Lec 15 | MIT 18.02 Multivariable Calculus, Fall 2007

Lecture 15: Partial differential equations; review.

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Tags:

• calculus
• vector-algebra
• determinants
• matrix
• matrices
• vector-valued-function
• space-motion
• scalar-function
• partial-differentiation
• gradient
• optimization-techniques
• double-integrals
• line-integrals
• exact-differential
• conservative-fields
• Green's-theorem
• triple-integrals
• surface-integrals
• applications

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[muslim86mus]

@mariomaruf Well, you should've mentioned that you didn't really know earlier....

Yes, they're related only by definition.

In fact, not only is a GS of a linear PDE often difficult to obtain, it also is usually not all tht useful in applications.

Simply put, we're more interested in finding PS of PDEs that generally appear in mathematical physics involving boundary-value (BV) problems as compared to ODEs.

Oh yeah, Orthogonal Expansions & Fourier series are indeed prerequisite topics for PDEs...

[mariomaruf]

@muslim86mus Are partial derivatives related to PDEs in the same way that derivatives are related to ODEs? I know about a semester's worth about ODEs, and so I assumed that the relation between derivatives and ODEs was the same as with partial derivatives and PDEs. I don't really know anything about PDEs though.