(1) A First Course in Higher Algebra (2) Problems in Dynamics (with Full Solutions) for the BA Students (Pass and Honours) of the Indian Universities

§ 1. The object of the present paper is to notice certain forms into which the series for the primary elliptic functions admit of being thrown, and to discuss the identical relations to which they give rise. These latter, it will be shown,. may be obtained directly by the aid of Fourier’s theorem, or in a less straightforward manner by ordinary algebra. § 2. Whenever we have a periodic function of x , say ψ x , such that ψ x =ψ( x+μ ), it is well known that we may assume, for all values of x , ψ x =A 0 +A 1 cos 2π x / μ +A 2 cos 4π x / μ +&c. +B 1 sin 2π x / μ +B 2 sin4π x / μ +&c.; and if ψ x be even, so that ψ x =ψ(‒ x ), then B 1 , B 2 , &c. all vanish; while if ψ x is uneven, so that ψ x =‒ψ(‒ x ), A 0 , A 1 , &c. vanish. If ψ x is such that ψ x =‒ψ( x + μ ), then we have ψ x =A 1 cos π x / μ +A 3 cos 3π x / μ + &c. or =B 1 sin π x / μ +B 3 ·sin 3π x / μ + &c., according as ψ x is even or uneven.

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Learn GCSE Maths on your Smartphone

10.20850/9781534202146 ◽

2017 ◽

Author(s):

Clive W. Humphris

Keyword(s):

Data Analysis ◽

Surface Area ◽

Linear Equations ◽

Personal Finance ◽

Algebra 1 ◽

Smartphone Apps ◽

Number Systems ◽

Algebra 2 ◽

Additional Charge

Learn GCSE Maths on your Smartphone - eBook covers all the topics of this popular software title used in schools and colleges worldwide for over twenty years and now available as PC, Tablet and Smartphone Apps. See Additional Notes at the back of the book for instructions to download the accompanying interactive App which brings the 250+ topics to life by allowing you to insert your own values. Visually on a phone or tablet it looks almost identical to the eBook content, except you can input your own values which update the graphics and calculations to reflect these changes. There is also a comprehensive PC version to download with even more features, both applications can be unlocked with your eBook purchase receipt for no additional charge. Education Bundle: eBook + PC software + App at a tiny fraction of the previously published price. Chapters (250 topics):- Number Systems, Number Conversion, Number Types, Compound Measures, Roots, Angles and Parallels, Triangle Ratios, Triangle Angles, Percentages, Ratios, Fractions, Vectors, Geometry, Circle Angles, Area, Surface Area and Symmetry, Volume, Laws, Algebra 0., Algebra 1., Algebra 2., Mathematical Rules, Powers and Indices, Simplifying, Linear Equations, Graphing, Slope and Translation, Curves and Angle Conversion, Personal Finance, Data Analysis ...

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