigonometric functions. Derivative of implicit functions, and
parametric functions and problems. Successive differentiation up to second order and problems
on them. Differentiation of Logarithmic functions of types ๐ข๐ฃ^ , Where u and v are functions of
x, Simple problems.
APPLICATIONS OF DIFFERENTIATION
Unit-9: 02 Mark
Equations of tangent and normal to the curve y = f(x) at a given point and problems. Derivative
as a rate measure i.e.to find the rate of change of displacement, velocity, radius, area, volume using differentiation and problems on them.
INTEGRAL CALCULUS
Unit-10: 05 Marks
Rules of integration and problems. Problems on integration by the method of substitution and by parts.
DEFINITE INTEGRALS
Unit-11: 02 Mark Simple problems on definite integrals. Problems on applications of definite integrals such as area
and volume.
DIFFERENTIAL EQUATIONS
Unit-12: 03 Mark
Order and Degree of Differential Equations, Formation of differential equation by eliminating
arbitrary constants up to second order. Problems on solution of linear differential equations of
first order by variable separable method and integrating factor method.
UNIT-IV WAVE MOTION: 08Marks
Simple Harmonic Motion : Periodic motion with example, SHM , expression for displacement of a particle executing SHM. Wave : Wave motion, wave period , wave frequency, wave amplitude, wave length and wave velocity, , relation between wave frequency , wave length and wave velocity-problems on V=nฮป. Mechanical waves and Non-Mechanical waves with examples, Longitudinal and Transverse waves with example. Propagation of sound waves in air : Newton โ Laplaceโs formula for velocity of sound in air and various factors affecting velocity of sound in air. Vibrations : Free vibration ,forced vibration and resonance with example. Laws of transverse vibration of stretched string, expression for fundamental frequency of vibration of stretched string โ simple problems on fundamental frequency. Stationary waves : Stationary waves and its characteristics, beat, beat frequency, application of
beats.
UNIT- V MODERN PHYSICS: 05 Mark Electromagnetic waves : Electromagnetic waves and its properties, electromagnetic spectrum and its applications. Laser : Laser, properties of laser and its applications. Nano-technology : Nanotechnology, advantages and dis-advantages of nanotechnology. Communication system : Basic elements of communication system, advantages and dis- advantages of satellite communication system, Optical fibre : Optical fibre-principle and its applications.
UNIT-VI INDUSTRIAL CHEMISTRY 08 Marks
Electrolysis: Electrolyte, types of electrolyte with example, electrolysis, Postulates of Arrhenius theory of electrolytic dissociation, Faradayโs First and Second law of electrolysis-simple problems on Faradayโs laws. Corrosion : Corrosion, conditions for corrosion, preventive methods of corrosion. Batteries : Battery, classification and its application. Fuel cells : Fuel cell, types and advantages of fuel cells. Metallurgy : Definition of mineral, ore, flux, slag and alloys. Purpose of making alloys and its applications. Polymers : polymers and its types, application of polymers. Composite materials : Composite material and its types, advantages and dis-advantages of composite material. pH Value : pH value of a solution , pH scale, application of pH in different fields.
