Maths 12th Std

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Maths 12th Std

Volume I

Chapter 1: Applications of Matrices and Determinants


=> Introduction
=> Inverse of a Non-Singular Square Matrix
=> Adjoint of a Square Matrix
=> Definition of inverse matrix of a square matrix
=> Properties of inverses of matrices
=> Application of matrices to Geometry
=> Application of matrices to Cryptography
=> Exercise 1.1: Inverse of a Non-Singular Square Matrix
=> Inverse of a Non-Singular Square Matrix: Solved Example Problems
=> Elementary Transformations of a Matrix
=> Row Echelon form
=> Rank of a Matrix
=> Gauss Jordan Method
=> Exercise 1.2: Elementary Transformations of a Matrix
=> Elementary Transformations of a Matrix: Solved Example Problems
=> Applications of Matrices: Solving System of Linear Equations
=> Formation of a System of Linear Equations
=> System of Linear Equations in Matrix Form
=> Solution to a System of Linear equations
=> Matrix Inversion Method
=> Exercise 1.3: Matrices linear equations by matrix inversion method
=> Matrices: Cramerís Rule
=> Exercise 1.4: Matrices: Cramerís Rule
=> Matrix: Gaussian Elimination Method
=> Exercise 1.5: Matrix: Gaussian Elimination Method
=> Solved Example Problems on Applications of Matrices: Solving System of Linear Equations
=> Matrix: Non-homogeneous Linear Equations
=> Exercise 1.6: Matrix: Non-homogeneous Linear Equations
=> Matrix: Homogeneous system of linear equations
=> Exercise 1.7: Matrix: Homogeneous system of linear equations
=> Choose the Correct Answers
=> Summary

Chapter 2: Complex Numbers


=> Introduction
=> Introduction to Complex Numbers
=> Exercise 2.1: Introduction to Complex Numbers
=> Complex Numbers
=> Exercise 2.2: Complex Numbers
=> Basic Algebraic Properties of Complex Numbers
=> Exercise 2.3: Properties of Complex Numbers
=> Conjugate of a Complex Number
=> Exercise 2.4: Conjugate of a Complex Number
=> Modulus of a Complex Number
=> Properties of Modulus of a complex number
=> Modulus of a Complex Number: Solved Example Problems
=> Square roots of a complex number
=> Exercise 2.5: Modulus of a Complex Number
=> Geometry and Locus of Complex Numbers
=> Exercise 2.6: Geometry and Locus of Complex Numbers
=> Polar form of a complex number
=> Eulerís Form of the complex number
=> Exercise 2.7: Polar and Euler form of a Complex Number
=> de Moivreís Theorem and its Applications
=> de Moivre's Theorem
=> Finding nth roots of a complex number
=> The nth roots of unity
=> Exercise 2.8: de Moivreís Theorem and its Applications
=> Solved Example Problems on de Moivreís Theorem
=> Choose the correct Answers
=> Summary

Chapter 3: Theory of Equations


=> Introduction
=> Basics and types of Polynomial Equations
=> Vietaís formula for Quadratic Equations
=> Vietaís formula for Polynomial Equations
=> Exercise 3.1: Vietaís Formulae and Formation of Polynomial Equations
=> Nature of Roots and Nature of Coefficients of Polynomial Equations
=> Imaginary Roots
=> Irrational Roots
=> Rational Roots
=> Applications of Polynomial Equation in Geometry
=> Exercise 3.2: Polynomial Equation in Geometry
=> Roots of Higher Degree Polynomial Equations
=> Polynomials with Additional Information
=> Exercise 3.3: Polynomials with Additional Information
=> Partly Factored Polynomial
=> Exercise 3.4: Partly Factored Polynomial
=> Rational Root Theorem
=> Reciprocal Equations
=> Non-polynomial Equations
=> Exercise 3.5: Polynomial Equations with no Additional Information
=> Descartes Rule
=> Exercise 3.6: Descartes Rule
=> Choose the correct Answers
=> Summary

Chapter 4: Inverse Trigonometric Functions


=> Introduction
=> Some Fundamental Concepts of Inverse Trigonometric Functions
=> Sine Function and Inverse Sine Function
=> Exercise 4.1: Sine Function and Inverse Sine Function
=> The Cosine Function and Inverse Cosine Function
=> Exercise 4.2: Cosine Function and Inverse Cosine Function
=> The Tangent Function and the Inverse Tangent Function
=> Exercise 4.3: Tangent Function and the Inverse Tangent Function
=> Cosecant Function and the Inverse Cosecant Function
=> The Secant Function and Inverse Secant Function
=> The Cotangent Function and the Inverse Cotangent Function
=> Principal Value of Inverse Trigonometric Functions
=> Exercise 4.4: Principal Value of Inverse Trigonometric Functions
=> Properties of Inverse Trigonometric Functions
=> Solved Example Problems on Inverse Trigonometric Functions
=> Exercise 4.5: Inverse Trigonometric Functions
=> Choose the correct answers
=> Summary

Chapter 5: Two Dimensional Analytical Geometry II


=> Introduction
=> Circle
=> Equation of a circle in standard form
=> Equations of tangent and normal at a point P on a given circle
=> Condition for the line y = mx + c to be a tangent to the circle and finding the point of contact
=> Circle: Solved Example Problems
=> Exercise 5.1: Circle
=> Conics
=> The general equation of a Conic
=> Parabola
=> Ellipse
=> Hyperbola
=> Exercise 5.2: Conics
=> Conic Sections
=> Exercise 5.3: Conic Sections
=> Parametric form of Conics
=> Tangents and Normals to Conics
=> Exercise 5.4: Tangents and Normals to Conics
=> Real life Applications of Conics
=> Exercise 5.5: Real life Applications of Conics
=> Solved Example Problems on Real life Applications of Conics
=> Choose the correct Answer
=> Summary

Chapter 6: Applications of Vector Algebra


=> Introduction
=> Geometric introduction to vectors
=> Scalar Product and Vector Product
=> Exercise 6.1: Scalar Product and Vector Product
=> Scalar triple product
=> Exercise 6.2: Scalar triple product
=> Vector triple product
=> Jacobiís Identity and Lagrangeís Identity
=> Exercise 6.3: Vector triple product, Jacobiís Identity and Lagrangeís Identity
=> Application of Vectors to 3-Dimensional Geometry
=> Exercise 6.4: Application of Vectors to 3-Dimensional Geometry
=> A point on the straight line and the direction of the straight line
=> Straight Line passing through two given points
=> Angle between two straight lines
=> Point of intersection of two straight lines
=> Shortest distance between two straight lines
=> Exercise 6.5: Point of intersection of two straight lines
=> Different forms of Equation of a plane
=> Equation of a plane when a normal to the plane
=> Equation of a plane perpendicular to a vector and passing through a given point
=> Intercept form of the equation of a plane
=> Exercise 6.6: Equation of a plane
=> Equation of a plane passing through three given non-collinear points
=> Equation of a plane passing through a given point and parallel to two given non-parallel vectors
=> Equation of a plane passing through two given distinct points and is parallel to a non-zero vector
=> Exercise 6.7: Equation of a plane
=> Condition for a line to lie in a plane
=> Condition for coplanarity of two lines
=> Equation of plane containing two non-parallel coplanar lines
=> Exercise 6.8: Equation of a plane
=> Angle between two planes
=> Angle between a line and a plane
=> Distance of a point from a plane
=> Distance between two parallel planes
=> Equation of line of intersection of two planes
=> Equation of a plane passing through the line of intersection of two given planes
=> Image of a Point in a Plane
=> Meeting Point of a Line and a Plane
=> Exercise 6.9: Equation of intersection of the planes
=> Choose the correct answer
=> Summary

Volume II

Chapter 7: Applications of Differential Calculus


=> Applications of Differential Calculus
=> Derivative as slope
=> Derivative as rate of change
=> Related rates
=> Exercise 7.1 : Meaning of Derivatives
=> Equations of Tangent and Normal
=> Angle between two curves
=> Exercise 7.2 : Equations of Tangent and Normal, Angle between two curves
=> Mean Value Theorem
=> Rolleís Theorem
=> Lagrangeís Mean Value Theorem
=> Applications - Mean Value Theorem
=> Exercise 7.3: Mean Value Theorem
=> Series Expansions: Maclaurinís and Taylorís Series
=> Exercise 7.4 : Series Expansions: Maclaurinís and Taylorís Series
=> Indeterminate Forms
=> Exercise 7.5 : Indeterminate Forms
=> Applications of First Derivative
=> Exercise 7.6 : Applications of First Derivative
=> Applications of Second Derivative
=> Exercise 7.7: Applications of Second Derivative
=> Applications in Optimization
=> Exercise 7.8: Applications in Optimization
=> Symmetry and Asymptotes
=> Sketching of Curves
=> Exercise 7.9: Symmetry and Asymptotes, Sketching of Curves
=> Exercise 7.10: Choose the correct or the most suitable answer
=> Summary

Chapter 8: Differentials and Partial Derivatives


=> Differentials and Partial Derivatives
=> Linear Approximation
=> Errors: Absolute Error, Relative Error, and Percentage Error
=> Exercise 8.1: Linear Approximation
=> Differentials
=> Exercise 8.2: Differentials
=> Functions of Several Variables
=> Recall of Limit and Continuity of Functions of One Variable
=> Limit and Continuity of Functions of Two Variables
=> Exercise 8.3: Functions of Several Variables
=> Partial Derivatives
=> Exercise 8.4: Partial Derivatives
=> Linear Approximation and Differential of a function of several variables
=> Exercise 8.5: Linear Approximation and Differential of a function of several variables
=> Function of Function Rule
=> Exercise 8.6: Function of Function Rule
=> Homogeneous Functions and Eulerís Theorem
=> Exercise 8.7: Homogeneous Functions and Eulerís Theorem
=> Exercise 8.8: Choose the correct answer
=> Summary

Chapter 9: Applications of Integration


=> Applications of Integration
=> Definite Integral as the Limit of a Sum
=> Exercise 9.1: Definite Integral as the Limit of a Sum
=> Limit Formula to Evaluate Definite Integral as the Limit of a Sum
=> Exercise 9.2: Limit Formula to Evaluate Definite Integral as the Limit of a Sum
=> Fundamental Theorems of Integral Calculus and their Applications
=> Exercise 9.3: Fundamental Theorems of Integral Calculus and their Applications
=> Bernoulliís Formula
=> Exercise 9.4: Bernoulliís Formula
=> Improper Integrals
=> Exercise 9.5: Improper Integrals
=> Reduction Formulae
=> Exercise 9.6: Reduction Formulae
=> Gamma Integral
=> Exercise 9.7: Gamma Integral
=> Evaluation of a Bounded Plane Area by Integration
=> Exercise 9.8: Evaluation of a Bounded Plane Area by Integration
=> Volume of a solid obtained by revolving area about an axis
=> Exercise 9.9: Volume of a solid obtained by revolving area about an axis
=> Exercise 9.10: Choose the correct answer
=> Summary

Chapter 10: Ordinary Differential Equations


=> Ordinary Differential Equations
=> Differential Equation, Order, and Degree
=> Exercise 10.1: Differential Equation, Order, and Degree
=> Classification of Differential Equations
=> Formation of Differential equations from Physical Situations
=> Exercise 10.2: Formation of Differential equations from Physical Situations
=> Formation of Differential Equations from Geometrical Problems
=> Exercise 10.3: Formation of Differential Equations from Geometrical Problems
=> Solution of Ordinary Differential Equations
=> Exercise 10.4: Solution of Ordinary Differential Equations
=> Variables Separable Method
=> Substitution Method
=> Exercise 10.5: Variables Separable Method, Substitution Method
=> Homogeneous Form or Homogeneous Differential Equation
=> Exercise 10.6: Homogeneous Form or Homogeneous Differential Equation
=> First Order Linear Differential Equations
=> Exercise 10.7: First Order Linear Differential Equations
=> Applications of First Order Ordinary Differential Equations
=> Exercise 10.8: Applications of First Order Ordinary Differential Equations
=> Exercise 10.9: Choose the correct answer
=> Summary

Chapter 11: Probability Distributions


=> Probability Distributions
=> Random Variable
=> Exercise 11.1: Random Variable
=> Types of Random Variable
=> Discrete random variables
=> Probability Mass Function
=> Cumulative Distribution Function or Distribution Function
=> Cumulative Distribution Function from Probability Mass function
=> Probability Mass Function from Cumulative Distribution Function
=> Exercise 11.2: Types of Random Variable
=> Continuous Distributions
=> Exercise 11.3: Continuous Distributions
=> Mathematical Expectation
=> Properties of Mathematical expectation and variance
=> Exercise 11.4: Mathematical Expectation
=> Theoretical Distributions: Some Special Discrete Distributions
=> Exercise 11.5: Theoretical Distributions: Some Special Discrete Distributions
=> Exercise 11.6: Choose the Correct answer
=> Summary

Chapter 12: Discrete Mathematics


=> Discrete Mathematics
=> Definitions of Binary Operations
=> Some more properties of a binary operation
=> Some binary operations on Boolean Matrices
=> Binary operations: Modular Arithmetic
=> Exercise 12.1: Binary operations
=> Mathematical Logic
=> Mathematical Logic: Statement and its truth value
=> Mathematical Logic: Compound Statements, Logical Connectives, and Truth Tables
=> Mathematical Logic: Logical Connectives and their Truth Tables
=> Mathematical Logic: Tautology, Contradiction, and Contingency
=> Mathematical Logic: Duality
=> Some Laws of Logical Equivalence
=> Exercise 12.2: Mathematical Logic
=> Exercise 12.3: Choose the correct answer
=> Summary



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