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English to Indonesian: Persamaan Bessel General field: Science Detailed field: Mathematics & Statistics
Source text - English 12. BESSEL'S EQUATION
This is (like Legendre's equation) another of the "named " equations which have been studied extensively and whose solutions you will find tabulated. There arc whole books on Bessel functions and almost any handbook or applied mathematics book will contain something about them (formulas and/or numerical tables). You can think of Bessel functions as being something like damped sines and cosines. In fact, if you had first learned about sin nx and cos nx as power series solutions of y" = n2y instead of in elementary trigonometry, you would not feel that Bessel functions were appreciably more difficult or strange than trigonometric functions. Like sines and cosines, Bessel functions are solutions of a differential equation; they are tabulated and their graphs can be drawn; they can be represented as series; and a large number of formulas involving them are known. Of special interest to science students is the fact that they occur in many applications. The following list of some of the problems in which they arise will give you an idea .of the great range of topics which may involve Bessel functions: problems in electricity, heat, hydrodynamics, elasticity, wave motion, etc., involving cylindrical symmetry (for this reason Bessel functions are sometimes called cylinder functions); the motion of a pendulum whose length increases steadily; the small oscillations of a flexible chain; railway transition curves; the stability of a vertical wire or beam; Fresnel integrals in optics; the current distribution in a conductor; Fourier series for the arc of a circle. We shall discuss some of these applications later.
Translation - Indonesian 12. PERSAMAAN BESSEL
Ini adalah (seperti persamaan Legendre) persamaan “bernama” lainnya yang telah dikaji secara luas dan yang memiliki penyelesaian yang akan Anda temui dalam keadaan telah tersusun. Ada satu buku yang khusus membahas fungsi Bessel dan hampir setiap buku pegangan atau buku matematika terapan akan memuat sesuatu tentangnya (rumus-rumus atau tabel-tabel numeriknya). Anda dapat membayangkan fungsi Bessel sebagai sesuatu seperti sinus dan cosinus teredam. Bahkan, jika Anda sebelumnya telah mempelajari tentang sin nx dan cos nx sebagai penyelesaian deret pangkat dari y” = n2y bukannya trigonometri dasar, Anda tidak akan merasa bahwa fungsi Bessel lumayan lebih sulit atau aneh daripada fungsi trigonometri. Seperti sinus dan cosiuns, fungsi Bessel adalah penyelesaian dari sebuah persamaan diferensial; mereka dihitung dan grafik mereka dapat digambar; mereka dapat direpresentasikan sebagai deret; dan sejumlah besar rumus yang melibatkan mereka telah dikenali. Salah satu minat khusus bagi mahasiswa sains adalah fakta bahwa mereka terjadi di banyak aplikasi. Daftar masalah berikut adalah apa yang timbul yang akan memberi Anda ide tentang luasnya jangkauan topik yang dapat melibatkan fungsi Bessel: masalah listrik, panas, hidrodinamika, elastisitas, gerakan gelombang, dll, yang melibatkan simetri silinder (untuk alasan inilah fungsi Bessel terkadang disebut fungsi silinder); gerakan pendulum yang panjangnya meningkat secara ajeg; osilasi kecil dari rantai fleksibel; kurva transisi kereta api; kestabilan kawat atau balok vertikal; integaral Fresnel dalam optik; perambatan arus dalam konduktor; deret Fourier untuk busur atau lingkaran. Kita akan membahas sebagian dari aplikasi tersebut nanti.
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Years of experience: 16. Registered at ProZ.com: Oct 2009.
I am a freelance translator and a physics teacher. I specialize on physics, mathematics, and natural science translations. You may contact me at any time.
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