# VITEEE Mathematics Syllabus

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## VITEEE  Mathematics Syllabus

1. 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.

2. 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 – nth Roots, Cube Roots, Fourth Roots.

3. 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 ( x1 , y1 ) to all the above said Curves.
• Asymptotes, Rectangular Hyperbola – Standard Equation of a Rectangular Hyperbola.

4. 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.

5. 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.

6. Differential Calculus

• Limits, continuity and differentiability of functions – Derivative as a  rate of Change, Velocity, Acceleration, Related Rates, Derivative as a Measure of Slope, Tangent, Normal and Angle between Curves.
• 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.

7. Integral Calculus and its Applications

• Simple Definite Integrals – Fundamental Theorems of Calculus, Properties of Definite Integrals.
• Reduction Formulae – Reduction Formulae for ∫ sinn xdx and ∫ cosn xdx, Bernoulli’s Formula.
• Area of Bounded Regions, Length of the Curve.

8. 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) = emx, sin mx, cos mx, x, x2.

9. 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.

10. 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. 