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Unit-I: Relations and Functions

1.      Types of relations: reflexive, symmetric, transitive and equivalence relations.

2.      One to one and onto functions. Injective + Surjective = Bijective Function

3.        Inverse Trigonometric Functions : Range, Domain, principal value branch.

4.       Graphs of inverse trigonometric functions.

 Unit-II: Algebra

5.      Matrices :  zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices.

6.       Invertible matrices: Proof of the uniqueness of inverse

7.      Determinants:  Aarea of a triangle. System of linear equations in two or three variables (having unique solution) using inverse of a matrix.

 Unit-III: Calculus

8.      Continuity and Differentiability : Chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin−1 𝑥 , cos−1 𝑥 and tan−1 𝑥, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

9.       Applications of Derivatives : Rate of change of quantities, increasing/decreasing functions, maxima and minima.

10.   Integrals : Integration of a variety of functions by substitution, by partial fractions and by parts,

11.  Evaluation of simple integrals of having Patterns:

12.   Properties of definite integrals and evaluation of definite integrals.

13.   Applications of the Integrals: Area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

14.  Differential Equations : Order and Degree, general and particular solutions , variables- Separable, homogeneous differential equations of first order and first degree. Linear differential equation of the type: dy dx + py = q, where p and q are functions of x or constants. d𝑥 d𝑦 + px = q, where p and q are functions of y or constants.

Unit-IV:

 Vectors and Three-Dimensional Geometry:

15.   Vectors : magnitude and direction,  Direction cosines and direction ratios , Properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

16.   Three - dimensional Geometry: Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.                                           

Unit-V:

17.   Linear Programming : Graphical method of solution for Linear inequation in two variables by corner methods.

18.  Probability : Conditional probability, multiplication theorem,  Bayes’ theorem, probability distribution, mean of random variable

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