Mathematical Modeling Learning - Fundamentals (PPT Courseware)

This is a fundamental PPT courseware for learning mathematical modeling. The courseware aims to provide beginners with basic knowledge and theories of mathematical modeling. It covers fundamental concepts, steps, and methods of mathematical modeling, along with practical applications in real-world problems. Through this courseware, learners are expected to master basic mathematical modeling skills and establish a solid foundation for further study and research. Chapter 1: Building Mathematical Models.ppt This chapter introduces the fundamentals of constructing mathematical models, including techniques for translating real-world systems into mathematical representations through differential equations and algebraic formulations. Chapter 2: Elementary Models.ppt Covers basic modeling approaches using simple mathematical relationships, often implemented through linear equations and basic statistical methods in programming environments. Chapter 3: Simple Optimization Models.ppt Focuses on fundamental optimization techniques, including implementation with algorithms like gradient descent and linear programming methods using computational tools. Chapter 4: Mathematical Programming Models.ppt Explores advanced programming-based modeling approaches, featuring implementations of linear programming, integer programming, and constraint optimization using specialized libraries. Chapter 5: Differential Equation Models.ppt Demonstrates modeling dynamic systems through ordinary and partial differential equations, with numerical solution methods like Euler's method and Runge-Kutta implementations. Chapter 6: Stability Models.ppt Examines system stability analysis using eigenvalue computation and Lyapunov methods, featuring code implementations for stability criteria evaluation. Chapter 7: Difference Equation Models.ppt Covers discrete-time modeling approaches with difference equations, including recursive algorithms and time-series analysis implementations. Chapter 8: Discrete Models.ppt Focuses on non-continuous modeling techniques, featuring graph theory applications, combinatorial optimization, and discrete event simulation coding examples. Chapter 9: Probability Models.ppt Introduces probabilistic modeling approaches, including Monte Carlo simulations, stochastic processes, and statistical inference implementations with probability distributions.