VITEEE 2012 Mathematics Study Material, Preparation, Sample Papers, Question Papers, Test Series, Online Coaching, Notes

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Mathematics (122 Study Packages) subscribe

Mathematics Syllabus for VITEEE

Applications of Matrices and Determinants

Adjoint, inverse - properties, computation of inverses, solution of system of linear equations by matrix inversion method. Rank of a matrix - elementary transformation on a matrix, consistency of a system of linear equations, Cramer's rule, non-homogeneous equations, homogeneous linear system and rank method.

Complex Numbers

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 polynomial 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 Conies with respect to eccentricity.

Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms - Directrix, Focus and Latusrectum - parametric form of conies and chords – Tangents and normals - cartesian form and parametric

form - Equation of Chord of contact of tangents from a point ( ) to all the above said curves. Asymptotes, Rectangular hyperbola – Standard equation of a rectangular hyperbola.

Vector Algebra

Scalar Product - Angle between two vectors, properties of scalar product, applications 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 10 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 points 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 line (coplanar 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 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,

Differential Calculus

Derivative 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's 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 formulae - Reduction formulae for

Bernoulli's formula.

Area of Bounded Regions, Length of the Curve.

Differential Equations

Differential Equations - Formation of differential equations, order and degree, solving differential equations (1st order), variable sepharable homogeneous, linear equations. Second order linear Differential Equations - Second order Linear Differential Equations with constant coefficients, Finding the Parti-cular Integral if

Probability Distributions

Probability - Axioms - Addition Law – Conditional Probability - Multiplicative Law - Baye's Theorem - Random variable - probability density function, distribution function, mathematical expectation, variance. Theoretical distributions –

discrete distnbutions, Binomial, Poisson distributions - Continuous distributions. Normal dis-trihution

Discrete Mathematics

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 Groups, Information