课程目标撰写指南

课程标题：微积分A
Course Title: Calculus A

课程学习目标（中文）
请根据下列目标组织教学与学习；使用动词清晰描述可衡量的表现。

- 明确函数与模型：识别并比较常见函数族（多项式、指数、对数、三角、分段函数）；用函数刻画实际变化并选择合适模型。
- 掌握极限与连续性：用图形、代数与ε-δ定义刻画极限；判断并分类间断点；处理无穷小与无穷大极限。
- 计算与解释导数：将导数理解为瞬时变化率与切线斜率；从定义和运算法则求导（幂、乘/商、链式、指数、对数、三角、反三角、隐函数、反函数）。
- 使用线性化与误差估计：用微分与一阶泰勒近似进行数值估计；描述误差阶并评估近似的适用范围。
- 应用导数解决问题：完成曲线描绘（单调性、极值、凹凸性、拐点、渐近线）；求解最优化与相关变化率问题；恰当应用平均值定理与（如纳入）罗必达法则。
- 构建与计算定积分：以黎曼和定义定积分，解释“累积量/净变化”；运用基本性质和换元法；把定积分与面积、位移、总成本等量联系。
- 连接微分与积分：正确应用微积分基本定理（I 与 II）求定积分与反导函数，并解释其含义。
- 选择积分方法与数值近似：熟练使用换元；（如纳入）掌握分部积分、部分分式；用梯形法或辛普森法近似并讨论误差。
- 建模与问题求解：把文字问题转化为变量、约束与目标；建立微积分模型并给出有单位、可解释的结论。
- 表达与论证（A 类要求）：书写清晰严谨的推导；能给出关键结论的证明纲要（如极限运算法则、平均值定理）或完成典型ε-δ证明。
- 合理使用技术工具：用计算器/CAS/编程进行可视化、数值检验与灵敏度分析；对结果做数量级与单位检查。
- 自我检验与学习策略：为每个主题完成“例题—变式—反例”练习；用估算与反例验证答案的合理性。

提示：
- 若课程仅覆盖单变量微分与积分，请将级数与多元内容标记为扩展或后续课程内容。
- 将每个目标映射到至少一种评估形式（计算题、证明题、应用建模、技术项目）。

Course Learning Objectives (English)
Use the following measurable, action-oriented objectives to guide instruction and study.

- Characterize functions and modeling: identify common families (polynomial, exponential, logarithmic, trigonometric, piecewise) and select appropriate models for change.
- Master limits and continuity: analyze limits graphically, algebraically, and via the ε–δ definition; classify discontinuities; handle infinite and infinitesimal limits.
- Compute and interpret derivatives: view derivatives as instantaneous rates and slopes; differentiate from the definition and rules (power, product/quotient, chain, exponential, logarithmic, trigonometric, inverse trig, implicit, inverse functions).
- Use linearization and error estimates: apply differentials and first-order Taylor approximations; describe error order and validity of approximations.
- Apply derivatives to solve problems: perform curve sketching (monotonicity, extrema, concavity, inflection, asymptotes); solve optimization and related-rates problems; apply the Mean Value Theorem and, if included, L’Hôpital’s Rule.
- Build and evaluate definite integrals: define integrals via Riemann sums; use basic properties and substitution; interpret area and net change in context.
- Connect differentiation and integration: use the Fundamental Theorem of Calculus (Parts I and II) to evaluate integrals and antiderivatives, and explain their meaning.
- Choose integration methods and numerical approximations: use substitution fluently; if included, apply integration by parts and partial fractions; approximate with trapezoidal or Simpson’s rules and discuss errors.
- Model and solve applied problems: translate word problems into variables, constraints, and objectives; construct calculus models and report unit-consistent, interpretable conclusions.
- Communicate and justify (A-track rigor): write clear, rigorous derivations; outline proofs of key results (e.g., limit laws, Mean Value Theorem) or complete typical ε–δ proofs.
- Use technology appropriately: employ calculators/CAS/programming for visualization, checks, and sensitivity analysis; validate results by unit and magnitude checks.
- Self-check and learning strategies: for each topic, complete an example–variation–counterexample triad; use estimation and counterexamples to test solution plausibility.

Notes:
- If the course scope is single-variable differential and integral calculus only, mark sequences/series or multivariable topics as extensions or for subsequent courses.
- Map each objective to at least one assessment type (procedural, proof, applied modeling, technology-based).

课程目标：周末班项目管理入门

总目标
- 在课程结束时，完成一个从立项到启动的“最小可行项目计划”，并能用结构化方式向干系人进行5分钟汇报。

具体达成目标与操作指引
1) 定义项目方向
- 明确项目愿景与SMART目标；写出不超过150字的项目陈述。
- 产出物：项目目标陈述（含成功标准与不在范围事项）。

2) 确定范围与交付物
- 列出主要可交付成果与验收标准；用Scope Statement记录边界。
- 产出物：范围说明书（包含交付物清单和非范围清单）。

3) 拆解工作与排期
- 以WBS将项目分解到可执行的工作包；绘制基础甘特图或看板列。
- 产出物：WBS（3层为宜）与初版进度计划；标注里程碑。

4) 估算资源与成本
- 标识关键角色与职责，用RACI明确分工；进行粗略量级估算（ROM）。
- 产出物：RACI表与成本估算表（列出主要成本项与假设）。

5) 识别与应对风险
- 建立风险登记册；评估概率与影响，指定应对策略（避免/减轻/转移/接受）。
- 产出物：前5大风险清单（含触发器与应对预案）。

6) 规划沟通与干系人
- 绘制干系人地图（影响力×关注度）；制定沟通计划（频率、渠道、责任）。
- 产出物：沟通矩阵与会议节奏表。

7) 设定质量与变更控制
- 定义完成定义（DoD）与验收标准；设计轻量变更流程（提交-评审-决策）。
- 产出物：质量标准清单与变更单模板。

8) 准备启动与汇报
- 编写一页项目章程；制作5分钟状态汇报（目标、范围、进度、风险、下一步）。
- 产出物：项目章程（1页）与简报（不超过6页）。

达成判据（用于自测或结课评估）
- 所有产出物齐备、逻辑一致、假设明确；关键路径与前三大风险可被清晰解释。
- 汇报在5分钟内完成，回答提问能回溯到相应计划或依据。

提示
- 使用现成模板（WBS、RACI、风险登记册）以节省时间。
- 将数字假设写清（如工时、费率、资源可用性）以便复核与调整。
- 以“足够好”为目标，避免过度细化；重点确保决策依据透明与可追踪。

Course goal: Build and deliver a reliable, decision-focused data dashboard from requirements to rollout.

To achieve this goal, do the following:
1) Define the use case
- Identify the target audience, key decisions, and business questions.
- Select 3–5 primary KPIs with clear owners, units, and refresh cadence.
- Write a one-page brief capturing scope, success criteria, and constraints.

2) Specify metrics and data
- List data sources, data grain, time windows, and required fields.
- Document metric definitions, filters, and calculations in a metric dictionary.
- Validate logic with sample queries or small test extracts.

3) Model and prepare data
- Connect to sources; clean, join, and aggregate as needed.
- Create a calendar/date table and conformed dimensions.
- Handle missing values, outliers, and time zone alignment.
- Implement row-level security if needed.

4) Design the dashboard
- Sketch wireframes; plan a clear visual hierarchy (overview → drill-down → detail).
- Choose appropriate chart types for each KPI and interaction (filters, drill-through, tooltips).
- Apply consistent labeling, number formats, and explanatory titles/subtitles.

5) Build in a BI tool
- Implement calculations, parameters, slicers/filters, and navigation.
- Standardize color semantics (e.g., status, variance) and use color-blind-safe palettes.
- Add helpful tooltips, annotations, and empty-state messages.

6) Assure quality and performance
- Reconcile every KPI against a source of truth; log test cases and results.
- Check edge cases (date boundaries, nulls, small/large numbers).
- Optimize load time by limiting high-cardinality visuals and pre-aggregating when appropriate.

7) Ensure clarity and accessibility
- Use readable fonts, adequate contrast, and concise labels.
- Avoid misleading axes and truncated scales where inappropriate.
- Provide keyboard-accessible interactions if supported by the tool.

8) Publish and govern
- Set permissions, data refresh schedules, and ownership.
- Version-control the workbook/model and maintain a changelog.
- Document data lineage and dependencies.

9) Measure adoption and iterate
- Track usage analytics and collect stakeholder feedback.
- Prioritize improvements; remove or simplify low-value elements.
- Review KPI relevance quarterly and update definitions as needed.

Deliverables to meet the goal:
- Production-ready dashboard URL/file with defined interactions.
- Metric dictionary and data model diagram.
- Test and validation checklist with results.
- User guide with example decision workflows.

Success criteria:
- All KPIs match the validated source within agreed tolerances.
- Dashboard loads within the target performance threshold for the chosen tool/environment.
- Stakeholders can complete top tasks in under two minutes each.
- Documentation is complete and up to date.