MATH 141 Chapter Notes - Chapter 5: Fluid Dynamics, Antiderivative, Level Set
Document Summary
Harmonic functions appear regularly and play a fundamental role in math, physics and engineering. In this topic we"ll learn the de nition, some key properties and their tight connection to complex analysis. The key connection to 18. 04 is that both the real and imaginary parts of analytic functions are harmonic. We will see that this is a simple consequence of the cauchy-riemann equations. In the next topic we will look at some applications to hydrodynamics. We start by de ning harmonic functions and looking at some of their properties. A function (, ) is called harmonic if it is twice continuously di erentiable and satis es the following partial di erential equation: So a function is harmonic if it satis es laplace"s equation. The operator 2 is called the laplacian and 2 is called the laplacian of . Here"s a quick reminder on the use of the notation . 5. 3. 1 analytic functions have harmonic pieces and sine and cosine.
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