Course Description:
Mathematical Engineering is a multidisciplinary field that applies advanced mathematics to solve engineering, scientific, and technological problems. It combines deep theoretical knowledge with practical applications, often overlapping with fields such as control systems, optimization, computational mechanics, data science, and financial engineering.
Key Topics:
Focus Areas:
- Mathematical modeling of physical, biological, or engineered systems
- Analytical and numerical methods for solving complex equations
- Optimization and control theory
- Partial differential equations (PDEs) and finite element methods
- Stochastic processes and probability in engineering
- Data-driven modeling and machine learning
- Signal and image processing
- Computational science and simulations
Primary Reference Books:
- “Numerical Recipes” by Press et al.
- “Partial Differential Equations for Scientists and Engineers” by Stanley Farlow
- “An Introduction to Mathematical Modelling” by Edward A. Bender
- “Applied Linear Algebra” by Peter J. Olver and Chehrzad Shakiban
- “Engineering Optimization” by S.S. Rao
- “Stochastic Processes” by Sheldon Ross
- “Computational Science and Engineering” by Gilbert Strang
Typical Course Contents:
- Mathematical Modeling
- Translating real-world systems into mathematical equations
- Dimensional analysis, scaling, and assumptions
- Numerical Methods
- Solving linear/nonlinear systems
- Finite difference and finite element methods
- Iterative solvers and convergence analysis
- Differential Equations & Dynamical Systems
- ODEs, PDEs, and stability analysis
- Applications in heat transfer, fluid dynamics, mechanics
- Optimization Techniques
- Linear programming, nonlinear optimization
- Control and decision-making in engineering systems
- Probability and Stochastic Processes
- Random variables, Markov chains, Monte Carlo methods
- Applications in reliability and risk analysis
- Applied Linear Algebra
- Eigenvalue problems, matrix factorization
- Applications in mechanics, systems engineering, and robotics
- Machine Learning & Data Science (optional in modern programs)
- Regression, classification, neural networks
- Scientific computing with Python/MATLAB
