Judul: Planning of Rainwater Reservoir as a Water Supply Alternative of Guest House Unit Bogor Barat Agrohills, Planning of Rainwater Reservoir as a Water Supply Alternative of Guest House Unit Bogor Barat Agrohills
Abstrak: Bogor Barat Agrohills terletak di Kabupaten Bogor dengan curah hujan 3619,34 mm/tahun. Kebutuhan air bersih di Bogor Barat Agrohills direncanakan bersumber dari sumur bor. Bogor Barat Agrohills yang direncanakan sebagai kawasan eduwisata memerlukan adanya alternatif lain yang ramah lingkungan untuk memenuhi kebutuhan air sehari-hari. Salah satu strategi yang dapat diterapkan adalah dengan menampung air hujan. Penelitian dari bulan Mei hingga Agustus 2022 ini bertujuan merencanakan sistem penampungan air hujan untuk alternatif penyediaan air bersih di Guest House Bogor Barat Agrohills. Analisis untuk perencanaan penampungan air hujan menggunakan data curah hujan tahun 2012 hingga 2021. Desain bak penampung menggunakan data curah hujan andalan maksimum pada bulan Maret sebagai batasan dalam perencanaan dengan curah hujan bulanan sebesar 705,3 mm. Total air yang dapat ditampung sebesar 4,40 m3 /hari. Ketersediaan air ini mampu memenuhi kebutuhan air bersih untuk dua unit Guest House yaitu sebesar 1,8 m3 /hari. Dimensi bak penampung air hujan berdasarkan perhitungan neraca air direncanakan memiliki panjang 5 m, lebar 5 m, dan tinggi 3,6 m dengan kapasitas tampungan sebesar 90 m3 . Total rencana anggaran biaya pembuatannya sebesar Rp110.814.500., Bogor Barat Agrohills is located in Bogor district with rainfall of 3619.34 mm/year. The need for clean water in the Bogor Barat Agrohills Guest House area is planned to be sourced from drilled wells. As an edutourism area, it is necessary to have other environmentally friendly alternatives to meet daily water needs. One of the strategy that can be applied is rainwater storage. This study, conducted in May until August 2022, aimed to plan a rainwater collecting system as an alternative to increase clean water availability at the Bogor Barat Agrohills Guest House. The design analysis of rainwater storage was conducted using rainfall data from 2012 to 2021. As a limitation in the design of the storage, the rainfall data used was the maximum reliable rainfall data in March with a monthly rainfall of 705.3 mm. The total water supply that could be accommodated was 4.40 m3 /day. The water availability of 1.8 m3 /day, is able to meet the clean water demand for two Guest House units. The dimensions of the rainwater storage based on the water balance calculation were planned with length of 5 m, width of 5 m, and height of 3.6 m with a storage capacity of 90 m3 . The total planned budget needed was IDR110,814,500.
Keyword: planned budget, rainwater storage, rainfall, water demand

Judul: Perencanaan Sumur Resapan dan Kolam Retensi di Bogor Barat Agrohills Kabupaten Bogor
Abstrak: Bogor Barat Agrohills adalah proyek kaveling berkonsep eduwisata di Kecamatan Leuwisadeng Kabupaten Bogor. Saat ini pemerintah berupaya untuk menyimpan air sebanyak mungkin ke dalam tanah dan berusaha untuk mencapai zero runoff. Sejalan dengan itu maka penelitian bertujuan merencanakan sumur resapan dan kolam retensi di Bogor Barat Agrohills. Dari hasil analisis diperoleh nilai permeabilitas tanah di lokasi tidak memenuhi syarat SNI 03-2453-2002 sehingga direncanakan hanya pembuatan kolam retensi. Dari analisis curah hujan dengan metode Gumbel, diperoleh curah hujan rencana sebesar 147,9 mm untuk periode ulang 5 tahun. Dari hasil pengamatan diperoleh 4 daerah tangkapan air (DTA) dan nilai koefisien limpasan gabungan sebesar 0,32. Kolam retensi direncanakan memiliki 3 tipe dan berjumlah satu buah di tiap DTA. Tipe 1 memiliki panjang 10,0 m dan lebar 6,7 m. Tipe 2 memiliki panjang 8,6 m dan lebar 5,8 m. Tipe 3 memiliki panjang 6,4 m dan lebar 4,3 m. Ketiga tipe kolam memilki kedalaman 4 m. Lokasi kolam retensi direncanakan di dekat outlet setiap DTA. Kolam tipe 1 berjumlah dua buah sedangkan kolam tipe 2 dan tipe 3 masing - masing satu buah. Biaya pembuatan kolam retensi tipe 1 (2 buah kolam) sebesar Rp159.620.000,00, tipe 2 sebesar Rp68.310.000,00, dan tipe 3 sebesar Rp52.150.000,00., Bogor Barat Agrohills is a land plot project with an edutourism concept in Leuwisadeng District, Bogor Regency. Currently the government is trying to store as much water as possible into the ground and to achieve zero runoff. Accordingly, this study aims to plan infiltration wells and retention ponds in Bogor Barat Agrohills. From the results of the analysis, the permeability value of the soil at the location does not meet the SNI 03-2453-2002 requirements, so only retention ponds were planned. From the rainfall analysis using the Gumbel method, a design rainfall was 147.9 mm for the 5-year return period. From the observations were obtained 4 water catchment areas and a combined runoff coefficient value of 0,32. Three types of retention ponds were planned and one pond in each catchment area. Type 1 had dimention of 10,0 m long and 6,7 m wide and type 2 had 8,6 m long and 5,8 m wide, while type 3 had 6,4 m long and 4,3 m wide. The three types of ponds had a depth of 4 m. The location of the retention ponds were planned near the outlet of each DTA. There were two ponds of type 1 pond and one each of type 2 and type 3 ponds. The construstion cost of retention pond type 1 (2 ponds) was IDR159.620.000.00, type 2 was ID68.310.000.00, and type 3 was IDR52.150.000.00.
Keyword: permeability, runoff coefficient, runoff volume

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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