Judul: Trench Dam Design for water needs of Permanent  Nursery IPB Dramaga University
Abstrak: Dam parit sebagai salah satu teknologi panen hujan dan aliran permukaan (rainfall and runoff harvesting) dapat memanen air hujan dan aliran permukaan sebagai dampak dari tidak meratanya curah hujan untuk setiap musim. Dam parit berfungsi dalam menahan dan membendung aliran air pada suatu aliran sungai/parit sehingga diperoleh cadangan air yang dapat dimanfaatkan untuk memenuhi kebutuhan irigasi sepanjang musim kemarau. Perencanaan dam parit bertujuan untuk memenuhi kebutuhan air pada Persemaian Permanen, Kampus IPB Dramaga. Prosedur kerja meliputi studi literatur, pengumpulan data primer dan sekunder, pengolahan data, dan perencanaan dimensi, analisis stabilitas, pembuatan gambar teknik dan perhitungan RAB. Debit banjir rencana dihitung menggunakan metode Haspers dan metode Passing Capacity. Dam parit direncanakan dari pasangan beton dengan tinggi bendung sebesar 2,1 m, jari-jari mercu bendung sebesar 0,44 m dan lebar bendung 7,825 m, panjang kolam loncat air sebesar 4,11 m. Dam parit memiliki keamanan terhadap kebutuhan stabilitas yang menjadi penyebab runtuhnya bangunan gravitasi yaitu geser (sliding), guling (overturning), dan erosi bawah tanah (piping). Rancangan Anggaran Biaya (RAB) yang dibutuhkan dalam konstruksi dam parit pada Persemaian Permanen IPB dramaga sebesar Rp. 342.000.000,00 (tiga ratus empat puluh dua juta rupiah)., Trench dam as rain and runoff harvesting technology can harvest rainwater and runoff as a result of the uneven rainfall for each season. Trench dam function to hold and stem the flow of water in a river/trough in order to obtain water reserves that can be used to meet irrigation needs throughout the dry season. The planning of the trench dam aims to meet the water needs of the Permanent Nursery, Dramaga Campus of IPB. Work procedures include literature study, primary and secondary data collection, data processing and dimensional planning, stability analysis, engineering drawings and cost budget design calculations. The planned flood discharge calculated by the Haspers method and the Passing Capacity method. The trench dam is planned from concrete pairs with a weir height of 2,1 m, a radius of dam crest of 0,44 m and a weir width of 7,825 m, a jump pool length of 4,11 m. The trench dam has safety against the need for stability that causes the collapse of gravity buildings, namely sliding, overturning, and underground erosion (piping). The Draft Budget (RAB) required for the construction of the trench dam in the Dramaga IPB Permanent Nursery is Rp. 342.000.000,00 (three hundred and forty two million rupiah).
Keyword: Design, Stability, Trench dam, Water

Judul: Karakteristik Hidrolika Dam Parit untuk Ketersediaan Air Persemaian Permanen Dramaga
Abstrak: Sebelum pembangunan dam parit, perlu adanya analisis karakteristik hidrolika, mengetahui debit yang tersedia pada parit dan diharapkan air yang tersedia pada parit dapat dimanfaatkan dalam pemenuhan irigasi Persemaian Permanen Dramaga baik pada musim hujan maupun musim. Data hujan diolah untuk menentukan nilai curah hujan rencana dengan metode Weibull dan metode Gumbel. Hasil dari Cubic Spline Interpolation didapatkan karakteristik hidrolika yaitu luas penampang basah 16,83 m2, keliling basah 12,05 m, jari-jari hidrolika 1,4 m, slope parit sebesar 0,0001, kekerasan manning 0,04, diperoleh rating curve Q = 0,1653 H2,8884 dan debit banjir rencana yaitu 5,38 m3/detik. Debit minimum yang cuaca cerah 0,04 l/detik. Debit maksimum pada saat hujan 5,03 l/detik. Dam parit direncanakan memiliki volume tampungan efektif sebesar 39,5 m3, luas 10,8 m2 pada elevasi 2,1 m. Kebutuhan air irigasi dengan Kc rata-rata 0,8 untuk mengairi lahan seluas 0,6 ha adalah 0,07 l/detik atau sekitar 6,2 m3/hari. Dengan volume efektif 39,5 m3 dan debit masukan 0,04 l/detik, mengalami defisit air sebesar 0,03 l/detik atau setara dengan 2,6 m3/hari. Dengan dibangunnya dam parit diharapkan akan menampung kelebihan air pada saat hujan agar terpenuhinya kebutuhan air tanaman saat musim kemarau., Before constructing a ditch dam, it is necessary to conduct an analysis of hydraulic characteristics, determine the available discharge in the ditch and it is hoped that the water available in the ditch can be used to fulfill the irrigation of the Dramaga Permanent Nursery in both the rainy and dry seasons. Rain data is processed to determine the value of the planned rainfall using the Weibull method and the Gumbel method. The results of Cubic Spline Interpolation are obtained hydraulic characteristics, namely wet cross-sectional area of 16.83 m2, wet cross-sectional area 12.05 m, hydraulic radius 1.4 m, trench slope 0.00038, manning hardness 0.04, obtained rating curve Q = 0.1653 H2.8884 and the design flood discharge is 5.38 m3/s. The minimum discharge in sunny weather is 0.04 l/s. The maximum discharge when it rains is 5.03 l/s. The trench dam is planned to have an effective storage volume of 39.5 m3, an area of 10.8 m2 at an elevation of 2.1 m. The need for irrigation water with an average Kc of 0.8 to irrigate an area of 0.6 ha is 0.07 l/s or about 6.2 m3/day. With an effective volume of 39.5 m3 and an input discharge of 0.04 l/second, it has a water deficit of 0.03 l/s or equivalent to 2.6 m3/day. With the construction of the trench dam, it is hoped that it will be able to accommodate excess water when it rains so that the plant's water needs are met during the dry season.
Keyword: Hydraulics, nurseries, trench dam, water availability

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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