Business Maths 12th Std

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Business Maths 12th Std

Chapter 1: Applications of Matrices and Determinants


=> Introduction
=> Rank of a Matrix: Concept
=> Elementary Transformations and Equivalent matrices
=> Echelon form and finding the rank of the matrix (upto the order of 3×4)
=> Testing the consistency of non homogeneous linear equations (two and three variables) by rank method
=> Rank of a Matrix: Solved Example Problems
=> Exercise 1.1 : Rank of a Matrix
=> Cramer’s Rule
=> Cramer’s Rule - Non Homogeneous linear equations upto three variables: Solved Example Problems
=> Exercise 1.2 : Cramer’s Rule
=> Transition Probability Matrices
=> Transition Probability Matrices: Solved Example Problems
=> Exercise 1.3: Transition Probability Matrices
=> Choose the correct answer
=> Miscellaneous problems
=> Summary

Chapter 2: Integral Calculus - I


=> Introduction
=> Concept of Indefinite Integral
=> Two important properties of Integral Calculus
=> Methods of Integration
=> Integration by decomposition: Type I
=> Integration by decomposition: Type II
=> Integration by decomposition: Type III
=> Integration by decomposition: Type IV
=> Integration by parts Method
=> Integration by substitution (or) change of variable method
=> Some special types of Integrals Method
=> Definite integrals
=> The fundamental theorems of Integral Calculus
=> The fundamental theorems of Integral Calculus: Exercise and Example Solved Problems
=> Properties of definite integrals
=> Evaluation of Problems using properties of definite integrals
=> Gamma Integral
=> Definite integral as the limit of a sum
=> Choose the correct answer
=> Miscellaneous problems
=> Summary

Chapter 3: Integral Calculus - II


=> Introduction
=> Geometrical Interpretation of Definite Integral as Area under a curve
=> The area of the region bounded by the curves: Example Solved Problems
=> Exercise 3.1: The area of the region bounded by the curves
=> Application of Integration in Economics and Commerce
=> Integration: Cost functions from marginal cost functions
=> Integration: Revenue functions from Marginal revenue functions
=> Integration: The demand functions from elasticity of demand
=> Exercise 3.2: Application of Integration in Economics and Commerce
=> Integration: Consumer’s surplus
=> Integration: Producer surplus
=> Exercise 3.3: Application of Integration in Economics and Commerce
=> Choose the best answer form the given alternatives
=> Miscellaneous problems
=> Summary

Chapter 4: Differential Equations


=> Introduction
=> Definition of ordinary differential equation
=> Order and degree of a differential equation
=> Formation of ordinary differential equation
=> Exercise 4.1: Formation of ordinary differential equations
=> Solution of a Differential Equation
=> First order and first degree differential
=> First order and first degree differential: Solved Example Problems
=> Exercise 4.2: First order and first degree differential
=> Homogeneous Differential Equations
=> Homogeneous Differential Equations: Solved Example Problems
=> Exercise 4.3: Homogeneous Differential Equations
=> Linear differential equations of first order
=> Linear differential equations of first order: Solved Example Problems
=> Exercise 4.4: Linear differential equations of first order
=> A general second order linear differential equation with constant coefficients is of the form
=> Second Order first degree differential equations with constant coefficients: Solved Example Problems
=> Exercise 4.5: Second Order first degree differential equations with constant coefficients
=> Choose the Correct answer
=> Miscellaneous Problems
=> Summary

Chapter 5: Numerical Methods


=> Introduction
=> Finite Differences
=> Forward Difference Operator(∆)
=> Backward Difference operator(∇)
=> Shifting operator (E)
=> Relations between the operators Δ, ∇ and E
=> Finite Differences: Solved Example Problems
=> Finite Differences operators: Finding the missing terms
=> Exercise 5.1: Finite Differences
=> Interpolation
=> Methods of interpolation
=> Graphical and Algebraic method of Interpolation: Solved Example Problems
=> Lagrange’s interpolation formula
=> Exercise 5.2: Interpolation
=> Choose the correct Answer
=> Miscellaneous Problems
=> Summary

Chapter 6: Random Variable and Mathematical Expectation


=> Introduction
=> Random variable
=> Definition and Types of Random Variable
=> Discrete random variable
=> Continuous random variable
=> Exercise 6.1: Random variable
=> Mathematical Expectation
=> Expected value and Variance
=> Properties of Mathematical expectation
=> Mathematical Expectation: Solved Example Problems
=> Exercise 6.2: Mathematical Expectation
=> Choose the correct Answer
=> Miscellaneous Problems
=> Summary

Chapter 7: Probability Distributions


=> Introduction
=> Types of Theoretical distributions
=> Binomial distribution
=> Exercise 7.1: Binomial distribution
=> Poisson Distribution
=> Exercise 7.2: Poisson Distribution
=> Normal Distribution
=> Exercise 7.3: Normal Distribution
=> Choose the correct Answer
=> Miscellaneous Problems
=> Summary

Chapter 8: Sampling Techniques and Statistical Inference


=> Introduction
=> Basic concepts of sampling
=> Types of Random sampling or Probability sampling
=> Sampling and Non-Sampling Errors
=> Sampling distribution
=> Computing standard error in simple cases
=> Exercise 8.1: Sampling Techniques
=> Statistical Inference
=> Estimation
=> Point and Interval Estimation
=> Hypothesis Testing
=> statistical hypothesis: Null Hypothesis and Alternative Hypothesis, Level of Significants, Type of Errors
=> Testing Procedure : Large sample theory and test of significants for single mean
=> Hypothesis Testing: Solved Example Problems
=> Exercise 8.2: Statistical Inference
=> Choose the correct Answer
=> Miscellaneous Problems
=> Summary

Chapter 9: Applied Statistics


=> Introduction
=> Time Series Analysis
=> Meaning, Uses and Basic Components of Time Series Analysis
=> Measurements of Trends
=> Measurements of Trends: Freehand or Graphic Method
=> Measurements of Trends: Method of Semi-Averages
=> Measurements of Trends: Method of Moving Averages
=> Measurements of Trends: Method of Least Squares
=> Measurements of Trends: Methods of measuring Seasonal Variations By Simple Averages
=> Exercise 9.1: Time Series Analysis and Measurements of Trends
=> Index Number
=> Meaning, Classifications, Construction and Uses of Index Numbers
=> Weighted Index Number
=> Test of adequacy for an Index Number
=> Construction of Cost of Living Index Number
=> Exercise 9.2: Index Number
=> Statistical Quality Control (SQC)
=> Process Control and Product Control
=> Construction of X and R charts
=> Statistical Quality Control (SQC): Example Solved Problems
=> Exercise 9.3: Statistical Quality Control (SQC)
=> Choose the correct Answer
=> Miscellaneous Problems
=> Summary

Chapter 10: Operations Research


=> Introduction
=> Transportation Problem
=> Methods of finding initial Basic Feasible Solutions
=> Methods of finding initial Basic Feasible Solutions: North-West Corner Rule (NWC)
=> Methods of finding initial Basic Feasible Solutions: Least Cost Method (LCM)
=> Methods of finding initial Basic Feasible Solutions: Vogel’s Approximation Method(VAM)
=> Exercise 10.1: Transportation Problem
=> Assignment Problem
=> Definition and formulation of Assignment Problem
=> Solution of assignment problems (Hungarian Method)
=> Exercise 10.2: Assignment problems(Hungarian Method)
=> Decision Theory
=> Meaning of Decision Theory
=> Situations- Certainty and uncertainty
=> Decision Theory: Maximin and Minimax strategy
=> Exercise 10.3: Decision Theory
=> Choose the correct Answer
=> Miscellaneous Problems
=> Summary



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