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In mathematics, relations and functions is one of the basic and important chapters that help to understand other numerous topics conveniently. There are tons of topics such as types of relations, one to one, composite functions, the inverse of a function and lastly binary operations that you will learn through our online class. However, most of the students find it hard to understand and end up facing problems with further topics. So, check out our Studykhazana online classes offered by Puneet Dogra in order to resolve your issues in respect of relations and functions with ease.
In this section, you will learn:
1) Definition of Inverse Trigonometric Functions
2) Range of Inverse Trigonometric functions
3) Domain of Inverse Trigonometric Functions
4) Principle branch values
5) Graph of Inverse Trigonometric Functions
6) Elementary properties of Inverse Trigonometric functions
In this section, you will learn:
1) Concept, notation, order, equality and types of matrices
2) Zero matrix, transpose of a matrix, symmetric and skew symmetric matrices.
3) Simple properties of addition, subtraction and scaler multiplication
4) Non-commutativity of multiplication of matrices
5) Existence of non-zero matrices whose product is the zero matrix
6) Concept of elementary row and column operations
7) Invertible matrices and proof of uniqueness of inverse, if it exist.
In this section you will learn the following:
1) Determinant of square matrix
2) Properties of determinants
3) Minors
4) Co-factors
5) Application of determinant in finding area of a triangle
6) Adjoint and Inverse of a square matric
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, 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. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.
In this section, you will learn the following:
1) Applications of derivatives
2) Rate of change of bodies
3) increasing/ decreasing functions
4) Tangents and Normal
5) Use of derivatives in approximation
6) Maxima and Minima
7) Simple word problem
Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).
Definition, order and degree, general and particular solutions of a differential equation.Formation of differential equation whose general solution is given.Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of 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.
Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.
In this section, you will learn the following:
1) Direction Cosines and direction ratios of a line joining two points.
2) Cartesian Equation and Vector Equation of a line.
3) Coplanar and skew lines
4) Shortest distance between two lines.
5) Cartesian and vector equation of a plane.
6) Angles between a) Two lines b) Two Planes c) a line and a plane
7) Distance of a point from a plane.
In this section, you will learn the following:
1) Introduction
2) Related terminology like constraints, objective function, optimization and different types of linear programming problems.
3) Mathematical formulation of L.P Problems.
4) Graphical method of solution for problems in two variables: feasible and infeasible regions.
5) feasible and infeasible solutions
6) Optimal feasible solutions
Conditional probability, multiplication theorem on probability. independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.