Judul: Product Development of Herbal Ginger Syrup
Abstrak: Jahe merupakan komoditas rempah-rempah yang banyak dikonsumsi dan diketahui manfaatnya, sehingga berpotensi untuk dikembangkan baik dalam pembuatan produk makanan maupun minuman. Selain komponen bahan aktif minyak atsiri, jahe juga memiliki kandungan pati berkisar 45-55% dari bobot rimpang kering. Dalam pembuatan minuman herbal, pati merupakan hasil samping dalam proses ekstraksi bahan aktif. Penelitian ini bertujuan untuk memanfaatkan kandungan pati dengan bantuan enzim alfa amilase serta meningkatkan penerimaan konsumen dengan penambahan rempah-rempah. Metode yang digunakan adalah Human Centered Design (HCD) yang diawali dari identifikasi masalah, verifikasi masalah, ideasi, prototipe, dan verifikasi solusi. Hasil observasi terhadap produk komersial menunjukkan tingkat rasa pedas terbilang rendah dibandingkan tingkat rasa manis pada produk. Prototyping sirup jahe merah dilakukan sebanyak 3 kali. Prototype 1 berdasarkan hasil uji organoleptik sudah menunjukkan beberapa parameter telah sesuai preferensi konsumen, namun masih terdapat beberapa parameter yang perlu diperbaiki. Selain itu, prototype 1 memiliki konsistensi yang kental dan berkabut, terdapat sedikit after-taste pahit, serta setelah disimpan di kulkas selama 24 jam produk membentuk gumpalan keras seperti gel. Prototype 2 telah memiliki konsistensi yang baik, namun rasa pahit yang dihasilkan masih terdeteksi. Hasil uji organoleptik prototype 3 menunjukkan tingkat rasa pedas dan rasa manis telah sesuai dengan preferensi konsumen dengan aroma yang lebih wangi dan manis. Formulasi terpilih sirup jahe merah menggunakan 250 g jahe merah, 125 g gula kristal, 500 g air, dan 35 g rempah-rempah., Product Development of Herbal Ginger Syrup. Supervised by TITI CANDRA SUNARTI. Ginger is a spice commodity that is widely consumed and its benefits are known, so it has the potential to be developed both in the manufacture of food and beverage products. In addition to the active ingredient components of essential oils, ginger also has a starch content ranging from 45-55% of the dry rhizome weight. In the manufacture of herbal drinks, starch is a by-product in the process of extracting the active ingredients. This study aims to utilize the starch content with the help of the enzyme alpha amylase and increase consumer acceptance with the addition of spices. The method used is Human Centered Design (HCD) which begins with problem identification, problem verification, ideation, prototype, and solution verification. The results of observations on commercial products show that the level of spicy taste is relatively low compared to the level of sweetness in the product. The red ginger syrup prototype was carried out 3 times. Prototype 1 based on the results of organoleptic tests has shown that several parameters are in accordance with consumer preferences, but there are still some parameters that need to be improved. In addition, prototype 1 has a thick and cloudy consistency, there is a slight bitter after-taste, and after being stored in the refrigerator for 24 hours the product forms hard lumps like gel. Prototype 2 already has a good consistency, but the resulting bitter taste is still detectable. The results of the organoleptic test of prototype 3 show that the level of spicy and sweet taste is in accordance with consumer preferences with a more fragrant and sweet aroma. The selected formulation of red ginger syrup uses 250 g of red ginger,
Keyword: alpha amylase, red ginger, starch, low sugar, red ginger syrup

Judul: Product Development of Low Sugar Instant Red Ginger in the Shape of Cube
Abstrak: Jahe merah instan merupakan salah satu minuman herbal yang sering dikonsumsi, namun seringkali jumlah gula tidak sebanding dengan jahe merah yang digunakan. Bentuk serbuk juga tidak efektif untuk menakar jumlah pemakaian ketika digunakan oleh konsumen. Untuk itu, penelitian ini bertujuan untuk mengembangkan produk cube jahe merah instan serta menentukan formulasi terbaik. Metode yang digunakan yaitu iterasi prototype melalui prototyping dan akan dihentikan saat terbentuk prototype terbaik. Prototype 1 memiliki kekurangan berupa waktu kelarutan yang tinggi. Dilanjutkan dengan prototype 2 yang memiliki kekurangan berupa rasa yang terlalu pedas dan terdapat after-taste pahit. Dilanjutkan dengan prototype 3 memiliki warna dan rasa pedas yang sama pekat dengan prototype 2 namun dengan aroma yang lebih wangi dan rasa yang lebih manis serta waktu kelarutan yang rendah, sehingga prototype 3 terpilih menjadi formula terbaik. Prototype 3 menggunakan 250 g jahe merah, 125 g gula pasir, 500 g air, serta 35 g rempah-rempah. Total gula yang terkandung dalam prototype 3 sebesar 33,82% dengan waktu kelarutan sebesar 34 detik. Hasil uji organoleptik menunjukan prototype 3 memiliki rasa manis dan rasa pedas yang paling dapat dinikmati oleh panelis, Instant red ginger is one of the herbal drinks that are often consumed, but the amount of sugar is often not comparable to the red ginger. The powder form is also not effective when used by consumers. For this reason, this study aims to develop instant red ginger cube products and determine the best formulation. The method is prototype iteration through prototyping and will be stopped when the best prototype is formed. Prototype 1 has a disadvantage in the form of a high solubility time. They were followed by prototype 2 which has the disadvantage of being too spicy and has a bitter after-taste. This was followed by prototype 3 which has the same color and spicy taste as prototype 2 but has a more fragrant aroma, sweeter taste, and low solubility time, so prototype 3 was chosen as the best formula. Prototype 3 uses 250 g of red ginger, 125 g of sugar, 500 g of water, and 35 g of spices. The total sugar contained in prototype 3 was 33.82% with a solubility time of 34 seconds. The results of the organoleptic test showed that prototype 3 had a sweet and spicy taste that the panelists could enjoy the most.
Keyword: instant drink powder, low sugar, red ginger, red ginger cube

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
Keyword: