آشنایی با هندسه منیفلد
دکتر بهزاد نجفی - دکتر مرتضی میرمحمد رضایی - علی صادقی
نسخه دیجیتال
smartphone
laptop_chromebook
قابل مطالعه فقط در پلتفرم‌های بوکت
نسخه فیزیکی
library_books
توضیحات
معمولاً در ابتدای مقطع کارشناسی ارشد در رشته ریاضی محض در دانشگاههای ایران سه درس جبر پیشرفته، آنالیز حقیقی و هندسه خمینه تدریس میشود. هندسه خمینهها در شاخههای زیادی مانند توپولوژی، جبر، فیزیک، هندسه هذلولوی، هندسه ریمانی، هندسه جبری، بهینه‌سازی و اقتصاد کاربرد دارد. گستردگی زمینههای کاربرد هندسه خمینهها، نشان‌دهنده اهمیت مطالعه آن می‌باشد. از ساده‌ترین خمینهها، خم و رویه می‌باشند که به ترتیب خمینه‌هایی یک و دو بُعدی می‌باشند. به عبارت دیگر، هر نقطه از یک خم را می‌توان با یک پارامتر و هر نقطه از یک رویه را می‌توان با دو پارامتر مستقل نمایش داد. به یک بیان ساده، یک خمینه n-بُعدی موجودی است که هر نقطه از آن را می‌توان با n پارامتر مستقل نمایش داد. هدف اصلی هندسه خمینهها، انتقال و گسترش حسابان روی خم‌ها و رویه‌ها به حسابان روی خمینه‌های n-بُعدی است. در سال‌های اخیر شاهد استقبال دانشجویان ریاضی و برخی دانشجویان فنی و مهندسی به گرایش هندسه هستیم. یکی از نیازهای دانشجویان مقاطع کارشناسی ارشد و دکتری دسترسی به مجموعه سوالات مناسب و هدفمند در شاخه تحصیلی خودشان می‌باشد. یکی از اهداف این کتابفراهم آوردن مجموعه‌ای از سوالات مناسب و هدفمند درباره هندسه خمینهها می‌باشد.,
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