Topics
Mathematical Logic
Matrices
Differentiation
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Inverse Functions
- Derivatives of Logarithmic Functions
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Second Order Derivative
- Overview of Differentiation
Applications of Derivatives
Integration
Definite Integration
Applications of Definite Integration
- Standard Forms of Parabola and Their Shapes
- Standard Forms of Ellipse
- Area Under Simple Curves
- Overview of Application of Definite Integration
Differential Equation and Applications
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equation by Eliminating Arbitary Constant
- Differential Equations with Variables Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
- Application of Differential Equations
- Overview of Differential Equations
Commission, Brokerage and Discount
- Commission and Brokerage Agent
- Concept of Discount
- Overview of Commission, Brokerage and Discount
Insurance and Annuity
- Insurance
- Types of Insurance
- Annuity
- Overview of Insurance and Annuity
Linear Regression
- Regression
- Types of Linear Regression
- Fitting Simple Linear Regression
- The Method of Least Squares
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Properties of Regression Coefficients
- Overview: Linear Regression
Time Series
- Introduction to Time Series
- Uses of Time Series Analysis
- Components of a Time Series
- Mathematical Models
- Measurement of Secular Trend
- Overview of Time Series
Index Numbers
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Overview of Index Numbers
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number
Linear Programming
- Introduction of Linear Programming
- Linear Programming Problem (L.P.P.)
- Mathematical Formulation of Linear Programming Problem
- Overview of Linear Programming
Assignment Problem and Sequencing
- Assignment Problem
- Hungarian Method of Solving Assignment Problem
- Special Cases of Assignment Problem
- Sequencing Problem
- Types of Sequencing Problem
- Finding an Optimal Sequence
- Overview of Assignment Problem and Sequencing
Probability Distributions
- Poisson Distribution
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
- Overview of Binomial Distribution
Estimated time: 7 minutes
Maharashtra State Board: Class 12
Definition: Time Series
A time series is a sequence of observations made on a variable at regular time intervals over a specified period of time.
Maharashtra State Board: Class 12
Key points: Components of Time Series
| No. | Component | Simple Definition |
|---|---|---|
| 1 | Secular Trend (T) | The long-term general direction in which the data moves over time. |
| 2 | Seasonal Variation (S) | Regular changes that repeat within a year. |
| 3 | Cyclical Variation (C) | Long-term up and down movements occur over several years. |
| 4 | Irregular Variation (I) | Sudden and unpredictable changes in data. |
Phases of Business Cycle:
-
Prosperity
-
Recession
-
Depression
-
Recovery
Maharashtra State Board: Class 12
Formula: Additive Model
\[X_t=T_t+S_t+C_t+I_t\]
Maharashtra State Board: Class 12
Formula: Multiplicative Model
\[X_t=T_t\times S_t\times C_t\times I_t\]
Maharashtra State Board: Class 12
Formula: Method of Moving Averages
First moving average:
\[\frac{X_1+X_2+\cdots+X_k}{k}\]
Second moving average:
\[\frac{X_2+X_3+\cdots+X_{k+1}}{k}\]
Maharashtra State Board: Class 12
Formula: Method of Least Squares
Linear Trend Equation:
\[X_t=a+bt\]
Normal Equations:
\[\sum X_t=na+b\sum t\]
\[\sum tX_t=a\sum t+b\sum t^2\]
