Steinharts-Hart equation: Calculating the coefficients marathon

[71GA]

Homework Statement:

I would like to calculate coefficients for the Steinharts-Hart equation but it is alarge system...

Relevant Equations:

Steinharts-Hart equation

I read about the Steinharts-Hart's equation here and I decided to try and calculate the four coefficients of the extended Steinharts-Hart's equation:

$$\frac{1}{T} = A + B \ln(R) + C \cdot (\ln(R))^2 + D\cdot (\ln(R))^3 $$

Where T is a temperature and R is a resistance of the e.g. NTC thermistor. On the supplied website it is written that:

Sometimes calculation of coefficients is done using special temperature values. Inserting four value pairs in the range of interest into the extended Steinhart-Hart poylonm leads to a system of linear algebraic equations (Three value pairs for the standard Steinhart-Hart polynom). Temperatures typically used are for example 0° C, 15° C, 25° C and 70° C. By solving this system the values for A, B, C and D can be determined.

Well I have chosen my NTC thermistor, found the documentation and took four of the temperature - resistance pairs. Then I tried to calculate the first coefficient, but it is a marathon (attachment)!

I would need someone to quick check for errors. I am not sure my substitutions were made corectly... Do you think I am even on the right track?

 

[71GA]

At this point I managed to calculate all the coefficients, but probably they are wrong. Here is the entire calculation. If anyone spots any errors please let me know.

 

[71GA]

As it turned out. Al lthe equations were correct, but I inputed the wrong numerical values in my calculator. At the end I inserted equatioins in C programming language and it calculated everything perfectly.