Е.А.Букетов атындағы Қарағанды мемлекеттік
университетінің ұйымдастыруымен
5-11сыныптар аралығында XVI – аймақтық
ғылыми-практикалық конференцияға
Жезқазған қаласындағы №1 орта мектебінен
Тіркеу
Тегі: Альмагамбетова
Аты: Айзада
Әкесінің аты: Сайлауовна
Сыныбы:10А
Мектебі:№1
Қаласы:Жезқазған қ.
Ғылыми жетекшісі:Кудинова Балгүл Амангелдиовна
Секциясы: Анализ бастамалары
Баяндама тақырыбы: Логарифмдік теңдеуді құрастыру жолдары
Тілі:Қазақша
Техникалық құралдың қажеті:жоқ
Логарифмдік теңдеуді құрастыру жолдары.
Альмагамбетова А.С.
10А, №1 орта мектебі,Жезқазған қаласы
Ғылыми жетекшісі: Кудинова Б.А.
Кіріспе.
Есептеу тәсілдерін жетілдіру XVIII ғасырдың өзекті сұрақтарының бірі болып табылады. XVI – ғасырдың екінші жартысында сауда жасау географиясын кеңейту үшін Англия, Франция , Голландия сияқты мемелекеттерге қарамастан есептеулер жүргізілетін инженерлер мен "арифметиктерге" деген үлкен сұраныс болды.Логарифмді ойлап табу – есептеу техникасынның үлкен жетістігі. Күрделі тригонометриялық кестелермен жұмыс істеуді жеңілдету мақсатында XVI ғасырдағы кейбір математиктер арифметикалық және геометриялық прогрессияларды салыстырумен айналысты. Осы бағытта үлкен жетістіктерге қол жеткізген – Шотландиялық Лорд Джон Непер. Ол 1914 жылы өзінің "Логарифмдік каньонын суреттеу" деп аталатын еңбегін жарыққа шығарды.
Алғашқы логарифмдік таблицаларды Шотландық Непер (1550-1617) мен Швейцариялық Бюрги (1552- 1632) бір-бірімен байланыссыз өз беттерімен жасаған болатын. Непер өзі жасаған таблицаларының алғы сөзінде былай деген екен "Есептеу жұмыстарымен шұғылданғандардың көпшілігін математикадан үркітіп, шошытып жіберетін, қиыншылықтардан жалықтырып жіберетін жағдайлардан шама – шарқым келгенше құтылуға тырысып бақтым". Непер таблицаларының Бюрги таблицаларына қарағанда, анағұрлым жеңілдетілген жақтары да бар еді. Солай бола тұра есептеу жұмысына ол таблицаны қолдануға ыңғайсыз болатын. Непер логарифмдері(Nep logx) бізге таныс таңбаларымен жазып көрсеткенде былай анықталады:
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