1. linear algebra: linear algebra is the basis of mathematical modeling, including matrix operation, vector space, eigenvalues and eigenvectors. This knowledge is very useful in solving practical problems, such as data analysis, image processing and signal processing.
2. Calculus: Calculus is a branch of mathematics that studies the rate of change and limit of functions, including derivatives, integrals and differential equations. In mathematical modeling, calculus is used to build a model, solve the optimal solution and analyze the stability of the system.
3. Probability theory and mathematical statistics: Probability theory and mathematical statistics are branches of mathematics that study the regularity of random phenomena, including probability distribution, hypothesis testing, regression analysis and time series analysis. In mathematical modeling, this knowledge is used to deal with uncertainty, risk assessment and prediction.
4. Optimization theory: Optimization theory is a mathematical method to find the optimal solution under certain conditions, including linear programming, nonlinear programming, integer programming and dynamic programming. In mathematical modeling, optimization theory is used to solve the problems of resource allocation, path planning and scheduling.
5. Numerical analysis: Numerical analysis is a branch of studying approximate solutions of mathematical problems by numerical methods, including numerical approximation, numerical integration and numerical differentiation. In mathematical modeling, numerical analysis is used to solve complex equations, interpolation and fitting.
6. Graph theory and network science: Graph theory and network science are branches of mathematics that study graph structure and network relations, including graph representation, shortest path, minimum spanning tree and network flow. In mathematical modeling, this knowledge is used to analyze the structure, communication and information dissemination of complex systems.
7. Discrete mathematics: Discrete mathematics is a branch of mathematics that studies discrete structures and their properties, including set theory, logic, combinatorial theory and graph theory. In mathematical modeling, discrete mathematics is used to describe discrete events, state transition and decision-making process.
8. Function approximation and spline interpolation: Function approximation and spline interpolation are methods to study how to approximate complex functions with simple functions, including polynomial interpolation, spline interpolation and wavelet transform. In mathematical modeling, this knowledge is used for data fitting, interpolation and signal processing.
9. Ordinary differential equations and partial differential equations: Ordinary differential equations and partial differential equations are branches of mathematics that study variables and their changing relationships, including initial value problems, boundary value problems and analytical solutions. In mathematical modeling, this knowledge is used to describe natural phenomena, dynamic systems and electromagnetic fields.
10. operational research: operational research is a branch of mathematics that studies decision-making problems, including linear programming, integer programming, nonlinear programming and dynamic programming. In mathematical modeling, operational research is used to solve the problems of resource allocation, path planning and scheduling.