- #1
m_s_a
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Homework Statement
Key in writing if possible f (z) with Onley z this mean We can get rid z bar be variable in terms of analytical
Is there a theory or conclude that Ithbt
Where was this idea
Or is the only conclusion
m_s_a said:[url=http://www.up07.com/up7][PLAIN]http://www.up07.com/up7/uploads/a8bbd62a7c.jpg[/url]
http://www.up07.com/up7/uploads/f733271dae.jpg
m_s_a said:[url=http://www.up07.com/up7][PLAIN]http://www.up07.com/up7/uploads/5f965970a0.jpg[/url][/PLAIN]
Dick said:Yes. It's general. d/d(zbar)=0 is the same thing as saying i*d/dx=d/dy using the chain rule for partial derivatives. If you apply that to f=u(x,y)+i*v(x,y) you get the Cauchy-Riemann equations.
Dick said:Basically ok. (n*i)^(1/2)=sqrt(n/2)+i*sqrt(n/2). Recheck the sqrt(5i). But remember to be careful how you define 'sqrt' or remember that every nonzero number has two different square roots.
Analytical functions, also known as window functions, are a type of function used in data analysis that operate on a set of rows and return a single result for each row. They are commonly used for tasks such as calculating running totals, ranking data, and finding moving averages.
Analytical functions and aggregate functions are both used for data analysis, but they differ in their scope. Aggregate functions operate on a set of rows and return a single result for the entire set, while analytical functions operate on a set of rows and return a result for each row.
The basic syntax for using analytical functions is:SELECT [function_name] OVER ([partition_clause] [order_clause] [windowing_clause]) FROM [table_name]
The partition clause specifies how the data is divided into groups, the order clause determines the order of the rows within each group, and the windowing clause specifies the range of rows to be included in the function's calculation.
Some common analytical functions include:
- ROW_NUMBER(): assigns a sequential integer to each row
- RANK(): assigns a rank to each row based on a specified criteria
- LAG() and LEAD(): retrieve data from a previous or subsequent row
- NTILE(): divides the rows into a specified number of groups
- SUM(), AVG(), MIN(), MAX(): calculate aggregate values over a specified window
Analytical functions allow for more complex and specific calculations to be performed on data compared to traditional aggregate functions. They also provide more flexibility in grouping and ordering data, making it easier to analyze trends and patterns. Additionally, analytical functions can help identify outliers and anomalies in data, leading to more accurate insights and decision making.