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"This textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts. These topics include, first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus."

"This book is a practical and mathematically well-informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included."

"ABSTRAKDalam tulisan ini dibahas beberapa kriteria osilasi persamaan diferensial linier homogen orde dua x''(t)+m(t)x'(t)+n(t)x(t)=0 , dimana m,n fungsi kontinu pada [0,∞). Kriteria osilasi persamaan ini tergantung dari fungsi m dan n yang diberikan. Jika m dan n fungsi sembarang asalkan kontinu pada [0,∞) maka dapat digunakan bentuk normal dari persamaan diferensial linier homogen orde dua dan jika fungsi m bernilai negatif maka kriteria osilasi ditentukan dengan beberapa syarat tertentu.

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ABSTRACTIn this thesis we discuss some oscillation criteria for homogenous second order linear differential equations x''(t)+m(t)x'(t)+n(t)x(t)=0, where m,n continuous functions on [0,∞). Some oscillation criteria of this equations are dependent from function m and n. If m and n any continuous function on [0,∞) can be used then normal form of homogenous second order linear differential equations and if function m is negative then the criteria of oscillation is determined by certain conditions."

"ABSTRAKRobust Knapsack Problem (RKP) adalah variasi dari masalah Knapsack, dimana dalam hal ini bobot dari setiap item belum diketahui secara pasti, dan hanya diketahui terletak dalam sebuah interval tentu. Pada RKP akan dicari solusi optimal yang merupakan keuntungan optimal yang akan didapatkan, dan item-item mana saja yang diletakkan ke dalam Knapsack sehingga menghasilkan solusi optimal. Terdapat dua metode alternatif yang akan dijelaskan untuk mencari solusi optimal pada RKP, yang kemudian dibandingkan efisiensi dari kedua metode tersebut dengan dilihat dari running time masing-masing metode. Sedangkan untuk mencari himpunan item-item yang menghasilkan solusi optimal pada RKP akan digunakan metode partisi rekursif, dimana ide awalnya adalah dengan mempartisi himpunan item menjadi dua subhimpunan item.

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ABSTRACTRobust Knapsack Problem (RKP) is a variation of the Knapsack Problem, where in this case the weight of each item is not exactly known in advance, but belongs to a given interval. On RKP, it will be sought optimal solution, which is the optimal benefit to be gained, and set of items placed into the Knapsack. There are two methods that will be discussed to find optimal solution in RKP, and then the efficiency of the two alternative methods will be compared with their running time. Whereas, to search the set of items that build optimal solutions in the RKP will be used recursive partitioning method. The main idea of this method is dividing the set of items into two subsets of items."