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What math subject comes after partial differential equations for physics and electrical engineering majors?
Success said:So next is complex analysis? Is that pure math or applied math?
Partial differential equations (PDEs) are mathematical equations that involve multiple independent variables, and their derivatives, to describe the relationships between different quantities. They are commonly used in physics, engineering, and other scientific fields to model and solve problems involving continuous systems.
The main difference between partial differential equations and ordinary differential equations is the number of independent variables involved. In partial differential equations, there are multiple independent variables, while in ordinary differential equations, there is only one independent variable. This means that PDEs are used to describe systems that vary in space and time, while ODEs are used for systems that only vary in time.
Partial differential equations have a wide range of applications in the real world, including modeling heat transfer, fluid dynamics, electromagnetism, and quantum mechanics. They are also used in finance to model stock prices and in biology to model population growth.
There are various methods for solving partial differential equations, including analytical methods, numerical methods, and computer simulations. Analytical methods involve finding exact solutions using mathematical techniques, while numerical methods use algorithms to approximate solutions. Computer simulations use software to solve PDEs and visualize the results.
Some common challenges in solving partial differential equations include dealing with complex boundary conditions, finding appropriate numerical methods for accurate solutions, and handling high-dimensional problems. PDEs can also be difficult to solve analytically, requiring advanced mathematical techniques and specialized knowledge in the specific field of application.