Differential of the arc of a curve of double curvature.
Applications to the cycloid, the spiral of Archimedes, the logarithmic spiral, the curve whose normal, sub-normal, or tangent, is constant; the curve whose normal passes through a fixed point; the curve whose arc is proportional to the angle which it subtends at a given point.
Derivatives and differentials of different orders of functions of one variable. Notation adopted.
Remarks upon the singular points of plane curves.
Lessons 10–13. Derivatives and Differentials of Functions of Several Variables.
Partial derivatives and differentials of functions of several variables. The order in which two or any number of differentiations is effected does not influence the result.
Total differentials. Symbolical formula for representing the total differential of the nth order of a function of several independent variables.
Total differentials of different orders of a function; several dependent variables. Case where these variables are linear functions of the independent variables.
The infinitesimal increment of a function of several variables may in general be regarded as a linear function of the increments assigned to the variables. Exceptional cases.
Tangent and normal planes to curved surfaces.