Topics
Mathematical Logic
Matrices
Differentiation
- Derivative of Composite Functions
- Derivative of Inverse Function
- 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
- Ellipse and its Types
- 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
- Equations in Variable Separable Form
- Homogeneous Differential Equations
- Linear Differential Equations
- Applications of Differential Equation
- 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
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
Estimated time: 4 minutes
- Simple curves: lines, parabolas, polynomial functions
Maharashtra State Board: Class 12
Key Points: Area Under Simple Curves
- \[\mathrm{A}=\int_{x=a}^{x=b}y\mathrm{d}x=\int_{a}^{b}\mathrm{f}(x)\mathrm{d}x\]
- If below x-axis → use |f(x)|
- Area w.r.t. Y-axis →\[\mathrm{A}=\int_{y=c}^{y=d}x\mathrm{d}y=\int_{c}^{d}\mathrm{f}(y)\mathrm{d}y\]
- If the curve crosses the axis → split the interval
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