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Volume 13 - Issue 191 - December 1927

Contents

Research Article

  • Term-by-Term Integration of Infinite Series

  • H. S. Carslaw
  • Published online by Cambridge University Press:
    03 November 2016, pp. 437-441

  • 1. The English student of Mathematics finds in his text-books a proof that the uniform convergence of a series of continuous functions is a sufficient condition for term-by-term integration. He knows that there are convergent series which cannot be integrated term-by-term,f and that there are series, not uniformly convergent in the interval of integration, which can be thus integrated. The last remark applies particularly to the Fourier’s Series of an ordinary function with discontinuities.

Other

Research Article

  • The Equation of Activity in Dynamics, and the Principle of Zero Activity in Statics.

  • H. R. Hassé
  • Published online by Cambridge University Press:
    03 November 2016, pp. 442-448

  • In spite of the great increase in the last fifteen years in the use of the Calculus in the higher forms of schools, and of its introduction into the Intermediate Examinations of many universities, it has not yet been used as much as it could be in the teaching of elementary Applied Mathematics.

    It has, of course, long been realised that in the kinematics of the motion of a particle in a straight line we have some of the best examples of the ideas that are the basis of the Calculus, and the notation and machinery of the Calculus is now extensively used in dealing with this part of the subject.

Other

Mathematical Notes

Reviews

Books Received

Front Matter

Back Matter