# VITEEE 2015 Mathematics Syllabus

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**VITEEE Mathematics Syllabus 2015
**

**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 – 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 :**

- 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}*xdx*and ∫ cos^{n}*xdx*, 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 :**

- 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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