• A new first screen for getting started: jump straight into three Chapter 1 problems, graded the moment you submit, with full solutions. Stuck? The animation and a worked example are one tap away. • Problems you've already done are skipped, so you pick up at the next one.

• Pages now reflow correctly when the screen size changes, such as rotating the device or switching screens on iPhone Duo. • Fixed garbled formulas in some card previews. • Fixed an issue that could block upgrading to Pro.

• Chapters 8–12 expanded: 73 new step-by-step examples and 352 new auto-graded problems covering analytic geometry in space and vector algebra, multivariable functions and partial derivatives, multiple integrals, line and surface integrals, and infinite series — including sets at final-exam and graduate-entrance difficulty. • Other refinements.

• The 5-minute tour now ends with a 3-problem set, graded instantly. Until you finish it, the tour stays at the top of the Learning tab. • Other refinements.

• New Research Desk: a 2-minute micro-experiment every day — drag a slider and watch the math happen. • Lab Notebook: save experiment snapshots, write down your own conjectures, and mark them as holding or refuted. • Counterexample Library: 219 claims that look true, each with the example that breaks it. Searchable. • Full course review: fixed math, animation and translation errors; 90 Chapter 8 exercises now have worked solutions. • Smoother practice: the Submit button stays at the bottom, and reading the solution after a correct answer no longer lowers your mastery. • A cleaner default look; Pro users can choose the Ivory Tower theme.

• New Theorem Studio: explore math through 18 interactive modules. The first three are free; Pro unlocks more. • New Chinese-language Exam Essentials: 12 chapters of key-point cards and exam drills for finals and entrance exams. • Corrected practice prompts, improved checking for Chinese answers, balanced answer choices and removed duplicates. • In-app feedback on practice explanations remains available.

• Tell us whether a practice explanation helped, is still unclear, or may contain an error, right below the explanation. • Send your feedback directly in the app without opening email. Additional details and contact information are optional.

• A clearer learning home: watch a concept animation, follow a worked example, then solve a problem. • Mistakes and reviews are prioritized in your next learning step. • After a 3D challenge, continue with the related lesson or practice problems. • Program creation and the program gallery are now in Calculator.

• Added app update notifications with release notes and a direct link to the App Store. • Added Check for Updates in the profile screen. • You can postpone optional updates and continue learning.

• New 3D adventure, Function Land: sled, ride the cable car and plant flags on Derivative Peak — 5 stages that teach derivatives, each gate opens when you solve a problem • New Programs: built-in Python in the calculator — draw, animate, make small games, even call the symbolic algebra engine • Gallery: 17 pieces such as the Lorenz attractor, golden-angle sunflower, Fourier epicycles and Snake — open, run and tweak • Program Square: publish your work, like and remix others'; share by QR code or link • Develop on Computer: write programs on your computer and send them to your phone in one step • Calculus Pro: try the yearly plan free for 7 days to unlock every chapter

• New Lab: hands-on concept experiments (play → definition → proof), a Daily Challenge and a Function Lab • New Calculator: textbook-style 2D input with six apps — Compute, Graph, Table, Matrix, Statistics & Regression, Units — and exact results • More reliable price loading on the unlock screen

• Lessons now in 8 languages: English, Spanish, French, Portuguese, Japanese, Arabic, Hindi and Chinese • Polished English lessons: clearer wording and 20+ corrected solution details • One purchase works on iPhone, iPad and Mac

• 全新解锁页：动画演示泰勒级数一项项逼近 sin x，9 章内容一目了然 • 例题改为「先想再看」：解题步骤逐条揭晓，看完直接练一道同知识点的题 • 修订 4 道极限例题的步骤细节（定义域条件、夹逼前提、最终数值与单位） • iPad 原生大屏布局；界面新增英语、日语、法语、西班牙语、葡萄牙语、阿拉伯语、印地语 • 现已支持 Mac：一次购买，iPhone、iPad、Mac 通用

• 新增「高数背后的故事」：芝诺的乌龟、阿基米德夹住 π、贝克莱嘲讽无穷小、处处不可导的「怪物」、dy/dx 的记号之争……每个故事一分钟，讲清这一节到底在解决什么问题 • 新增 6 道数学史原题：算一算阿基里斯在哪追上乌龟、用刘徽割圆术求 π、接下笛卡尔给费马的挑战题 • 故事全部免费阅读，史实均核对过出处

• 做题不再「一错就结束」：答错会指出可能错在哪（符号、链式法则、上下限等）并自动给出提示，每题有 3 次机会，也可随时直接看解析 • 近似值也能判对：像 ln2/3 这类答案写 0.231 即可，同时告诉你精确形式 • 答对有反馈：连对计数、概念掌握度实时上涨；做完可以直接点「下一题」 • 动画全面升级：曲线一笔笔画出、面积逐步扫出、场景播完自动接下一段，并修正了多处数学细节 • 未解锁章节可以先试看动画，并直接看到解锁后这一节有多少讲解、例题和练习 • 答题时系统键盘可以用「完成」收起；提示改为按钮，一点即看

• 修复了打开购买页时可能一直停在“正在加载 App Store 价格”、按钮点不动的问题 • 进入购买页会自动重新获取价格；网络恢复后不必重启 App • 完善匿名的功能使用统计，用于定位上面这类问题；仍然只统计页面与按钮的次数，不包含题目、答案、学习进度或联系方式

• 练习答对后可以直接给 App 评分，不用再跑去 App Store • 新增匿名的功能使用统计，只统计页面与按钮的次数，不包含题目、答案、学习进度或联系方式 • 此前购买过收费版 App 的用户无需重复购买；如未自动解锁，请点击“恢复购买”

这是一次从内容到学习体验的完整升级： • 第一章完整免费：动画讲概念、例题拆步骤、练习自动批改，先体验再决定 • 新增「5 分钟快速体验」，首次打开即可走完完整学习闭环 • 扩充至 9 章、51 个交互概念、119 道分步精讲例题和 422 道自测练习 • 新增无穷级数、多元函数微分与重积分核心内容；补齐介值/最值定理与微分方程章节 • 完整题库支持搜索、按难度筛选；分步例题可逐步查看关键变形 • 修正公式渲染、概念动画取景与窄屏公式显示问题 • 修正掌握度、错题、复习与章节归属逻辑 • 优化永久解锁、恢复购买与老买断用户自动迁移 • 此前购买过收费版 App 的用户无需重复购买；如未自动解锁，请点击「恢复购买」 • 意见反馈改为由用户确认发送的邮件草稿，不再上传设备标识或诊断数据

1. 现已支持免费下载，第一章免费试学全部功能；可一次性解锁后续全部章节（买断制、无订阅、永久使用）。已购买用户自动保留全部权限，换设备可「恢复购买」。 2. 加速首次展示数学公司的渲染速度。 3. 新增交互动画。