VITEEE Syllabus for Mathematics
Matrices and Determinants
Rank of a matrixconsistency of a system of linear equationselementary transformation on a matrixCramer’s rulehomogeneous linear system, nonhomogeneous equationsrank method. Types of matricessolution of system of linear equations by matrix inversion methodaddition and multiplicity of matricescomputation of inversesproperties.
Theory of Equations, Sequence and Series
Arithmetic, harmonic and geometric progressionsspecial series: logarithmic and exponential seriesbinomialsummation of series. Relation between G.M., A.M. and H.M. Quadratic equationsnature of rootsincreasing and diminishing of rootscoefficients relations between rootssymmetrical functions of rootsreciprocal equations.
Vector Algebra
Planespassing through a given point and perpendicular to a vector, passing through a given point and parallel to two given vectors, passing through three given noncollinear 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. Sphereequation 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. Linespassing through two given points, equation of a straight line passing through a given point and parallel to a given vector. Skew linescondition for two lines to intersect, collinearity of three points, shortest distance between two lines, points of intersection. Vector productproperties of vector product left handed and right handed systems, applications of cross product. Product of three vectorsproperties 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 functionaddition formula and their applicationsinverse trigonometric functionstrigonometrical ratios of related anglestrigonometric equationsproperties and solution of triangle. Complex number system, conjugateordered pair representation, properties. Modulusgeometrical representation meaning, conjugate, difference, vector interpretation, De Moivrre’s theorem and its applicationspropertiespolar form principle value, sum, product quotient, solutions of polynomial equations. Roots of a complex numbercube roots, angle measures, nth roots fourth roots.
Analytical Geometry
Parabolaother 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. Ellipsetracing of the ellipse, standard equation of the ellipse, other standard form of the ellipse, some practical problems, some general forms. Hyperbolatracing of the hyperbola, standard equation, other form of hyperbola, chords, parametric forms of a coincs, tangents and noramalsCartesian equation of chord of contact of tangents from a point, form and parametric form, asymptotes. Rectangular hyperbolastandard equation of a rectangular hyperbola.
Differential Calculus
Errors and approximationsrelative, curve tracing, Euler’s theorem, absolute, percentage errors, partial derivatives. Derivatives as a rate measurevelocityrelated ratesrate of changeaccelerationderivatives as a measure of slopetangent, angle and normal between curves. Minim and maxima. Rolle’s theoremmean value theoremLagrange mean value theoremMaclaurin and Taylor’s series, L’Hospital’s rule. Concavity convexity points of inflexion, minim, maxima, stationary pointsdecreasing, 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.
Differential Equations
Linear equations, degree and order, variable separable homogeneous, formation of differential equations, solving differential equations. Second order linear equations with constant coefficient.
Discrete Mathematics
Binary operationsmonoidssemi groups, groups (simple properties and problem only), order of an element, truth tables, order of a group, mathematical logicconnectives, tautologies, logical statements, sets, induction, algebraic properties, function, relations, combination, permutation.
Probability Distribution
Distribution function, variance, poisson, mathematical expectation, discrete distributionsbinomial, continuous distributionnormal, axioms, conditional probability, probability density function, probability theorems on probability, random variable, distribution function.
