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
Definition: Assignment Problem
The assignment problem is a special type of problem which deals with the allocation of various resources to various activities on a one-to-one basis.
Key Points: Hungarian Method
The Hungarian Method is an optimisation algorithm that solves an Assignment Problem.
Step 1: Row Reduction
Step 2: Column Reduction
Step 3: Assignment
Step 4: Cover Zeros
Step 5: Create Additional Zeros
Definition: Unbalanced Assignment Problem
An unbalanced assignment problem is one in which the number of resources is not equal to the number of activities i.e. the cost matrix of an assignment problem is not a square matrix (no. of rows ≠ no. of columns).
Definition: Maximization Problem
A maximization assignment problem is an assignment problem in which the objective is to maximize total profit, revenue, or effectiveness instead of minimizing cost.
This conversion to a minimisation problem can be done in either of the following ways:
- Subtracting all elements of the matrix from the largest element in the matrix, or
- Multiplying all the elements of the matrix by -1.
Definition: Restricted Assignment Problem
An assignment problem involving restrictions on allocation due to personal, technical, legal or other reasons is called a restricted assignment problem.
Definition: Alternative Optimal Solution
An alternate (multiple) solution exists for an assignment problem when the final assignment matrix contains more than the required number of zeros.
Definition: Sequencing Problem
A sequencing problem is a problem in which the order or sequence of processing a set of jobs on one or more machines is to be determined so as to minimize the total processing time or overall completion time.
Key Points: Types of Sequencing Problems
- n jobs on 2 machines
-
n jobs on 3 machines
-
2 jobs on m machines
Definition: Total Elapsed Time
It is the time required to complete all the jobs, i.e. the entire task.
or
The total elapsed time is the time between the beginning of the first job on the first machine till the completion of the last job on the last machine.
Definition: Idle Time
Idle time is the time when a machine is available but not being used, i.e. the machine is available but is waiting for a job to be processed.
