Name of the Organisation : Andhra Pradesh State Council of Higher Education (apecet.org)
Type of Announcement : Syllabus
Designation : ECET-2013 Engineering Common Entrance Test
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Syllabus for ECET-2013 :
FOR DIPLOMA HOLDERS
Syllabus for Common Entrance Test ECET [FDH & B.Sc (Mathematics)] – 2013

MATHEMATICS
Unit-I Matrices:
Matrices of 3rd order: Types of matrices-Algebra of matrices-Transpose of a matrix- Symmetric, skew symmetric matrices-Minor, cofactor of an element-Determinant of a square matrix-Properties-Laplace’s expansion-singular and non singular matrices-Adjoint and multiplicative inverse of a square matrix-System of linear equations in 3 variables-Solutions by Crammer’s rule, Matrix inversion method,-Gauss-Jordan methods.
Partial Fractions: Resolving a given rational function into partial fractions.

Unit –II:
Trigonometry: Properties of Trigonometric functions – Ratios of Compound angles, multiple angles, sub multiple angles – Transformations of Products into sum or difference and vice versa – Simple trigonometric equations – Properties of triangles – Inverse Trigonometric functions.
Complex Numbers: Modulus and conjugate, arithmetic operations on complex number—Modulus-Amplitude form (Polar form)-Euler form (exponential form)-Properties- De Movire’s Theorem and its applications.

Unit – III : Analytical Geometry
Circles-Equation given center and radius-given ends of diameter-General equation-finding center and radius. Standard forms of equations of Parabola, Ellipse and Hyperbola – simple properties.

Unit – IV : Differentiation and its Applications
Functions and limits – Standard limits – Differentiation from the First Principles – Differentiation of sum, product, quotient of functions, function of function, trigonometric, inverse trigonometric, exponential, logarithmic, Hyperbolic functions, implicit, explicit and parametric functions – Derivative of a function with respect to another function-Second order derivatives –Geometrical applications of the derivative (angle between curves, tangent and normal) – Increasing and decreasing functions – Maxima and Minima (single variable functions) using second order derivative only – Derivative as rate measure -Errors and approximations - Partial Differentiation – Partial derivatives up to second order – Euler’s theorem.

Unit – V : Integration and Its Applications
Indefinite Integral – Standard forms – Integration by decomposition of the integrand of trigonometric, algebraic, exponential, logarithmic and Hyperbolic functions – Integration by substitution – Integration of reducible and irreducible quadratic factors – Integration by parts – Definite Integrals and properties, Definite Integral as the limit of a sum – Application of Integration to find areas under plane curves and volumes of Solids of revolution – Mean and RMS value.

Unit – VI: Differential Equations
Definition of a differential equation-order and degree of a differential equation- formation of differential equations-solution of differential equation of the type first order, first degree, variable-separable, homogeneous equations, exact, linear differential equation of the form dy/dx + Py = Q, Bernoulli’s equation

PHYSICS
Unit-1: Units and dimensions: Physical quantity-fundamental and derived physical quantitiesunits- fundamental and derived units-SI units-multiples and sub-multiples in SI units-advantages of SI units-dimensions and dimensional formulae-dimensionless quantities-applications and limitations of dimensional analysis-problems.

Unit-2: Elements of vectors:
Scalar and vector quantities-examples–graphical representation of a vector-types of vectorsaddition and subtraction of vectors-triangle law-parallelogram law and its cases-polygon lawresolution of a vector-unit vectors (i, j, k)-dot product and cross product of two vectorscharacteristics of dot and cross products-examples-problems.

Unit-3: Kinematics and Friction
Equations of motion-acceleration due to gravity-equations of motion under gravity-expressions for maximum height, time of ascent, time of descent, time of flight, velocity on reaching the point of projection-motion of a body projected from the top of a tower-projectile motionexamples- horizontal and oblique projections-expressions for maximum height, time of ascent, time of flight, horizontal range, magnitude and direction of resultant velocity-problems. Friction-normal reaction-laws of friction-coefficients of friction-angle of friction-methods of reducing friction-advantages and disadvantages of friction-motion of a body over a smooth inclined plane and a rough inclined plane–problems.

Unit-4: Work, Power and Energy
Work, power and energy-definitions and units-potential and kinetic energies-examples and expressions-law of conservation of energy-problems-renewable and non-renewable sources of energy (solar, wind, biogas, tidal, nuclear energies etc)

Unit-5: Simple harmonic motion and acoustics
Definition-conditions of SHM-examples of SHM-expressions for displacement, velocity, acceleration, time period, frequency and phase of SHM-time period of a simple pendulumseconds pendulum-problems. Sound-musical sound and noise-noise pollution-Effects and methods of control of Noise Pollution-Beats and echoe-problems-Doppler effect – Explanation, cases and Applications Acoustics of buildings-Reverberation-Sabines’ formula-characteristics of a good building-problems.

Unit:6: Heat and Thermodynamics
Expansion of gases-Boyle’s law-Absolute scale of temperature-charle’s laws-Ideal gas equation-Universal gas constant and its value-SI Units-problems-external work done by a gas-isothermal process-adiabatic process-first law of thermodynamics and its applications to isothermal process and adiabatic process-two specific heats of a gas-relation between Cp and Cv-problems-second law of thermodynamics and its applications.

Unit:7 Modern Physics
Photoelectric effect – explanation and its laws-applications of photoelectric effect (photocell) – critical angle and total internal reflection – optical fibers - principle, working , types and applications-concept of super conductivity – its properties and applications.

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