Overview

This course provides a comprehensive introduction to mathematical modeling techniques, equipping students with essential skills to analyze and solve complex real-world problems using mathematical tools. It begins with foundational concepts, including power series, differential equations, and Laplace transforms, and gradually explores specialized topics such as Bessel functions, Legendre polynomials, and simulation models.The course delves into both theoretical and applied aspects, covering methods for solving differential equations, generating random numbers, and modeling deterministic and probabilistic systems. Additionally, students will engage in optimization modeling, learning linear programming methods including geometric and algebraic solutions, as well as the Simplex Method and sensitivity analysis. By the end of the course, students will be adept at applying mathematical modeling to a variety of disciplines, making it a valuable resource for further study or practical application in engineering, physics, economics, and beyond.

Syllabus

Weeks Weekly Lecture Topics (Module Titles) Assignment (No. & Type)*
1 Day 1 Introduction to Mathematical Modeling, Power series and related concepts 2 (Assignment, Quiz) Day 2 Ordinary and Singular Points 2 (Assignment, Quiz) Day 3 Power Series Solutions 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 2 Day 1 Power series solution of a differential equation about an ordinary point 2 (Assignment, Quiz) Day 2 Singular points and their classification 2 (Assignment, Quiz) Day 3 Power series solution about a singular point-Problems 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 3 Day 1 Solution of Bessel’s Equation 2 (Assignment, Quiz) Day 2 Bessel Function of the First and Second Kind 2 (Assignment, Quiz) Day 3 Differential Equations Solvable in Terms of Bessel Functions 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 4 Day 1 Modified Bessel Functions 2 (Assignment, Quiz) Day 2 Solution of Legendre’ s Equation 2 (Assignment, Quiz) Day 3 Legendre Polynomials 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 5 Day 1 Laplace Transform 2 (Assignment, Quiz) Day 2 Linearity of the Laplace Transform 2 (Assignment, Quiz) Day 3 Sufficient Conditions for Existence of Laplace transform of functions 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 6 Day 1 Inverse Transforms 2 (Assignment, Quiz) Day 2 Partial Fractions - Distinct Linear Factors 2 (Assignment, Quiz) Day 3 Transforms of a Derivatives 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 7 Day 1 Solving a Second-Order IVP using Laplace transform method 2 (Assignment, Quiz) Day 2 Simulation Modeling-Simulating Deterministic Behavior- Area Under a Curve 2 (Assignment, Quiz) Day 3 Simulating Deterministic Behavior-Volume Under a Surface 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 8 Day 1 Simulation Modeling- Problems 2 (Assignment, Quiz) Day 2 Generating Random Numbers-Middle Square Method 2 (Assignment, Quiz) Day 3 Generating Random Numbers-Linear Congruence 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 9 Day 1 Generating Random Numbers-Problems 2 (Assignment, Quiz) Day 2 Queuing Models 2 (Assignment, Quiz) Day 3 Queuing Models-Harbor System 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 10 Day 1 Queuing Models - Morning Rush Hour 2 (Assignment, Quiz) Day 2 Optimization Modeling - An overview 2 (Assignment, Quiz) Day 3 Optimization Modeling-Problems 1 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 11 Day 1 Optimization Modeling-Problems 2 2 (Assignment, Quiz) Day 2 Linear Programming-Geometric Solutions 2 (Assignment, Quiz) Day 3 Linear Programming-Geometric Solutions Problems 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 12 Day 1 Linear Programming-Algebraic Solutions 2 (Assignment, Quiz) Day 2 The Simplex Method 2 (Assignment, Quiz) Day 3 The Simplex Method-Example 1 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments. 13 Day 1 The Simplex Method-Example 2&3 2 (Assignment, Quiz) Day 2 Linear Programming- Sensitivity Analysis 2 (Assignment, Quiz) Day 3 Sensitivity Analysis: Changes in the Amount of Resource Available and Economic Interpretation 1 2 (Assignment, Quiz) Day 4 Interaction based on the topics covered. Day 5 Deadline for submitting assignments.
14 Day 1 Sensitivity Analysis: Changes in the Amount of Resource Available and Economic Interpretation II 2 (Assignment, Quiz) Day 2 Revision Day 3 Revision Day 4 Revision Day 5 Revision