9.14.3 Can you answer these questions?

9.14.3.1 Efficiently threading with a default value for missing parts / defining custom behavior for addition of expressions with a given head
9.14.3.2 How to speedup the integration of a tabulated function?
9.14.3.3 Insight into coupled pair of complex equations
9.14.3.1 Efficiently threading with a default value for missing parts / defining custom behavior for addition of expressions with a given head

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=283958

In short, I would like to be able to "add" expressions with a particular head (call it  h  for our purposes) which will always appear with a sequence of (... 
[functions] [performance-tuning] [function-construction] [customization]
 
asked by max https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=92409 Score of 3
9.14.3.2 How to speedup the integration of a tabulated function?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=283863

The problem 
Consider some pre-generated  list  with coordinates  x1,x2,x3,x4  and values of some function ... 
[numerical-integration] [performance-tuning] [interpolation] [compile] [system-performance]
                                                                                  

                                                                                  
 
asked by John Taylor https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=41058 Score of 1
answered by Roland F https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=92018 Score of 0
9.14.3.3 Insight into coupled pair of complex equations

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=283900

I have two complex functions $Z_1 = \frac{1}{\alpha_1 -i(Z_2 - \alpha_2)}$ and $Z_2=\frac{i Z_1^2}{ \beta_1 + i\beta_2}$, where $\alpha_1, \alpha_2, \beta_1, \beta_2$ all lie between $0$ and $1$. How ... 
[plotting] [equation-solving] [complex]
 
asked by Zubin https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=80852 Score of 2
answered by Daniel Huber https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=46318 Score of 0