VITEEE Syllabus for Mathematics
Matrices and Determinants
Rank of a matrix-consistency of a system of linear equations-elementary transformation on a matrix-Cramer’s rule-homogeneous linear system, non-homogeneous equations-rank method. Types of matrices-solution of system of linear equations by matrix inversion method-addition and multiplicity of matrices-computation of inverses-properties.
Theory of Equations, Sequence and Series
Arithmetic, harmonic and geometric progressions-special series: logarithmic and exponential series-binomial-summation of series. Relation between G.M., A.M. and H.M. Quadratic equations-nature of roots-increasing and diminishing of roots-coefficients relations between roots-symmetrical functions of roots-reciprocal equations.
Planes-passing through a given point and perpendicular to a vector, passing through a given point and parallel to two given vectors, passing through three given non-collinear points, the distance between a point and a plane, angle between two given planes, equation plane, given the distance from the origin and unit normal, passing through two given points and parallel to a given vector, passing through the line of intersection of two given lines, angle between a line and a plane. Sphere-equation of a sphere when the extremities of the diameter are given, equation of the sphere whose centre and radius are given. Scalar product- properties of scalar product, angle between two vectors, applications of dot products. Lines-passing through two given points, equation of a straight line passing through a given point and parallel to a given vector. Skew lines-condition for two lines to intersect, collinearity of three points, shortest distance between two lines, points of intersection. Vector product-properties of vector product left handed and right handed systems, applications of cross product. Product of three vectors-properties of scalar triple product, vector product of four vectors, scalar triple product, vector triple product, scalar product of four vectors.
Complex Numbers and Trigonometry
Circular function-addition formula and their applications-inverse trigonometric functions-trigonometrical ratios of related angles-trigonometric equations-properties and solution of triangle. Complex number system, conjugate-ordered pair representation, properties. Modulus-geometrical representation meaning, conjugate, difference, vector interpretation, De Moivrre’s theorem and its applications-properties-polar form principle value, sum, product quotient, solutions of polynomial equations. Roots of a complex number-cube roots, angle measures, nth roots fourth roots.
Parabola-other standard parabolas, standard equation of a parabola tracing of the parabola, the process of shifting the origin, some practical problems, general form of the standard equation. Ellipse-tracing of the ellipse, standard equation of the ellipse, other standard form of the ellipse, some practical problems, some general forms. Hyperbola-tracing of the hyperbola, standard equation, other form of hyperbola, chords, parametric forms of a coincs, tangents and noramals-Cartesian equation of chord of contact of tangents from a point, form and parametric form, asymptotes. Rectangular hyperbola-standard equation of a rectangular hyperbola.
Errors and approximations-relative, curve tracing, Euler’s theorem, absolute, percentage errors, partial derivatives. Derivatives as a rate measure-velocity-related rates-rate of change-acceleration-derivatives as a measure of slopetangent, angle and normal between curves. Minim and maxima. Rolle’s theorem-mean value theorem-Lagrange mean value theorem-Maclaurin and Taylor’s series, L’Hospital’s rule. Concavity convexity points of inflexion, minim, maxima, stationary points-decreasing, increasing.
Integral Calculus and its Application Methods of Integration Standard Types
Reduction formulae for cos^n (x) and sin^n (x), properties of definite integrals, surface area, area, volume and length.
Linear equations, degree and order, variable separable homogeneous, formation of differential equations, solving differential equations. Second order linear equations with constant co-efficient.
Binary operations-monoids-semi groups, groups (simple properties and problem only), order of an element, truth tables, order of a group, mathematical logic-connectives, tautologies, logical statements, sets, induction, algebraic properties, function, relations, combination, permutation.
Distribution function, variance, poisson, mathematical expectation, discrete distributions-binomial, continuous distribution-normal, axioms, conditional probability, probability density function, probability theorems on probability, random variable, distribution function.