english learning

 凭借DEEPSEEK R1的帮助，完成了积分部分的讲义和练习题准备 - 不定积分 - 定积分 - 换元法 - 分部积分 - 多重积分（双/三） 这样子，微分，积分部分的学习材料都准备好了 下面，还有微分方程的部分要准备

 今天依赖DEEPSEEK R1的帮助，完成了微积分的，微分部讲义和练习 - 一阶导数求导 - 链式法则 - 乘法规则 - 商规则 - 二阶导数 - 函数极值 - 左右极限分析 - 洛必达法则 自己感觉比较满意。给娃做导数的入门练习，足够了。

 中考作文的练习，琢磨这个方法也许不错。弄到一个满分作文集，覆盖常见的主题，亲情，成长，劳动... 让deepseek R1 模仿每篇满分作文，写一篇新的 自己背下来，或者消化下来 再来面对考试作文，能不能做到下笔如有神，可以试下

 中学生的数学题，可以出到难度超过高考要求的题 你不会做的难题多，并不代表你应付不了高考数学 所以，你在的中学也许很重要 根据学校成绩，在高考中的排位，可以帮你界定自己的自信，和学习能力的衡量 这样，凭借集体的力量，衡量自己在学校里的分数位置，帮助自己定位自己的成绩层次

 学一份新的知识，最初的状态可以类比于混沌。这也不会，那也不会，学得还很慢 这个时候，重要的点在于 - 相信自己，一定能学会 - 捏软柿子，从简单的点入手突破 - 构建环路。捏破一个软柿子，手上沾满柿子汁，感受欣喜 - 迭代够快。捏破一个，再来一个。追求捏破软柿子的速度 不知不觉，走出混沌状态。感受到自己学习能力的提升

 新的模块，对孩子来说都是新的挑战 大人眼里，很简单的正弦定理，余弦定理，孩子用起来有各种磕磕绊绊 弄错了对应角关系，列不出方程，想不起公式 所以，最开始是一个混沌时代 面对这种混沌，重要的是不要慌，陪孩子慢慢熟悉 最重要的是，要帮孩子养成对细微的进步也要捕捉到开心 建立起正反馈，然后一直走下去就好 重复的次数多了，正反馈的次数多了，自然而然能学得比较扎实 开始时，混沌不可怕，慢启动也不可怕。一旦建立正反馈，加速度起来了，学习就是孩子自己能把握的事情了

 初中的平面几何，如果花很多时间陷入辅助线的泥沼，不知道是不是合算 作为平替，用代数方法，去解析平面几何，也许是一条路子 代数方法就是三角函数，以及解析几何，向量，复数 从三角函数切入，学习步骤考虑如下 1）直角三角比 2）三角函数的性质 这里要覆盖 正弦定理，余弦定理，正弦算面积，以及海伦公式 3）常见三角公式 和差公式，积化和差，正切公式 这些三角公式的推导，都可以从欧拉三角公式开始 4）用三角函数知识解平面几何问题 以上三角函数的学习，并不轻松，消化时间还是蛮长的 但掌握熟练之后，好处也很明显。依赖于代数计算方法，而不是灵机一动的辅助线方法。 考试的时候，填空，选择，会比较容易。 大题，可以用解析的方法，列出方程，然后用三角函数，或者复数计算。然后把答案写上，但省略掉具体的解题过程。 这样，即使在要求不超纲方法的考试，也可以只扣过程分，但大部分得分可以保证。

# The Brave Little Cat in the Castle In an ancient town, there lived a cat named Arch. It led an almost isolated life in an abandoned castle at the edge of the town, surrounded by dense bushes and ancient trees. The castle's walls were covered with moss, and its windows were broken, but for Arch, it was a world full of adventures and secrets. ## Discovering the Diary One day, while exploring a corner of the castle, Arch discovered an old diary. The diary recorded the daily life of the castle’s former owner and some perplexing chemistry experiments. Arch, though not understanding these complex terms, was driven by curiosity to continue its exploration. The diary mentioned a mysterious potion that could grant superhuman abilities, made from rare ingredients including a special bacterium and a herb found only in the deep mountains. ## The Journey Begins Determined, Arch decided to embark on a journey to find these ingredients. It first visited the town center, where it met a...

 Every summer, the calls of thousands of swamp sparrows can be heard across North America’s wetlands. These little brown birds know only a few songs, but they know them very well. In fact, their musical set list1 probably hasn’t changed much for centuries. Like humans, baby swamp sparrows learn to communicate by copying adults. From a young age, they learn to copy, or mimic, songs sung by their elders. “Swamp sparrows very rarely make mistakes when they learn their songs,” says biologist Robert Lachlan. In fact, their mimicry is so accurate that the music changes little between generations. Just like children, the sparrows don’t remember every song they hear, Lachlan says. “They don’t just learn songs at random; they pick up commoner songs rather than rarer songs.” In other words, they learn songs they hear most often. It’s an example of a strategy that scientists call conformist bias.2 Until recently, this learning ability was thought to be special only to humans. Between 2008 and...

A Herman Melville, the writer of the famous whale story Moby Dick, once wrote that humpback whales were “the most lighthearted1 of all the whales.” A favorite of whale watchers everywhere, they often swim in ocean areas close to land and are active at the surface. They can often be seen breaching, or rising out of the water, and then coming down with a great splash. Humpbacks are intelligent animals, and can be seen working together to hunt schools of small fish. And, if you listen closely, you might even hear one singing. Recording Gentle Giants Marine biologist2 Jim Darling has studied the songs of humpback whales for more than 25 years. While recording whale songs on a boat near Hawaii, he invited author Douglas Chadwick to experience diving with a humpback. In the water, Chadwick heard the whale’s songs in a way he had never heard them before. “Suddenly, I no longer heard the whale’s voice in my ears,” he said. “I felt it inside my head and bones.” When swimming with the whale, Cha...

 n 1845, a deadly disease struck the farms of Ireland, killing all the Lumper potato plants. The death of a single crop species might not seem so important. But in Ireland, in 1845, people depended almost solely on the potato for food. The death of one species caused a terrible famine.1 Now, some scientists are worried that such a famine could happen again—but on a much wider scale. Over the centuries, farmers have discovered thousands of different species of food crops. Each species has special qualities. Some can be grown in very hot or cold climates. Others are not affected by certain diseases. However, you won’t find many of these species in your local supermarket. To feed the seven billion people on Earth, most farmers today are growing only species of plants that are easy to produce in large numbers. Meanwhile, thousands of other species are becoming extinct.2 For example, in the Philippines, there were once thousands of varieties of rice; now fewer than 100 are grown there. ...

 Many scientists believe our love of sugar may actually be an addiction. When we eat or drink sugary foods, the sugar enters our blood and affects the parts of our brain that make us feel good. Then the good feeling goes away, leaving us wanting more. All tasty foods do this, but sugar has a particularly strong effect. In this way, it is in fact an addictive drug, one that doctors recommend we all cut down on. “It seems like every time I study an illness and trace a path to the first cause, I find my way back to sugar,” says scientist Richard Johnson. One-third of adults worldwide have high blood pressure,1 and up to 347 million have diabetes.2 Why? “Sugar, we believe, is one of the culprits, if not the major culprit,” says Johnson. Our bodies are designed to survive on very little sugar. Early humans often had very little food, so our bodies learned to be very efficient in storing sugar as fat. In this way, we had energy stored for when there was no food. But today, most people ha...