## VITEEE Syllabus 2019 for Mathematics

**Matrices and their Applications**

- 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.
- Solution of linear programming problems (LPP) in two variables.

**Trigonometry and Complex Numbers**

- Definition, range, domain, principal value branch, graphs of inverse trigonometric functions and their elementary properties.
- 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 – n
^{th}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 and Latus rectum – parametric form of conics and chords. – Tangents and normals – cartesian form and parametric form- equation of chord of contact of tangents from a point (x
_{1}, y_{1}) 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 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 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 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 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**

- Limits, continuity and differentiability of functions – 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 ∫ sin
^{n }x dx and ∫ cos^{n }x dx , 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), 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) = e
^{mx}, sin mx, cos mx, x, x^{2}.

**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 distributions, Binomial, Poisson distributions- Continuous distributions, Normal distribution.

**Discrete Mathematics**

- Functions – Relations – Basics of counting
- 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.

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