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"Annotation These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well asan overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions."

"Dalam tugas akhir ini dibahas tentang solusi dari persamaan differensial dalam bentuk khusus yang dinamakan fungsi Bessel spherical. Juga dibahas tentang aplikasi dari fungsi Bessel spherical yang berhubungan dengan bidang fisika yaitu partikel dalam sphere."

"This book offers a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. Includes nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts. Included in the presentation are, a section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter, thorough discussions of the analytical methods used to solve many types of integral equations, an introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations, over 80 illustrative examples that are explained in meticulous detail, nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts, and guides to computation to assist the student with particularly complicated algorithmic procedures."

"ABSTRAKSaat ini, semakin meningkatnya pembebanan dari beban non linier, membuat arus beban tidak lagi berbentuk gelombang sinus. Padahal idealnya bentuk gelombang tegangan dan arus adalah sinusoidal murni (smooth sine wave). Hal ini disebut harmonisa. Distorsi tegangan dan arus dapat menyebabkan kegagalan kerja sistem atau kegagalan kerja operasi peralatan disisi beban. Pada transformator, harmonisa dapat meningkatkan rugi-rugi beberapa diantaranya adalah arus RMS trafo menjadi lebih tinggi dari kapasitasnya, eddy current losses dan core losses.Dalam tesis ini dilakukan analisis hubungan THD (Total Harmonic Distortion) dengan rugi-rugi berbeban (Total Load Losses) transformator (PLL) dan Arus maksimum fasa (Imax) serta hubungan orde harmonic dominan dengan PLL dengan bantuan aplikasi Transformer Harmonic Analysis Program (THAP) yang dirancang-bangun menggunakan perangkat lunak Borland Delphi 7 Enterprise.THAP memiliki fungsi utama menghitung rugi-rugi berbeban transformator, derating kapasitas dan arus netral yang muncul karena adanya harmonisa. Selain ketiga fungsi utama tersebut, THAP juga dapat menghitung peningkatan rugi-rugi I2R (delta I2R), peningkatan rugi-rugi arus Eddy (delta PEC), k-factor, arus maksimum fasa (Imax) dan THD arus. THAP juga dapat menyajikan grafik spectrum arus harmonic tiap fasa dan tiap transformator yang dihitung, serta dapat menampilkan rincian hasil hitung dalam Microsoft excel.Pada proses validasi THAP, arus netral hasil hitung memiliki selisih sebesar 0,0528 ampere dengan hasil simulasi, sehingga memiliki kesalahan sebesar 0,04% dan sudutnya memiliki selisih 0,0110 sehingga memiliki kesalahan sekitar 0,02%. Untuk THD arus, THAP memiliki kesalahan rata-rata sebesar 6,2% terhadap hasil ukur. Pada analisis yang telah dilakukan, hubungan THD arus dengan PLL, THD arus dengan Imax, dan THD arus dengan Rasio PLL/Imax adalah polynomial dengan masing-masing memiliki nilai keandalan trend an tingkat akurasi ramalan persamaan yang dibuat sebesar 99,9 %, 99,7% dan 99,8%. Pada THD arus yang sama, arus harmonik yang dominan pada orde yang lebih tinggi memiliki nilai PLL yang lebih besar dibanding arus harmonik yang dominan pada orde yang lebih rendah.

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ABSTRACTNowadays, the increasing imposition of non-linear load, the load current is no longer made in the form of a sine wave. Though ideally the voltage and current waveforms are pure sinusoidal (smooth sine wave). It is called harmonics. Voltage and current distortion can cause a system failure or failure of labor work equipment operation load side. At transformer, harmonics can increase the losses some of which is the RMS current transformer becomes higher than its capacity, eddy current losses and core losses.In this thesis analyzes the relationship THD (Total Harmonic Distortion) with Total Load Losses transformer (PLL) and the maximum current phase (Imax) and the relationship the dominant harmonic order with PLL by Transformer Harmonic Analysis Program (THAP) application which is designed, built using the software Borland Delphi 7 Enterprise.THAP?s main functions are calculates transformer load losses, derating capacity and neutral currents that arise due to the presence of harmonics. In addition to the three main functions, THAP can also calculate the increase of I2R losses (delta I2R), eddy current losses (delta PEC), k-factor, the maximum current phase (Imax) and THD current. THAP also can present a spectrum graph of harmonic current of each phase and each transformer are calculated, and can display the details of the results calculated in Microsoft Excel.In the THAP validation process, neutral current calculated results have a difference of 0.0528 amperes with the simulation results, so it has an error of 0.04% and the angle has a difference of 0.0110 that has an error about 0.02%. For THD current, THAP has an average error of 6.2% of the measuring results. In the analysis that has been done, the relationship with the PLL current THD, THD current with PLL, and THD current the ratio of PLL / Imax is polynomial with each having a value of reliability and accuracy rate trend forecast equation is made of 99.9%, 99, 7% and 99.8%. At the same THD current, harmonic currents which are dominant in the higher-order has PLL value greater than the dominant harmonic currents in the lower order."

"Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, and other scientists an elementary level explanation of integral equations of the first kind. It maintains a casual, conversational approach. The book emphasizes understanding, while deliberately avoiding special methods of highly limited application."