2AEPC201
Mathematical Modeling and Problem Solving
Teaching - Learning Scheme :
02 Hours Lectures/Week
01 Hour Tutorial/Week
03 Credits
Assessment Scheme :
In-Semester Evaluation (ISE) : 40 % Weightage
Mid-Semester Evaluation (MSE) : 30 % Weightage
End-Semester Evaluation (ESE) : 30 % Weightage
Course Objectives
1. Introduce the use of mathematics for solving engineering problems
2. Make them aware of mathematical modelling and problem-solving techniques
3. Make them aware of mathematical modelling and problem-solving techniques
Course Outcomes
1. Identify and define real-world problems that can be modelled mathematically
2. Choose appropriate mathematical tools and techniques to model real-world problems
3. Apply and interpret the results of mathematical tools to validate/justify the results
4. Present and communicate the results of mathematical modelling and problem-solving by using Modern Tools
5. Use mathematical modelling to solve problems in the discipline of Aeronautical engineering
Course Contents
Capsule I
Unit 1 : Introduction to Mathematical Modeling
Models and Reality, assumptions in mathematical modeling
Steps/Stages in mathematical modeling
Conversion of a real world problem to equivalent mathematical model
Mathematical tools and techniques
Unit 2 : Graphical Methods for Problem Solving
Introduction to use of graphical methods for problem solving
Linear programming problems
Optimization problems with two variables
Unit 3 : Numerical Methods for Problem Solving
Basic concepts of numerical methods
Rounding errors, Truncation errors and Convergence
Numerical Integration Technique's
Numerical Differentiation Technique's
Numerical solutions to linear system of equations and optimization problems
Capsule II
Unit 4 : Dimensional Analysis
Physical quantities, their units and dimensions
Applications of dimensional analysis
Rayleigh's methods
Buckingham Pi theorem
Unit 5 : Statistical Analysis
Applications of statistical analysis
Steps in using statistical analysis to solve problems
Regression analysis
Time series analysis
Cluster analysis
Unit 6 : Introduction to Optimization
Key concepts of optimization
Classical Optimization methods
Linear programming method
Gradient descent method
Newton's method
In-Semester Evaluation (ISE) Policy
Activity Based Assessment (ABA): 20 Marks
Activity 1 : Group Discussion and Presentation (Team Activity)
Identifying real world engineering problems that can be mathematically modeled
Due Date: 30 September 2023
Activity 2 : Quiz Competition (Individual Activity)
Mathematical Tools and Techniques
Due Date: 20 October 2023
Activity 3 : Programming Assignment (Individual Activity)
Mathematical modeling and problem solving using Python programming language
Due Date: 24 November 2023
Activity 4 : Micro Project (Team Activity)
Application of mathematical modeling to solve problems related to Aeronautical Engineering
Due Date: 05 January 2024
Continuous Assessment (CAS): 20 Marks
Active participation in classroom and tutorial discussions
Solving and Submission of Tutorial Exercises
Presentation of CAS Portfolio built during the course
Mid & End Semester Evaluation (MSE & ESE) Policy
30 October - 03 November 2023
Course Contents : Unit 1 - 3
Maximum Marks : 50
Time Duration : 02 Hours
08 - 15 January 2024
Course Contents : Unit 4 - 6
Maximum Marks : 50
Time Duration : 02 Hours
Reference Books
