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19:T1046,物理が得意ではないと感じていた中で、微積物理に興味を持ち、実際に微積を使って自由落下の問題を解いてみたところ上手くいったとのこと、大変素晴らしい成果だと思います。物理学は、一見すると抽象的で難解に思える部分がありますが、微積分を用いることで物理現象の背後にある本質をより深く理解することができます。気象大の受験のみならず、あらゆる大学を受験するにあたり、微積分を基盤とした物理学の理解は極めて重要です。
私自身も塾の先生や物理が得意な友達に、微積分や複素数を使って解釈するように指導され、物理が得意になり、東大の受験本番でも９割以上の点数を取ることができました。いくつかの具体的なアドバイスをお伝えします。参考になれば幸いです。

【 微分方程式の理解と応用】
物理の多くの分野では、微分方程式を解く能力が不可欠です。例えば、運動方程式  F = ma  は、加速度 a を速度の時間微分として表現することで、
　　F = m dv/dt
となり、さらに速度を位置の時間微分として表現すると、
　　F = m d^2x /dt^2
という二階微分方程式として書き換えられます。このように、物理現象を微分方程式で表現し、それを解くことで、物体の運動やエネルギーの変化を詳細に分析できます。

自由落下の問題において、例えば空気抵抗を考慮すると、抵抗力を速度 vの関数として
　　F = -kv
とモデル化できます。このとき、運動方程式は次のような一次の微分方程式として表現されます。
　　m dv/dt = mg - kv
これは変数分離型の一次微分方程式なので簡単に解くことができ、
　　v = mg{1-exp(-kt/m)}/k 
と解くことができます。このような問題を解くことで、単なる運動だけでなく、力やエネルギーのバランスについても理解が深まります。

【微積物理の応用範囲】
微積分の考え方は、力学だけでなく、電磁気学や波動、熱力学など、多くの分野で必要とされます。特に、電磁気学では次のような微分形式を理解することが重要です。
・電流 　I = dQ/dt
・ファラデーの法則　E = -N dφ/dt

電磁気の問題は特に、立式をして微分方程式を使うだけでほぼ全ての問題を解くことができますので、積極的に微積を利用していきましょう！

【複素インピーダンスの重要性】
電磁気学の理解を深めるには、複素数の知識を活用することも大いに役立ちます。特に、交流回路における複素インピーダンスの概念は重要です。たとえば、インダクタンス L 、電気容量C  が出てくる交流回路の問題って最初は難しく思えますよね。しかし、
　　コイル：R = i ωL　の抵抗
　　コンデンサー：R = -i/ωC　の抵抗　(i：虚数単位、ω：角周波数)
と考えるだけで、文系でも解けるようなただのオームの法則を使うだけの簡単な回路の問題に置き換わります！苦手にする人の多い交流回路の分野ですが、複素インピーダンスを使って得点源にしてしまいましょう！

【 結論】
気象大の試験に限らず、あらゆる大学の受験において、微積物理を深く理解することは極めて有益です。微分方程式の解法や複素インピーダンスの理解を進めることで、物理現象をより正確に解析できるようになります。そして何より、難しい問題を効率よく解くための視点や技術を習得することが可能です。こうした裏技的な知識や手法を活用できることが、合否を分ける要因になる現状なので、利用しない手はありません！しっかりと勉強してライバルと差をつけましょう！心から応援しています！1b:Tc2a,こんにちは！

高校3年から微積物理をして理学部に現役合格したものです。

私の経験、また周りの意見を総合すると、ずばり「役には立つが合格には必要なし」と言ったところです。

大学入試は、高校での学習指導要領に基づいて作られます。それは東北大学でも同様です。いかなる問題も通常の教科書、問題集を解いておけば解けるように設定されているのです。つまり微積を使った理解をする必要はありません。

私は「物理重要問題集」を使って高2から演習をしていましたが、微積物理を始める前から模試の成績は安定していました。その他にも「名問の森」などでも良いでしょう。

しかしながら、電磁気分野では、公式だけではどうしてもしっくり来ない部分が出てくる可能性があります。そういった場合には2つの対処法があります。

1つ目は「そういうものだ」と受け入れるということです。物理の公式は全て物の性質を表しているので、「そういう性質なんだな〜」と流してあげてください。

それでももやもやすれば、その部分だけインターネットで調べてみて下さい。各大学や学術機関がきっとその分野の説明を「微分積分を用いて」あげてくれています。

もしあなたが大学でも物理を続けるのであれば、高校で微積物理をすることは大いに役立ちます。なぜなら大学の力学や電磁気学=微分方程式を解くことであるからです。多くの理系大学1年生は微分方程式に慣れていないので、かなり苦労しています(京大生でも)。

逆に、物理は高校までと考えられているのであっても、微積物理をすることは後に役立ちます。ほぼ全ての理系大学生は1年生で「微分積分学」を履修します。読んで字のごとく微分と積分をしまくるので、これに慣れておけばスタートダッシュ間違いなしです。

参考までに、私がなぜ微積物理をしていたかを説明します。

第一に私は物理を武器にしたかったからです。英語が得意だったので、もうひとつ安定して点数を稼げる科目が必要だったので、他の人に理解度で差をつけるためにしていました。

また、単純に微積を使った物理は非常に楽しいものだったので辞める理由がありませんでした。いわば「息抜きとしての学問」でした。

結論としまして、「入試で高得点をとるのに微積は必要ないが、大学や内容理解には有益な時がある」ということです。

受験生時代は私も同様に微積すべきかどうか悩みましたが、結局は高得点に必要ないものでしたし、今から慣れ親しんだ公式を手放すリスクは負わなくていいです！

自分を信じて頑張ってください！2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=e0qaxnIBTqPwDZPuxo1u","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"微積物理について"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",7,") コメント(",0,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"6/18 17:45"}]]}],["$","div",null,{"className":"coach-mark 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mb-1","children":"すいさん、こんばんは。\n\n確かに物理を学ぶ際に微積を使って学んだ方が良いのではないかと疑問を持つことがありますよね。僕にもありました。しかし、高校では物理の公式を暗記して解くように言われます。ではどうすればいいのでしょう。僕の意見をこれから述べますね。(そもそも微積物理の対比としてのものは公式物理(？)なのかな…)\n\nまず、大学入試で出る物理の問題はどの大学でも必ず微積を使わないでも解けるように作られています。なぜなら全ての高校生が物理を学ぶ際に微積を使うとは限らないからです。ですので、微積物理を習うことは必要不可欠というわけではないのです。\n\nですが、物理という学問を語る上では数学(微分積分ベクトル指数対数三角関数etc…)は切っても切れない関係にあります。大学に行けば物理は必ず数学とセットでやります。つまり、物理の“本質”を理解するためには数学を使って物理を学ぶ必要があります。\n\n物理が苦手な人の多くは、実際に起こる現象を理解していないのだと思います。物理の問題を解く上でどういう現象が起きるのかわからない状態では、まず問題は解けません。物理という学問は現象ありきの理論です。現象を理論で理由づけするのです。\n\nつまり、物理を得意科目にするためには、あらゆる現象の根本的な原理を理解する必要があります。微積物理といっても、「三角関数の微分積分」「合成関数の微分」「置換積分」「ベクトル」などを理解していれば、大学受験で使う微積物理で躓くことはないはずです。\n\n物理が苦手な人に微積物理は厳しいのではないです。物理が苦手な人こそ微積物理を使って根本的なことを理解することに努めるべきです。高校2年生の冬からでも十分間に合います。\n\nただ、どの問題も微積を使って解くことはしなくて大丈夫です。大学受験は決まった時間内でどれだけより多くの点数を稼げるかで合否が決まります。微積物理で1から解くよりも公式を使った方が早いときもありますので、どちらを使うかはケースバイケースです。たくさんの演習をして経験を積んでください。\n\n頑張ってくださいね。\n応援しています📣"}],["$","div",null,{"className":"flex 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mb-1","children":"まずは当然ですが公式を暗記しましょう。この時に文字だけで覚えるのではなく日本語で覚えるのがオススメです。例えば運動方程式だったら物体に働く力は質量×加速度で求められるみたいに。(実際は物体に働く力によって加速度が生まれるので因果関係が逆ですが。)\n\n次に公式の使い方を知る。\n加速度を求める問題が出たとしましょう。これだけ言われれば単位時間あたりの速度変化、力を質量で割る、円運動であれば半径×角加速度の二乗などいくらでも求める方法はありますが、それぞれ使える場面が異なりますよね。\n１つ目でしたら速度と時間が分かっている時、２つ目でしたら物体の質量と力が分かっている時、３つ目でしたは円運動していて半径と角加速度が分かっている時。(円運動だったら速度と角加速度や半径と速度の２つでも加速度は出せますね。)\nこのように公式はたくさんありますが必要な情報がそれぞれ異なっているので何が与えられているからどの公式を使うのか判断する必要があります。\nこれは二次試験レベルの問題集を使うよりはセミナー等の基本的な問題集で多くの問題を解く上で身につける力だと思っています。\n\n最後に公式の使える条件に注意する。\n例えば有名なところですと2物体の運動量保存則は系に外力が働かないことが運動量が保存する条件ですが、これを意識せずに公式を使って間違えている受験生が多いように思います。\nこれは教科書に書いてありますが、問題を解きながら間違えた時にしっかりと復習をして身に付けていくのが1番だと思います。\n\n長くなりましたが高校物理は数学と似ています。基本的な問題に関しては解き方を理解した上で暗記してしまうぐらいに復習をして似たような問題が出題されれば即答できるようにしましょう。実際数学よりも問題のバリエーションは少ないため同じような問題は何度も出題されます。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"理３又は京医の二次物理には、微積物理は必要？"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"名大医学部の者です。\n\n僕は名大入試の本番196/200でしたが、微積物理は使っていませんでした。（易化した年なので東大京大に比べたらずいぶん簡単ですが）\n結論僕は大学受験の物理で微積を用いる必要はないと思います。浪人時に河合塾の近畿トップ講師に習っていましたがその方も微積物理はいらないと言われていました。\nもちろん微積で物理を理解することが深い理解への一助となることは間違いありません。しかしその能力が大学受験で問われることは今はほぼありません（昔は京大や東大の後期でそのような問題も出たことがあったようですが）。河合の講師の方は全ての教科で合格ラインが取れるようになって物理でさらに得点を安定させたい人やよほどやることがない人だけが微積物理に手を出して良いと言われてました。\n主さんはまだ高2とのことですので、微積物理やろうと思えばやれる時間はあると思いますが、焦って微積物理をする必要はないと個人的にも思います。\n補足として、矛盾するようですが、微積の考え方自体は大学受験でも役立ちます。例えば、ファラデーの電磁誘導の法則など電磁誘導関連の難問ではライプニッツの記号を用いることがそれなりにあります。ただこれは微積物理を完璧に理解していなくとも、加速度は速度を微分したものである、くらいの基本的なことがしっかり理解できていれば対応できる範囲内です。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"物理の効果的な勉強方法を教えてください"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"勉強お疲れさまです\n\n物理難しいですよね\nなかなか理解することが出来ない科目でした\n\n運動の法則の理解が難しいとの事ですが、\n\n問題を解いていく\nor\n数学が得意なら簡単な微分積分を予習しちゃう\n\nの2通りがあるかなと\n\n問題を解いていくのも、闇雲に解けばいいわけでもなく、どこでどの公式を使う理由が説明できるように頑張ればいいのです\n分からないところは先生に聞いたり、河合塾の物理のエッセンスを読んだり解いてみてください\n\nそして、2つ目の、微積を予習しちゃう手段ですが、古典力学の公式は運動方程式から全て導くことができます。その事を踏まえて、微分積分を勉強する事で運動方程式から公式を導いたりする流れで問題を気づいたら解き終わってるみたいなことが出来るわけです。\n\n正直、高校の古典力学に微積は大袈裟かなと思うところはありますが、数学の予習と力学の理解で一石二鳥な面もあるので、数学が得意なら是非挑戦してみて貰いたいです\n\nちなみに、運動方程式と同じように電気回路についても微分積分で解けるようになるのでおすすめです\n\n"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary mr-1","children":["$undefined",[["$","path","0",{"fill":"none","d":"M0 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"物理の公式をただただ暗記したくない"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"定理(公式)を暗記するかどうかはサクラサクさんの力量次第だと思います。\n\nそもそも物理法則は人間が生活する中で考えた知恵を数式的に定義づけて、定理(サクラサクさんが言うところの公式)として使いやすくしているものだと思います。あんまり突っ込んだことを言うと物理の専門の方から怒られるかもしれませんが認識として持っていて欲しいのは、定義は必ず理解しなくてはいけませんし、定理を導く事ができない人は覚える(覚えるというより問題を解きながら理解する事で自由に使えるようになると言う表現の方が近いと思います)必要があります。\n\n例えば運動方程式f=maはもともと人間の経験則からニュートンが定義したものなので覚えるのが嫌だとしたら、自分で実験をしながら導くしかないです…天才じゃなきゃ無理ですね。\n定理で言うと例えば速度の式なんかは、加速度が速度の微小変化という定義さえ知っていれば定理はそれを積分すると出ますよね。(積分を習っていなければグラフ化して導出して考えると良いと思います。)\n\nどちらにせよ何度も導出している間に覚えてしまうのでそれをそのまま使うことになると思います。丸暗記でなにも考えずに公式に当てはめるのはお勧めしませんが、導出出来るものはしながら解いて慣れてきたら時間を短縮するために必要な公式を使うのが良いんじゃないでしょうか。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"公式理解について"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"　導出方法を知っているか公式をそのまま覚えているかというのは、問題を解けるか否かというところに直接は関与しないように思います（導出を知らなくても公式を完璧に覚えていて運用できれば解けます）。導出が難しいものも時にはあったりするので、全部が全部無理に導出まで覚える必要はないです。\n\n　ただ、公式の形をそのまま覚えるよりも導出方法をセットで覚えておく方が「解きやすい」と思います。というのも、微積だとか比を取るだとかいう作業は（公式そのものに比べて比較的）使い慣れている方だと思うので、いざ問題を解く時に公式そのものを忘れてしまってもその場でパパッと導出できるようになります。そうすると式そのもので覚えなくてはならない情報量がぐんと減るので、要求される記憶力も低くて済みます。\n　あとは質問の意図からずれるかも知れませんが、得体の知れない文字の羅列よりも、出身と意味のわかるものの方が頭に残りやすくて覚えやすいと感じます。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary mr-1","children":["$undefined",[["$","path","0",{"fill":"none","d":"M0 0h24v24H0V0z","children":[]}],["$","path","1",{"d":"M12 6c1.1 0 2 .9 2 2s-.9 2-2 2-2-.9-2-2 .9-2 2-2m0 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"答案の再現性の高め方"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"電磁気が終わっているのかよくわかりませんが、本質的に物理の問題を理解するのにお勧めなのが、新物理入門という参考書か、東進の苑田先生の授業です。僕は前者で勉強しました。友達は後者をやったのですが、彼に参考書を見せたところやってることはほぼ同じっていってました。これらの共通点で他の参考書にないのは、微積分をつかうということです。\n\n東工大は東大京大並みに難しいといいますが、正直過去問をあまり見たことがないので、よくわかりませんが、少なくとも京大の入試は、微積分の理解があると、ただの数学の計算問題になります。ただ東工大はよくわからないので、あまりかきません。もし近似などの操作がよくでてくるのなら、また質問してください。この続きをかきます。\n\nまた、本質的な理解を助けるのに大事だと考えているのは、定義の確認です。例えば慣性力についてですが、いつ描くべきなのかとかを自信を持って答えられないとダメです。加速の方向の反対側にf=ma(aは加速度)という理解はまちがつてはいませんが、これは→a(aベクトルとします)が時間的に同じ方向なら直感的に理解しやすいですが、円運動など向きがかわるとき、もっと一般化した定義での理解が必要です。これは→aの定義を、座標系の移動するベクトルと定義することで、理解できます。(説明がとてもわかりづらいですが、新物理入門を読んだら必ずわかります。)\n\nですから、物理の勉強をするとき、出来るだけ公式を丸暗記しないというスタンスで学習すべきです。極端にいえばすべては→F=m→aから導出できるそうですが、これはやりすぎです。でも、覚える公式をすくなくすれば、必要な情報を取り出すときに本質的な理解を必要とします。そのために定義を学ぶことが必要です。新物理入門は教科書に公式として載っていることを詳しく導出しています。そしてこの時に微積を必要とするのです。\n\n数学で4倍角の公式を暗記することが馬鹿馬鹿しく、倍角あるいは加法定理からその場で導出することが好ましいことと同じように、物理を得意にするには暗記を減らすというスタンスで取り組むことが大事だと思います。"}],["$","div",null,{"className":"flex 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"物理の勉強法"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"初めまして。rockyyyと申します。\n物理では、覚えておくことが必要な公式と、自分で「ああ、確かにこうなるな」と理解しておく必要がある公式があります。しかし高校物理の範囲であれば、まずは公式とその使い方をある程度覚えて、問題を解くということを繰り返してその公式の意味を理解していくということをした方が良いと思います。なので結論としては、まずは公式とその使い方を覚えて、それで問題を解いていって理解を深めるということです。\n\n例えば、等加速度直線運動の公式であれば、速度を求める時にはこれ、距離を求めるときはこれを使うなどを覚えておくことから始めるということです。そうして問題を解いていると、間違えてしまうことがたくさんあると思います。その間違いが非常に重要です。「なぜこの時にはこの公式は使えないのか。」「この時にはこの公式で速度や距離を求めることができるのに、なぜこの状況では使うことができないのか」ということを考えることになると思います。それを考えて、またそれに加えて解説を読むことで、「あ、この物理現象において、この条件があったらこの公式は使えないんだ」とか「こういった力が働いているときはこうすることでこの公式を使うんだ」などの理解が物理において非常に重要です。そういった理解は実際に問題を解いていく中でわかっていくものなので、公式を覚えてたらそれを使う基本問題から応用問題まで解いてみることがお勧めです。そしてそれでわかったことをノートに目立つように書いておくとなお良いと思います。そうすることで次第に問題に対する解法が思いつくようになると思うのでよかったらぜひやってみてください。\n\nよって、結論としては物理で公式を理解(その公式の導出など)することはもちろん大切ですが、高校物理の範囲であれば、まずはその公式をどのように使うのかということを学ぶことが先決だと思います。そうすると次第に物理がわかってくるのではないかなと思います。公式によっては、高校物理の範囲では理解して導出することが難しいまたはできないものもありはするので、まず使ってみるという意識が大切ではないかなと思います。\n\n以上になります。拙い文章失礼しました。物理の各分野について僕が意識していたことやその勉強法についてまとめている投稿もあるので(物理苦手ですという投稿です。)、よかったら参考にしてみてください！受験応援しています！"}],["$","div",null,{"className":"flex 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