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rdfs:label
Matematika terapan Angewandte Mathematik Matemática aplicada 应用数学 Matemàtiques aplicades Matematika aplikatuak 応用数学 Matematica applicata Прикладна математика Toegepaste wiskunde Εφαρμοσμένα μαθηματικά Aplika matematiko رياضيات تطبيقية Matematyka stosowana Matemática aplicada Mathématiques appliquées Прикладная математика Aplikovaná matematika Applied mathematics Tillämpad matematik Matamaitic fheidhmeach 응용수학
rdfs:comment
Matematyka stosowana – gałąź matematyki zajmująca się przede wszystkim technikami i ich stosowaniem w innych dziedzinach. Interakcja między zastosowaniami matematyki a rozwojem matematyki czystej powoduje, iż obszar matematyki stosowanej nie jest precyzyjnie zdefiniowany. Zalicza się do niej działania rozwijające aparat matematyczny na potrzeby innych nauk, w szczególności medycyny, biologii, informatyki i techniki. Można wyróżnić w niej działy takie jak: 응용수학(應用數學, 영어: applied mathematics)는 수학 중에 다른 학문을 설명하는데 유용한 부분을 이용하여 다른 학문을 수학적으로 형식화하여 문제를 해결하는 학문이다. 예를 들어 전산학, 수리 물리학, , , 등이 있다. 수학의 극히 일부만이 다른 학문에 응용되고 있다. 미적분학, 선형대수학, 편미분 방정식론, 함수해석학, 확률론, 수치해석학, 최적화 이론 등 응용이 많이 되는 대표적인 수학분야들이 있다. 그러나, 예를 들어, 편미분 방정식론, , 최적화 이론등이 자주 응용된다고 해서 응용수학이라고 분류 할 수는 없다. 반드시 수학 이외의 내용과 연결점이 같이 다뤄져야만 응용수학이다. 최적화 이론을 예로 들어보자. 최적화 이론에서 최소값을 구하므로, 당연히 물리학, 경제학, 공학 등에 자주 응용되겠다. 그러나 최소값을 구하는 건 그냥 수학 내에서도 중요하고, 여러 가지 부등식들이나 리만 기하학의 최소 곡면론 같은 흔히 순수수학이라고 일컬어지는 내용과도 밀접하다. 편미분 방정식론도, 경제학, 과학, 공학 등에서 구축한 수리적 모형에서 편미분 방정식을 쓰는 경우가 자주 있어서 응용이 많이 되는 것일뿐이다. 그래서, 편미분 방정식론, , 최적화 이론등은 응용이 자주되는 수학이지만, 응용수학이 아니고 그냥 수학(또는 순수수학)이다. 반면에 수리 물리학, , 등에서는 수학 이외의 내용을 수리적 모형으로 만드는것 같은 수학 이외의 내용이 나오기 때문에 응용수학이다. Is brainse den mhatamaitic í an mhatamaitic fheidhmeach a bhaineann úsáid as uirlisí teibí matamaitice chun fadhbanna a réiteach sna heolaíochtaí, i ngnó agus i réimsí eile nach iad. Is réimse tábhachtach matamaitice feidhmí é an staidreamh a bhaineann leas as teoiric na dóchúlachta mar uirlis agus a cheadaíonn tuairisciú, anailísiú agus réamhaisnéis na bhfeiniméan ina bhfuil ról ag seans. De naam toegepaste wiskunde duidt de beroepsactiviteit aan van wetenschappers die de wetenschap of de technologie trachten voort te stuwen door de invoering van wiskundige technieken. Het is dus geen tak van de wiskunde, maar eerder een visie op de rol van de wiskunde in de maatschappij. Daardoor houdt deze term soms een impliciet waarde-oordeel in. Vaak ligt de vernieuwing eerder in het voor het eerst toepassen van een bestaande wiskundige techniek in een bestaande wetenschap, dan in het uitvinden van nieuwe wiskundige methoden per se. La matemàtica aplicada o matemàtiques aplicades són tots aquells mètodes i eines matemàtiques que es poden fer servir en l'anàlisi o solució de problemes en l'àmbit de les ciències aplicades o socials. Molts mètodes matemàtics han resultat efectius en l'estudi de problemes de física, química, biologia, medicina, ciències socials, , enginyeria, economia, finances, ecologia entre altres. La definició no és precisa, ja que, a priori, qualsevol part de la matemàtica podria ser utilitzada en problemes reals; tanmateix una possible diferència és que en matemàtiques aplicades es procura el desenvolupament de la matemàtica "cap a fora", és a dir cap a la resta de les àrees. I en menor grau "cap a dins" és a dir, cap al desenvolupament de les matemàtiques mateixes. Aquest últim seria el cas de les La matematica applicata è un ramo della matematica che si occupa dello studio delle tecniche matematiche usate nell'applicare le conoscenze matematiche ad altri campi scientifici e tecnici. Aplikovaná matematika je odvětví matematiky zabývající se studiem těch oblastí matematiky, které se používají jako vhodný nástroj v nějakém nematematickém oboru. Rozvíjí matematické metody používané mimo samotnou matematiku, upřesňuje způsob, kterým je takové metody možné použít, a ručí za správnost jimi dosažených výsledků. Die Angewandte Mathematik beschäftigt sich sowohl mit der Entwicklung neuer Methoden zur Lösung von Problemen aus anderen Gebieten (wie Chemie, Biologie, Physik, Wirtschaft, Informatik, Technik usw.), als auch der Anwendung bereits bekannter mathematischer Methoden auf wohlbekannte Probleme. Insbesondere gehören dazu Die mathematischen Methoden werden auf ein Modell des betrachteten Systems angewandt. Les mathématiques appliquées sont une branche des mathématiques qui s'intéresse à l'application du savoir mathématique aux autres domaines.L'analyse numérique, les mathématiques de l’ingénierie ; la physique mathématique ; l'optimisation linéaire, la programmation dynamique, l'optimisation et la recherche opérationnelle ; les biomathématiques, la bio-informatique, la théorie de l'information, la théorie des jeux ; les probabilités et les statistiques ; les mathématiques financières et l'actuariat ; la cryptographie et, jusqu'à un certain point, la combinatoire ; la théorie des graphes telle qu'appliquée à l'analyse de réseaux, ainsi qu'une bonne partie de ce qu'on appelle l'informatique sont autant de domaines d'application des mathématiques. الرياضيات التطبيقية (بالإنجليزية: Applied mathematics)‏ هي تطبيق الأساليب الرياضية في مجالات مختلفة مثل العلوم والهندسة والأعمال وعلوم الحاسوب والصناعة. الرياضيات التطبيقية هي مزيج من العلوم الرياضية والمعرفة المتخصصة. يصف مصطلح «الرياضيات التطبيقية» أيضًا التخصص المهني الذي يعمل فيه علماء الرياضيات على حل المشكلات العملية من خلال صياغة النماذج الرياضية ودراستها. في الماضي، حفزت التطبيقات العملية على تطوير نظريات رياضية، والتي أصبحت بعد ذلك موضوع الدراسة في الرياضيات البحتة حيث تتم دراسة المفاهيم المجردة من أجلها. يرتبط نشاط الرياضيات التطبيقية ارتباطًا وثيقًا بالبحث في الرياضيات البحتة. Прикладна́я матема́тика — область математики, рассматривающая применение математических методов, алгоритмов в других областях науки и техники. Примерами такого применения будут: численные методы, математическая физика, линейное программирование, оптимизация и исследование операций, моделирование сплошных сред (Механика сплошных сред), и биоинформатика, теория информации, теория игр, теория вероятностей и статистика, финансовая математика и актуарные расчёты, криптография, а следовательно комбинаторика и в некоторой степени конечная геометрия, теория графов в приложении к сетевому планированию, и во многом то, что называется информатикой. В вопросе о том, что является прикладной математикой, нельзя составить чёткую логическую классификацию. Математические методы обычно применяются к специф Aplika matematiko estas branĉo de matematiko kiu uzas la matematikajn metodojn por solvi problemojn el aliaj sciencoj, kiel fiziko, kemio, ekonomio, komputiko kaj statistiko. Ĝi estas la kontraŭparto de pura matematiko. Εφαρμοσμένα μαθηματικά είναι κλάδος των μαθηματικών που ασχολείται με τις μαθηματικές μεθόδους που χρησιμοποιούνται για την επιλύση προβλημάτων στους τομείς των άλλων θετικών επιστημών, όπως είναι η φυσική, η χημεία, η πληροφορική και τα οικονομικά. Τα εφαρμοσμένα μαθηματικά είναι ο ένας μεγάλος κλάδος των μαθηματικών - ο άλλος είναι τα καθαρά ή θεωρητικά μαθηματικά που ασχολούνται με την επίλυση προβλημάτων μέσα στα ίδια τα μαθηματικά. A matemática aplicada é uma área da matemática no qual se trata da aplicação do conhecimento matemático a outros domínios. Tais aplicações incluem cálculo numérico, matemática voltada a engenharia, programação linear, otimização, modelagem contínua, biomatemática e bioinformática, teoria da informação, teoria dos jogos, probabilidade e estatística, matemática financeira, criptografia, combinatória e até mesmo geometria finita até certo ponto, teoria de grafos como aplicada em análise de redes, e grande parte do que se chama ciência da computação. Matematika aplikatuek edo aplikatutako matematikek matematikaren hainbat metodo eta tresnari egiten diote erreferentzia, analisiak egiteko eta problemak ebazteko arlokoak diren neurrian. Aplikaziorako matematikaren hainbat arloko metodoak erabiltzen dira, kalkulua, aljebra lineala eta ekuazio diferentzialak, besteak beste. Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. Matematika terapan merupakan cabang matematika yang terkait dengan teknik matematika yang digunakan dalam aplikasi ilmu matematika untuk disiplin ilmiah. Penerapan matematika terapan dilakukan pada bidang fisika, biologi, sosiologi, dan mekanika. yang lain. Matematika terapan berkenaan dengan penggunaan alat matematika abstrak guna memecahkan masalah-masalah konkret di dalam ilmu pengetahuan, bisnis, dan wilayah lainnya. Sebuah lapangan penting di dalam matematika terapan adalah statistika, yang menggunakan teori peluang sebagai alat dan membolehkan penjelasan, analisis, dan peramalan gejala di mana peluang berperan penting. Sebagian besar percobaan, survei, dan pengkajian pengamatan memerlukan statistika. Matematika terapan merupakan ilmu yang diperlukan untuk menghitung segala sesuatu ya 応用数学(おうようすうがく、英語: applied mathematics)とは、数学的知識を他分野に適用することを主眼とした数学の分野の総称である。 数学のさまざまな分野のどれが応用数学であるかというはっきりした合意があるわけではなく、しばしば純粋数学と対置されるものとして、大まかには他の科学や技術への応用に歴史的に密接に関連してきた分野がこう呼ばれている。 應用數學(英語:Applied Mathematics)是以應用為目的的明確的數學理論和方法的總稱,研究如何應用數學知識到其他範疇(尤其是科學)的數學分支,可以說是純數學的相反,應用純數學中的結論擴展到物理學等其他科學中,應用數學的發展是以科學為依據,作為科學研究的後盾。包括線性代數、矩陣理論、向量分析、複變分析、微分方程、拉普拉斯變換、傅里葉分析、數值分析、概率论、數理統計、運籌學、博弈論、控制理論、組合數學、資訊理論等許多數學分支,也包括從各種應用領域中提出的數學問題的研究。而大部分應用數學是以作為物理分析的工具。計算數學有時也可視為應用數學的一部分。應用數學大部分的教學範疇都是以物理的模型為基礎進行分析,當中或許搭配了各種數學工具,就為了更貼近物理的系統。應用數學的內容是在不斷演化的,例如數論一直是純粹數學,但是在發現了RSA加密算法之後,數論被大量使用在計算安全學中。 圖論應用在網絡分析,拓撲學應用在電路分析,群論應用在結晶學,微分幾何應用在規範場,自動控制理論應用在計算,黎曼幾何應用於相對論,數理邏輯應用於計算機,最小二乘法應用於飛機起降時自動控制,利用數字合成計算機輔助的X射線斷層成像技術(1979年數學家獲得諾貝爾醫學獎)數論應用在密碼學,博弈論、概率論、統計學應用在計量經濟學,線性規劃用於生產安排調度,都可見數學在不同範疇的應用。 La matemática aplicada (o también matemáticas aplicadas) se refiere a aquellos métodos y herramientas matemáticas que pueden ser utilizados en el análisis o resolución de problemas pertenecientes al área de las ciencias básicas o aplicadas, como el cálculo, el álgebra lineal, las ecuaciones diferenciales y otros procedimientos ideados desde que se acuñó el concepto. Прикладна математика — галузь математики, що розглядає застосування математичних знань в інших сферах діяльності. Прикладами такого застосування будуть: чисельні методи, математична фізика, математична хімія, лінійне програмування, оптимізація і дослідження операцій, моделювання суцільних середовищ (механіка суцільних середовищ), біоматематика і біоінформатика, теорія інформації, теорія ігор, теорія ймовірності і статистика, фінансова математика і , актуарна математика, криптографія, а також комбінаторика і деякою мірою , теорія графів в додатку до мережевому плануванню, і багато в чому те, що називається інформатикою. У питанні про те, що є прикладною математикою, не можна скласти чітку логічну класифікацію. Математичні методи звичайно застосовуються до специфічного класу прикладних завда Tillämpad matematik är matematik som används för problemlösning. Det kan dels syfta på de grenar av matematiken som mer kännetecknas av specialisering än teori (till exempel optimering och transformteori), dels på alla tänkbara av matematiskt vetande.
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A matemática aplicada é uma área da matemática no qual se trata da aplicação do conhecimento matemático a outros domínios. Tais aplicações incluem cálculo numérico, matemática voltada a engenharia, programação linear, otimização, modelagem contínua, biomatemática e bioinformática, teoria da informação, teoria dos jogos, probabilidade e estatística, matemática financeira, criptografia, combinatória e até mesmo geometria finita até certo ponto, teoria de grafos como aplicada em análise de redes, e grande parte do que se chama ciência da computação. A matemática voltada à engenharia descreve processos físicos, e portanto, é muito similar à física teórica. Subdivisões importantes incluem: dinâmica dos fluidos, teoria acústica, equações de Maxwell que governam o eletromagnetismo, mecânica etc. Historicamente, a matemática era mais importante para as ciências naturais e engenharia. No entanto, desde a Segunda Guerra Mundial, campos fora das ciências físicas geraram a criação de novas áreas de matemática, como teoria dos jogos e teoria da escolha social, e o conceito de redes neurais, que surgiram do estudo do cérebro em neurociência. Matematika terapan merupakan cabang matematika yang terkait dengan teknik matematika yang digunakan dalam aplikasi ilmu matematika untuk disiplin ilmiah. Penerapan matematika terapan dilakukan pada bidang fisika, biologi, sosiologi, dan mekanika. yang lain. Matematika terapan berkenaan dengan penggunaan alat matematika abstrak guna memecahkan masalah-masalah konkret di dalam ilmu pengetahuan, bisnis, dan wilayah lainnya. Sebuah lapangan penting di dalam matematika terapan adalah statistika, yang menggunakan teori peluang sebagai alat dan membolehkan penjelasan, analisis, dan peramalan gejala di mana peluang berperan penting. Sebagian besar percobaan, survei, dan pengkajian pengamatan memerlukan statistika. Matematika terapan merupakan ilmu yang diperlukan untuk menghitung segala sesuatu yang memerlukan rumus. Прикладна́я матема́тика — область математики, рассматривающая применение математических методов, алгоритмов в других областях науки и техники. Примерами такого применения будут: численные методы, математическая физика, линейное программирование, оптимизация и исследование операций, моделирование сплошных сред (Механика сплошных сред), и биоинформатика, теория информации, теория игр, теория вероятностей и статистика, финансовая математика и актуарные расчёты, криптография, а следовательно комбинаторика и в некоторой степени конечная геометрия, теория графов в приложении к сетевому планированию, и во многом то, что называется информатикой. В вопросе о том, что является прикладной математикой, нельзя составить чёткую логическую классификацию. Математические методы обычно применяются к специфическому классу прикладных задач путём составления математической модели. По ироническому утверждению В. И. Арнольда, разница между чистой и прикладной математикой не научная, а социальная и заключается в том, что чистому математику платят за открытие математических фактов, в то время как прикладному математику платят за решение практических задач. Арнольд также замечает, что в России почти каждый математик сочетал «чистую» и «прикладную» математику. La matematica applicata è un ramo della matematica che si occupa dello studio delle tecniche matematiche usate nell'applicare le conoscenze matematiche ad altri campi scientifici e tecnici. 応用数学(おうようすうがく、英語: applied mathematics)とは、数学的知識を他分野に適用することを主眼とした数学の分野の総称である。 数学のさまざまな分野のどれが応用数学であるかというはっきりした合意があるわけではなく、しばしば純粋数学と対置されるものとして、大まかには他の科学や技術への応用に歴史的に密接に関連してきた分野がこう呼ばれている。 Εφαρμοσμένα μαθηματικά είναι κλάδος των μαθηματικών που ασχολείται με τις μαθηματικές μεθόδους που χρησιμοποιούνται για την επιλύση προβλημάτων στους τομείς των άλλων θετικών επιστημών, όπως είναι η φυσική, η χημεία, η πληροφορική και τα οικονομικά. Τα εφαρμοσμένα μαθηματικά είναι ο ένας μεγάλος κλάδος των μαθηματικών - ο άλλος είναι τα καθαρά ή θεωρητικά μαθηματικά που ασχολούνται με την επίλυση προβλημάτων μέσα στα ίδια τα μαθηματικά. Ο όρος «εφαρμοσμένα μαθηματικά» περιγράφει τον κλάδο που στοχεύει στην επίλυση πρακτικών προβλημάτων και στη διαμόρφωση και μελέτη . Στο παρελθόν, οι πρακτικές εφαρμογές ήταν το κίνητρο για την ανάπτυξη των μαθηματικών θεωριών, οι οποίες στη συνέχεια γίνονταν αντικείμενο μελέτης από τα καθαρά μαθηματικά: τα μη εφαρμοσμένα μαθηματικά, τα οποία αναπτύσσονται και μελετώνται χωρίς να είναι στόχος η άμεση εφαρμογή τους στην επίλυση προβλημάτων από άλλες επιστήμες. Γι' αυτό και η λειτουργία των εφαρμοσμένων μαθηματικών είναι εξαιρετικά συνδεδεμένη με την έρευνα σε καθαρά μαθηματικά. Τα όρια ταξινόμησης των γνωστικών αντικειμένων σε πεδία δεν είναι ξεκάθαρα, αλλά ενδεικτικά δίνονται παρακάτω κάποια επιμέρους πεδία των μαθηματικών που συνήθως κατατάσσονται στα εφαρμοσμένα μαθηματικά: * διαφορικές εξισώσεις * αριθμητική ανάλυση * θεωρία πιθανοτήτων * στατιστική * θεωρία αυτομάτου ελέγχου * θεωρία γραφημάτων * θεωρία πληροφορίας * κρυπτογραφία * θεωρία παιγνίων * επεξεργασία σήματος 應用數學(英語:Applied Mathematics)是以應用為目的的明確的數學理論和方法的總稱,研究如何應用數學知識到其他範疇(尤其是科學)的數學分支,可以說是純數學的相反,應用純數學中的結論擴展到物理學等其他科學中,應用數學的發展是以科學為依據,作為科學研究的後盾。包括線性代數、矩陣理論、向量分析、複變分析、微分方程、拉普拉斯變換、傅里葉分析、數值分析、概率论、數理統計、運籌學、博弈論、控制理論、組合數學、資訊理論等許多數學分支,也包括從各種應用領域中提出的數學問題的研究。而大部分應用數學是以作為物理分析的工具。計算數學有時也可視為應用數學的一部分。應用數學大部分的教學範疇都是以物理的模型為基礎進行分析,當中或許搭配了各種數學工具,就為了更貼近物理的系統。應用數學的內容是在不斷演化的,例如數論一直是純粹數學,但是在發現了RSA加密算法之後,數論被大量使用在計算安全學中。 圖論應用在網絡分析,拓撲學應用在電路分析,群論應用在結晶學,微分幾何應用在規範場,自動控制理論應用在計算,黎曼幾何應用於相對論,數理邏輯應用於計算機,最小二乘法應用於飛機起降時自動控制,利用數字合成計算機輔助的X射線斷層成像技術(1979年數學家獲得諾貝爾醫學獎)數論應用在密碼學,博弈論、概率論、統計學應用在計量經濟學,線性規劃用於生產安排調度,都可見數學在不同範疇的應用。 الرياضيات التطبيقية (بالإنجليزية: Applied mathematics)‏ هي تطبيق الأساليب الرياضية في مجالات مختلفة مثل العلوم والهندسة والأعمال وعلوم الحاسوب والصناعة. الرياضيات التطبيقية هي مزيج من العلوم الرياضية والمعرفة المتخصصة. يصف مصطلح «الرياضيات التطبيقية» أيضًا التخصص المهني الذي يعمل فيه علماء الرياضيات على حل المشكلات العملية من خلال صياغة النماذج الرياضية ودراستها. في الماضي، حفزت التطبيقات العملية على تطوير نظريات رياضية، والتي أصبحت بعد ذلك موضوع الدراسة في الرياضيات البحتة حيث تتم دراسة المفاهيم المجردة من أجلها. يرتبط نشاط الرياضيات التطبيقية ارتباطًا وثيقًا بالبحث في الرياضيات البحتة. Tillämpad matematik är matematik som används för problemlösning. Det kan dels syfta på de grenar av matematiken som mer kännetecknas av specialisering än teori (till exempel optimering och transformteori), dels på alla tänkbara av matematiskt vetande. La matemática aplicada (o también matemáticas aplicadas) se refiere a aquellos métodos y herramientas matemáticas que pueden ser utilizados en el análisis o resolución de problemas pertenecientes al área de las ciencias básicas o aplicadas, como el cálculo, el álgebra lineal, las ecuaciones diferenciales y otros procedimientos ideados desde que se acuñó el concepto. Muchos métodos matemáticos han resultado efectivos en el estudio de problemas en física, química, biología, ingeniería, medicina, ciencias sociales, informática, economía y las actividades económico-financieras o ecología. Sin embargo, una posible diferencia es que en matemáticas aplicadas se procura el desarrollo de las matemáticas «hacia afuera», es decir su aplicación o transferencia hacia el resto de las áreas. Y en menor grado «hacia dentro» o sea, hacia el desarrollo de la matemática misma. Este último sería el caso de las matemáticas puras o matemáticas.​ Las matemáticas aplicadas se usan con frecuencia en distintas áreas tecnológicas para modelado, simulación y optimización de procesos o fenómenos, como el túnel de viento o el diseño de experimentos. En las últimas décadas, una de las aplicaciones más directas de la matemática tales como: álgebra lineal, geometría plana y del espacio, cálculo y física han sido un fundamento para el desarrollo de simuladores y videojuegos en 3D. Matematyka stosowana – gałąź matematyki zajmująca się przede wszystkim technikami i ich stosowaniem w innych dziedzinach. Interakcja między zastosowaniami matematyki a rozwojem matematyki czystej powoduje, iż obszar matematyki stosowanej nie jest precyzyjnie zdefiniowany. Zalicza się do niej działania rozwijające aparat matematyczny na potrzeby innych nauk, w szczególności medycyny, biologii, informatyki i techniki. Można wyróżnić w niej działy takie jak: * Analiza numeryczna * Informatyka matematyczna, teoria obliczeń, algorytmy, teoria złożoności * Zastosowania rachunku prawdopodobieństwa i procesów stochastycznych * Mechanika cząstek i układów * Mechanika ciał deformowalnych * Zastosowania matematyki w mechanice płynów * Zastosowania matematyki w optyce i elektromagnetyzmie * Zastosowania matematyki w termodynamice klasycznej * Mechanika kwantowa * Mechanika statystyczna, budowa materii * Teoria względności * Zastosowania matematyki w astronomii i astrofizyce * Zastosowania matematyki w geofizyce * Badania operacyjne, programowanie matematyczne * Teoria gier, ekonomia, nauki społeczne * Biomatematyka i matematyka w innych naukach przyrodniczych * Teoria systemów, teoria sterowania * Teoria informacji, teoria sygnałów, , teoria obwodów, zbiory rozmyte * Edukacja matematyczna * Geometria wykreślna * Rachunek wyrównawczy Aplikovaná matematika je odvětví matematiky zabývající se studiem těch oblastí matematiky, které se používají jako vhodný nástroj v nějakém nematematickém oboru. Rozvíjí matematické metody používané mimo samotnou matematiku, upřesňuje způsob, kterým je takové metody možné použít, a ručí za správnost jimi dosažených výsledků. Les mathématiques appliquées sont une branche des mathématiques qui s'intéresse à l'application du savoir mathématique aux autres domaines.L'analyse numérique, les mathématiques de l’ingénierie ; la physique mathématique ; l'optimisation linéaire, la programmation dynamique, l'optimisation et la recherche opérationnelle ; les biomathématiques, la bio-informatique, la théorie de l'information, la théorie des jeux ; les probabilités et les statistiques ; les mathématiques financières et l'actuariat ; la cryptographie et, jusqu'à un certain point, la combinatoire ; la théorie des graphes telle qu'appliquée à l'analyse de réseaux, ainsi qu'une bonne partie de ce qu'on appelle l'informatique sont autant de domaines d'application des mathématiques. La classification logique des mathématiques appliquées repose davantage sur la sociologie des professionnels qui se servent des mathématiques que sur la question d'en déterminer la nature exacte. Habituellement, les méthodes mathématiques sont appliquées au domaine d'un problème particulier à l'aide d'un modèle mathématique. Les mathématiques de l'ingénierie s'attachent à décrire des processus physiques, de sorte qu'elles se distinguent rarement de la physique théorique. Parmi les principales subdivisions de celles-ci, on peut mentionner : * la mécanique des fluides ; * l'acoustique ; * les équations de Maxwell, lesquelles régissent l'électromagnétisme ; * la mécanique ; * les phénomènes d'échanges. « Pour rassurer les puristes, signalons que le calcul numérique, dont l'intérêt pratique est si essentiel, est souvent l'origine et l'occasion de travaux théoriques fondamentaux. Théorie et pratique s'etayent ainsi l'une l'autre, comprenons que les mathématiques étant nées outils, cultivées en outils par des hommes éminents, ce ne serait pas les mépriser que de les faire servir à quelque chose. » Aplika matematiko estas branĉo de matematiko kiu uzas la matematikajn metodojn por solvi problemojn el aliaj sciencoj, kiel fiziko, kemio, ekonomio, komputiko kaj statistiko. Ĝi estas la kontraŭparto de pura matematiko. De naam toegepaste wiskunde duidt de beroepsactiviteit aan van wetenschappers die de wetenschap of de technologie trachten voort te stuwen door de invoering van wiskundige technieken. Het is dus geen tak van de wiskunde, maar eerder een visie op de rol van de wiskunde in de maatschappij. Daardoor houdt deze term soms een impliciet waarde-oordeel in. Vaak ligt de vernieuwing eerder in het voor het eerst toepassen van een bestaande wiskundige techniek in een bestaande wetenschap, dan in het uitvinden van nieuwe wiskundige methoden per se. Ter contrast wordt vaak de even dubbelzinnige term zuivere wiskunde gehanteerd. Men zou kunnen argumenteren dat de activiteit van een wiskundige, om zinvol te zijn, tegelijkertijd zuiver (dat wil zeggen exact) moet zijn, en toepasbaar moet zijn in een andere context dan de oorspronkelijke (anders is er weinig behoefte aan abstractie). Het adjectief toegepast wordt hier echter meestal enger geïnterpreteerd als "rechtstreeks, uitdrukkelijk en onmiddellijk toegepast buiten de wiskunde en de natuurwetenschappen". Als dusdanig is de term nauw verwant met "toegepaste wetenschappen" als synoniem voor de ingenieurswetenschappen. Veel universiteiten hebben afzonderlijke departementen voor zuivere en voor toegepaste wiskunde. Door de dubbelzinnigheid van de terminologie varieert de bevoegdheidsgrens nogal sterk. Voorbeelden van activiteiten die onbetwist tot de toegepaste wiskunde behoren, zijn: * statistische methoden in de sociale wetenschappen; * wiskundige risicoanalyse voor verzekeringsportfolio's; * wiskundige modellen voor de bouwkunde en de waterbouwkunde. Voorbeelden van activiteiten die weliswaar nuttige toepassingen vinden buiten de wiskunde, maar die vaak aan het departement zuivere wiskunde worden beoefend, zijn: * getaltheorie; * gewone (analytische) en algebraïsche topologie; * maattheorie en functionaalanalyse. Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. Прикладна математика — галузь математики, що розглядає застосування математичних знань в інших сферах діяльності. Прикладами такого застосування будуть: чисельні методи, математична фізика, математична хімія, лінійне програмування, оптимізація і дослідження операцій, моделювання суцільних середовищ (механіка суцільних середовищ), біоматематика і біоінформатика, теорія інформації, теорія ігор, теорія ймовірності і статистика, фінансова математика і , актуарна математика, криптографія, а також комбінаторика і деякою мірою , теорія графів в додатку до мережевому плануванню, і багато в чому те, що називається інформатикою. У питанні про те, що є прикладною математикою, не можна скласти чітку логічну класифікацію. Математичні методи звичайно застосовуються до специфічного класу прикладних завдань шляхом складання математичної моделі системи. У минулому практичні додатки мотивували розвиток математичних теорій, які потім стали предметом вивчення з чистої математики, де абстрактні поняття вивчаються заради себе. Таким чином, діяльність прикладної математики тісно пов'язана з дослідженнями чистої математики. Is brainse den mhatamaitic í an mhatamaitic fheidhmeach a bhaineann úsáid as uirlisí teibí matamaitice chun fadhbanna a réiteach sna heolaíochtaí, i ngnó agus i réimsí eile nach iad. Is réimse tábhachtach matamaitice feidhmí é an staidreamh a bhaineann leas as teoiric na dóchúlachta mar uirlis agus a cheadaíonn tuairisciú, anailísiú agus réamhaisnéis na bhfeiniméan ina bhfuil ról ag seans. La matemàtica aplicada o matemàtiques aplicades són tots aquells mètodes i eines matemàtiques que es poden fer servir en l'anàlisi o solució de problemes en l'àmbit de les ciències aplicades o socials. Molts mètodes matemàtics han resultat efectius en l'estudi de problemes de física, química, biologia, medicina, ciències socials, , enginyeria, economia, finances, ecologia entre altres. La definició no és precisa, ja que, a priori, qualsevol part de la matemàtica podria ser utilitzada en problemes reals; tanmateix una possible diferència és que en matemàtiques aplicades es procura el desenvolupament de la matemàtica "cap a fora", és a dir cap a la resta de les àrees. I en menor grau "cap a dins" és a dir, cap al desenvolupament de les matemàtiques mateixes. Aquest últim seria el cas de les matemàtiques pures. La matemàtica aplicada es fa servir freqüentment en diferents àrees tecnològiques per al modelatge, simulació i optimització de processos o fenòmens. Àrees de la matemàtica que tenen força aplicacions: * Física matemàtica * Fluidodinàmica matemàtica * Anàlisi numèrica * Optimització * Probabilitat * Estadística * Matemàtica financera * Teoria dels jocs 응용수학(應用數學, 영어: applied mathematics)는 수학 중에 다른 학문을 설명하는데 유용한 부분을 이용하여 다른 학문을 수학적으로 형식화하여 문제를 해결하는 학문이다. 예를 들어 전산학, 수리 물리학, , , 등이 있다. 수학의 극히 일부만이 다른 학문에 응용되고 있다. 미적분학, 선형대수학, 편미분 방정식론, 함수해석학, 확률론, 수치해석학, 최적화 이론 등 응용이 많이 되는 대표적인 수학분야들이 있다. 그러나, 예를 들어, 편미분 방정식론, , 최적화 이론등이 자주 응용된다고 해서 응용수학이라고 분류 할 수는 없다. 반드시 수학 이외의 내용과 연결점이 같이 다뤄져야만 응용수학이다. 최적화 이론을 예로 들어보자. 최적화 이론에서 최소값을 구하므로, 당연히 물리학, 경제학, 공학 등에 자주 응용되겠다. 그러나 최소값을 구하는 건 그냥 수학 내에서도 중요하고, 여러 가지 부등식들이나 리만 기하학의 최소 곡면론 같은 흔히 순수수학이라고 일컬어지는 내용과도 밀접하다. 편미분 방정식론도, 경제학, 과학, 공학 등에서 구축한 수리적 모형에서 편미분 방정식을 쓰는 경우가 자주 있어서 응용이 많이 되는 것일뿐이다. 그래서, 편미분 방정식론, , 최적화 이론등은 응용이 자주되는 수학이지만, 응용수학이 아니고 그냥 수학(또는 순수수학)이다. 반면에 수리 물리학, , 등에서는 수학 이외의 내용을 수리적 모형으로 만드는것 같은 수학 이외의 내용이 나오기 때문에 응용수학이다. Die Angewandte Mathematik beschäftigt sich sowohl mit der Entwicklung neuer Methoden zur Lösung von Problemen aus anderen Gebieten (wie Chemie, Biologie, Physik, Wirtschaft, Informatik, Technik usw.), als auch der Anwendung bereits bekannter mathematischer Methoden auf wohlbekannte Probleme. Insbesondere gehören dazu * Computermathematik * Finanzmathematik * Geomathematik * Graphentheorie * * Kryptologie * Mathematische Chemie * Mathematische Physik * Mathematische Psychologie * Mathematische Statistik * Numerische Mathematik * Optimierung und Operations Research * Theoretische Biologie * Versicherungsmathematik * Wirtschaftsmathematik * Wissenschaftliches Rechnen Die mathematischen Methoden werden auf ein Modell des betrachteten Systems angewandt. Die Grenze zwischen reiner und angewandter Mathematik ist fließend, wie der Begriff angewandte Wissenschaft an sich problematisch ist. Die Zuordnung von Arbeiten in eines dieser beiden großen Felder hängt stark von der persönlichen Auffassung der beteiligten Mathematiker ab. Angewandte Mathematik, die sich mit mathematischen Methoden beschäftigt (und damit ein Teilgebiet der Mathematik ist), ist von den Anwendungen der Mathematik in der Naturwissenschaft, den Ingenieurwissenschaften und anderen Bereichen zu unterscheiden. So wird man nicht sagen, dass ein Biologe, der mathematische Methoden der Populationsdynamik benutzt und bekannte Mathematik anwendet, selbst angewandte Mathematik betreibt – er verwendet sie lediglich. Häufig ziehen Nichtmathematiker diese Grenze nicht, und sie ist nicht immer klar. Die Verwendung der Mathematik zur Lösung industrieller Probleme wird Industriemathematik genannt; hier ist als Teilgebiet besonders die Technomathematik zu nennen, die sich mit aus der Technik stammenden Problemen befasst. Matematika aplikatuek edo aplikatutako matematikek matematikaren hainbat metodo eta tresnari egiten diote erreferentzia, analisiak egiteko eta problemak ebazteko arlokoak diren neurrian. Aplikaziorako matematikaren hainbat arloko metodoak erabiltzen dira, kalkulua, aljebra lineala eta ekuazio diferentzialak, besteak beste. Metodo matematiko asko eraginkorrak izan dira fisika, kimika, biologia, ingeniaritza, medikuntza, gizarte zientziak, informatika, ekonomia, finantzak edo ekologia arloko problemak aztertzeko eta ebazteko. Hala ere, balizko desberdintasun bat da matematika aplikatuetan matematikaren garapena “kanporantz” bideratzen dela, hau da, bestelako arloetara aplikatzea edo transferitzea. Eta maila apalagoan “barrurantz”, hau da, matematika bera garatzeari begira. Azken hori matematika puruen edo matematika hutsen kasua izango litzateke. Matematika aplikatuak hainbat arlo teknologikotan erabiltzen dira maiz prozesuak edo fenomenoak modelatzeko, simulatzeko eta optimizatzeko, hala nola haize-tunelean edo esperimentuen diseinuan. Azken hamarkadetan, matematikaren aplikazio zuzenenetako bat, hala nola aljebra lineala, geometria laua eta espazioarena, kalkulua eta fisika oinarri izan dira simulagailuak eta 3Dko bideojokoak garatzeko.
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