هندسه خمینه ها
ندا ابراهیمی - طیبه واعظیزاده
نسخه دیجیتال
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قابل مطالعه فقط در پلتفرم‌های بوکت
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ارسال از طریق شرکت ملی پست ایران
توضیحات
واژه خمینه معادل فارسی کلمه Manifold است که از واژه المانی Manningfaltigkeit گرفته شده است. در حقیقت خمینهها تعمیمی از منحی‌ها، رویه‌ها و همچنین ایده‌های کلی در توپولوژی و جبر خطی هستند. پیشینه پیدایش خمینهها به نتایج مهمی در قرن 19 و 18 بر می گردد که قدیمی‌ترین آنها هندسه نااقلیدسی است. ,ریمان اولین کسی بود که ایده تعمیم مفهوم رویه به بعد های بالاتر را ارایه کرد. در حقیقت ریمان مجموعه تمام مقدارهای ممکن یک متغیر با قید مشخص را Manningfaltigkeit نامید. زیرا متغیر میتواند مقادیر متعدد بگیرد. این واژه توسط دانشمند بنام انگلیسی ویلیام کینگدم کلیفورد به Manifoldness ترجمه شده است. ,شاید گاوس اولین کسی باشد که به مطالعه فضاها به صورت مجرد بدون تکیه بر فضایی که در آن قرار دارند پرداخت. او در قضیه ای یک روش برای محاسبه انحای رویه، بدون در نظر گرفتن اینکه رویه در چه فضایی قرار گرفته است ابداع کرد. قضیه ثابت می کرد انحنای فضا یک خاصیت ذاتی است. نظریه خمینه ها برای بررسی خواص ذاتی فضا به وجود آمده است. سرانجام در سال 1912 هرمان وریل یک تعریف برای خمینه مشتق‌پذیر ارایه نمود. در سالهای دهه 30، ویتنی و دیگران بیشتر به مطالعه خمینه ها پرداختند و در نیتکه دوم قرن بیستم کارهای آنها سبب پیشرفت فوق‌العاده هندسه دیفرانسیل و گروه‌های لی شد. ,کتاب حاضر مقدمه ای بر نظریه خمینه هاست که به دلیل کمبود منابع فارسی نگارش شده است. مولفین در این کتاب قصد دارند با زبانی گویا و ساده مفاهیم اولیه هندسه را به گونه ای ارایه کنند که فهم آن برای دانشجو در اولین برخورد با هندسه خمینهها آسان باشد. تمرین‌ها و مثال های زیاد این کتاب در فهم بهتر مطالب کمک شایانی می کند.
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خمینه معادل فارسی کلمه Manifold است که از واژه المانی Manningfaltigkeit گرفته شده است. در حقیقت خمینهها تعمیمی از منحی‌ها، رویه‌ها و همچنین ایده‌های کلی در توپولوژی و جبر خطی هستند. پیشینه پیدایش خمینهها به نتایج مهمی در قرن 19 و 18 بر می گردد که قدیمی‌ترین آنها هندسه نااقلیدسی است. \r","ریمان اولین کسی بود که ایده تعمیم مفهوم رویه به بعد های بالاتر را ارایه کرد. در حقیقت ریمان مجموعه تمام مقدارهای ممکن یک متغیر با قید مشخص را Manningfaltigkeit نامید. زیرا متغیر میتواند مقادیر متعدد بگیرد. این واژه توسط دانشمند بنام انگلیسی ویلیام کینگدم کلیفورد به Manifoldness ترجمه شده است. \r","شاید گاوس اولین کسی باشد که به مطالعه فضاها به صورت مجرد بدون تکیه بر فضایی که در آن قرار دارند پرداخت. او در قضیه ای یک روش برای محاسبه انحای رویه، بدون در نظر گرفتن اینکه رویه در چه فضایی قرار گرفته است ابداع کرد. قضیه ثابت می کرد انحنای فضا یک خاصیت ذاتی است. نظریه خمینه ها برای بررسی خواص ذاتی فضا به وجود آمده است. سرانجام در سال 1912 هرمان وریل یک تعریف برای خمینه مشتق‌پذیر ارایه نمود. در سالهای دهه 30، 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