Mathematical Modeling

Master the Art of Mathematical Modeling: Transform Complex Systems into Predictive Solutions

Mathematical modeling is a vital tool for you to understand how complex systems function and interact with their environment. By developing mathematical models, you can reveal insights that may not be easily observed through experimentation alone. These models enable you to predict system behavior, optimize performance, and design systems that respond efficiently to various inputs. Whether in engineering, biotech, finance, or other disciplines, mathematical modeling is crucial for detailed analysis, system optimization, and decision-making.

This course provides you with the knowledge and techniques needed to develop mathematical models for systems in various domains. It focuses on creating models from first physical principles, making it especially useful for engineers and engineering students. The course emphasizes structured methodologies applicable to systems of varying scales and complexities.

• Introduction to Mathematical Modeling: Learn the fundamentals of mathematical models, their purpose, and how they are used in various systems. Understand the differences between modeling from data and modeling from physical principles.
• Model Classification: Explore different types of models including static vs. dynamic, linear vs. non-linear, time-varying vs. time-invariant, and deterministic vs. stochastic models.
• First Principles Modeling: Gain hands-on experience in deriving small-scale mathematical models from first physical principles, such as the Bernoulli equation, spring-mass systems, linear electrical circuits, and dynamic pneumatic models for ventilated patients.
• Applications of Models: Discover how mathematical models are used for simulating system behavior, performing system analysis, designing optimized systems, and synthesizing complex structures.
• Complex Systems Modeling: Learn principles and methods for developing complex models, including model decomposition, component integration, and constraint management.
• Graph-based Modeling: Utilize graphs for modeling interconnected and networked systems, enhancing your ability to tackle complex system interactions.
• Real-world Examples: Study practical applications through examples such as models of oxygen transport in patients, dynamic models of truss structures, and wafer exposure models in lithography systems.

• Hands-on Learning: Gain practical experience in creating models for both simple and complex systems.
• Problem-Solving Skills: Enhance your ability to analyze and optimize systems in various fields, including engineering and biotech.
• Career Advancement: Equip yourself with essential skills in mathematical modeling that are highly valued across industries such as engineering, finance, healthcare, and technology.
• Structured Thinking: Develop the ability to break down complex problems, model their behavior, and optimize system parameters for better performance.