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Syllabus of Mathematics: Unit -I: Relations and Functions

**Relations and Functions**

Types of relations: reflexive, transitive, symmetric and equivalence relations. Composite functions, One to one and onto functions, inverse of a function.

**Inverse Trigonometric Functions**

Definition, domain, range, principal value branch.Graphs of inverse trigonometric. Functions Elementary properties of inverse trigonometric functions.

Unit-II: Algebra

**Matrice**

Concept, notation, equality, order, types of matrices, transpose of a matrix, zero and identity matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition, Subtraction and multiplication and multiplication with a scalar. Simple properties of multiplication, addition and scalar multiplication.

Non- conversion of multiplication of matrices, existence of non-zero matrices whose product is the zero matrix.Concept of column operations and elementary row.Invertible matrices and also proof of the uniqueness of inverse.

**Applications of Derivatives**

Applications of derivatives: rate of change of bodies, use of derivatives, increasing/decreasing functions, tangents and normals, maxima and minima.

**Integrals**

Integration as inverse process of differentiation.Integration by substitution method, by partial fractions and by parts, Evaluation of simple integrals problems based on them.

**Differential Equations**

Definition, order and degree.General solutions of a differential equation.Formation of differential equation.Solutions of homogeneous differential equations of first order and first degree,Solution of differential equations by method of separation of variables.Solutions of linear differential equation of the type as follows is given as: (dy/dx) + py = q, here q and p are functions of x.

Unit-III: Calculus

**Continuity and Differentiability**

Continuity and differentiability, derivative of composite functions,derivative of implicit functions, derivative of inverse trigonometric functions.Concept of logarithmic and exponential functions. Derivatives of logarithmic and exponential functions.Logarithmic differentiation, derivative of functions shown in parametric forms. Lagrange’s Mean Value Theorems and its geometric interpretation. Second order derivatives.

**Applications of Derivatives**

Applications of derivatives: rate of change of bodies, use of derivatives, increasing/decreasing functions, tangents and normals, maxima and minima.

**Integrals**

Integration as inverse process of differentiation. Integration by substitution method, by partial fractions and by parts, Evaluation of simple integrals problems based on them.

**Differential Equations**

Definition, order and degree. General solutions of a differential equation. Formation of differential equation. Solutions of homogeneous differential equations of first order and first degree, Solution of differential equations by method of separation of variables. Solutions of linear differential equation of the type as follows is given as: (dy/dx) + py = q, here q and p are functions of x.

Unit-IV: Vectors and Three-Dimensional Geometry

**Vectors**

Definition and operations performed on Vectors, scalars, magnitude and direction of a vector. Types of vectors (zero, equal, unit, collinear and parallel vectors), position vector of a point, components of a vector, multiplication of a vector by a scalar, addition of vectors. Definition, Geometrical Interpretation, application of scalar/ dot product of vectors, vector/ cross product of vectors, scalar triple product of vectors.

**Three – dimensional Geometry**

Direction cosines of a line joining two points. Vector equation and Cartesian equation of a line, coplanar and skew lines, shortest distance between two lines. Vector and cartesian equation of a plane. Angle between (i) two planes, (ii) two lines, (iii) a plane and a line.

Unit-V: Linear Programming(L .P.)

**Linear Programming**

Introduction, different types of linear programming problems, mathematical formulation of L.P. problems, graphical method for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions.

Unit-VI: Probability

**Probability**

Conditional probability, independent events, Random variable and its probability distribution, multiplication theorem on probability, total probability, Bayes’ theorem, mean and variance of random variable.