How to find the derivative of f(x) for a basic problem?

Thread starter jimit shah
Start date Sep 8, 2012
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In summary, partial differential equations (PDEs) have many applications in various fields and are used to model and analyze complex phenomena. They differ from ordinary differential equations (ODEs) in that they involve multiple independent variables and often require numerical methods for solving. Some common methods for solving PDEs include separation of variables, Fourier series and transforms, finite difference methods, and finite element methods. PDEs are used in real-world applications such as disease spread, weather prediction, and engineering design, but solving them can be challenging due to their complexity and the need for numerical methods. The accuracy of the solution can also be affected by the choice of boundary conditions and initial conditions.

Sep 8, 2012

jimit shah

find the valu of local extremum for f(x)=sin x-cos x,0<x<2∏.

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Sep 8, 2012

HallsofIvy

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Kind of a basic problem isn't it? Can you find the derivative of f(x)?

Looks like homework to me so I am going to move it.

I will also point out that, because there is only the single independent variable, x, there is NO "partial differentiation" here.

FAQ: How to find the derivative of f(x) for a basic problem?

What is the application of partial differential equations (PDEs)?

PDEs have many applications in a variety of fields, including physics, engineering, economics, and biology. They are used to model and analyze complex phenomena such as heat transfer, fluid dynamics, and population growth. PDEs are also essential in the development of mathematical models for predicting and simulating real-world systems.

How do partial differential equations differ from ordinary differential equations (ODEs)?

While ODEs involve only one independent variable, PDEs involve multiple independent variables, making them more complex to solve. PDEs also have a wider range of solutions, including functions of multiple variables, rather than just a single function as in ODEs. Additionally, PDEs often require numerical or computational methods for solving, whereas many ODEs have analytical solutions.

What are some common methods for solving partial differential equations?

Some common methods for solving PDEs include the method of separation of variables, Fourier series and transforms, finite difference methods, and finite element methods. The choice of method depends on the type of PDE and the boundary conditions of the problem.

What are some real-world examples of partial differential equations?

PDEs are used in a wide range of real-world applications, some examples include modeling the spread of diseases, predicting weather patterns, analyzing financial markets, designing aircraft and car engines, and understanding the behavior of fluids in pipes and channels.

What are the challenges in solving partial differential equations?

Solving PDEs can be challenging due to their complexity and the wide range of possible solutions. In many cases, analytical solutions are not feasible, and numerical methods must be used, which can be time-consuming and computationally expensive. Additionally, the choice of boundary conditions and initial conditions can greatly affect the accuracy of the solution.