`   Regretfully I must agree with the first commenter.  Not only is the use of partial derivatives unnecessary, the author demonstrates a lack of understanding of what a derivative (of any kind)is -  ``alpha = (1/Lo) dL/dT where  is the original length,  the new length, and the temperature.``  In dL/dT or its partial equivalent L and T do not have the significance attributed to them. L and T are general concepts of length and temperature, not particular values of length and temperature.  Andrew Smith`