Mathematics Syllabus for VIT EEE 2015 Examinations:
The Vellore Institute of Technology, Engineering Entrance Examinations are conducted and convened once in a year. These Engineering Entrance Examinations are conducted in the month of April every year. Even the Upcoming Engineering Entrance Examinations will probably be conducted in the month of April 2015.
The Vellore Institute of Technology, Engineering Entrance Examinations comprises of 2 subjects: namely Physics, Chemistry, Mathematics and Biology. The paper pattern and the syllabus for all the subjects have already been mentioned in our Educational website www.careersamosa.com
You could also visit the link mentioned above to know more about the application forms and the date of the examination and the results of the examination from the above mentioned link.
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Applications of Matrices and Determinants:
Adjoint, inverse – properties, compounds of inverses, solution of systems of linear equations by matrix inversions method.
Rank of a matrix- elementary transformation on a matrix, consistency of a system of linear equation, Cramers’s rule, non- homogeneous equation, homogeneous linear system and rank method.
Complex Number system – conjugate, properties, ordered pair representation.
Modulus-properties, geometrical representation, polar form, principal value, conjugate, sum, difference, product, quotient, vector, interpretation, solutions of polymial equations, De Moivre’s theorem and its applications.
Roots of a Complex number- nth roots, cube roots, fourth roots.
Analytical Geometry of Two dimensions:
Definition of a conic- general equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity.
Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms- Directrix, Focus andLatus Rectum – parametric forms of conic and chords. Tangents and normals – Cartesian form and parametric form- equation of chord of contact of tangents from a point (x1, y1) to all the said above curves.
Asymptotes, Rectangular hyperbola- Standard Equation of a Rectangular hyperbola
Scalar Product- angle between two vectors, properties of scalar product, application of dot, products, vector product, right handed and left handed systems, properties of vector product, applications of cross product.
Product of three vectors – scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors.
Analytical geometry of three Dimensions:
Direction Cosines – direction ratios- equation of a straight line passing through a given point and parallel to a given line, passing through two given points, angle between two lines.
Planes – equation of a plane, passing through a given point and perpendicular to a line, given the distance from the origin and unit normal, passing through a given point and parallel to two given lines, passing through two given pints and parallel to a given line, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines (co-planar lines) angle between a line and a plane
Skew lines: Shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity of the three points.
Sphere: equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.
Derivatives as a rate, measurer- rate of change, velocity, acceleration, related rates, derivative as a measure of slope, tangent, normal and angle between curves, maxima and minima.
Mean value theorem- Rolle’s theorem, Lagrange Mean Value Theorem, Taylor’s and Maclaurin’s Series, L’ Hospital Rule, Stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion.
Errors and approximations – absolute, relative, percentage errors- curve tracing, partial derivatives, Euler’s theorem.
Integral Calculus and its Applications:
Simple definite integrals- fundamental theorems of Calculus, properties of definite integrals
Reduction formula- reduction formula for sin xdx and cos xdx, Bernoulli’s Formula.
Area of bounded reigions, length of the curve
Differential equations- formation of differential equation, order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations.
Second order linear differential equations- second order linear differential equations with constant co-efficients, finding the particular integral if f(x) =emx, sin, mx, cos mx, x, x2.
Probability – axioms- addition law- conditional probability – multiplicative law- Baye’s theorem- random variable- probability density function, distribution function, mathematical expectation, variance
Theoretical distributions, discrete distributions, binomial, poisson distributions – Continuous distributions, normal distributions
Mathematical logic- logical statements, connectives, truth tables, logical equivalence, tautology, contradiction,
Groups – binary operations, semigroups, monoids, groups, order of a group, order of an element, properties of a group.