commit a779590a7567d209234df2c76ad795dbe9a18c94 Author: ALE Seeder Date: Thu Jan 1 00:00:00 2026 +0000 seed: example course content diff --git a/COURSE.md b/COURSE.md new file mode 100644 index 0000000..5aef5e4 --- /dev/null +++ b/COURSE.md @@ -0,0 +1,28 @@ +--- +id: calculus-it-ale-example +title: "Basic Calculus for IT — First Year" +year: 2026 +language: en +description: "Introductory calculus (limits, derivatives, integrals) with light programming-oriented tasks." +instructors: + - "Instructor Name" +tags: + - calculus + - it + - first-year +version: "0.1" +--- + +# Basic Calculus for IT — First Year (ALE Example) + +This repository is an **ALE example course**. + +## How to use this course in ALE +1) Add this repository URL and a branch in ALE (Instructor role). +2) Click **Sync Course Content**. +3) Students will see Activities and can start/continue sessions. + +## Authoring notes (quick) +- Materials live in `materials/` and headings become anchors. +- Activities live in `activities/`. +- Every task/question includes `Refs:` in the form `material_id#anchor`. diff --git a/README.md b/README.md new file mode 100644 index 0000000..0bc90c7 --- /dev/null +++ b/README.md @@ -0,0 +1,11 @@ +# Basic Calculus for IT — Example ALE Course + +This repository demonstrates the ALE activity content format: +- `COURSE.md` +- `materials/` (Markdown with headings) +- `activities/` (mode-aware tasks with refs) + - understanding activity + - homework activity + - strict test activities + +It is intentionally deterministic-friendly for sync and contract fixtures. diff --git a/activities/01-limits-and-derivatives-understanding.md b/activities/01-limits-and-derivatives-understanding.md new file mode 100644 index 0000000..247e732 --- /dev/null +++ b/activities/01-limits-and-derivatives-understanding.md @@ -0,0 +1,56 @@ +--- +id: act-01-limits-and-derivatives-understanding +title: "Unit 01 — Limits and Derivatives" +mode: understanding +open_at: "2026-02-01T00:00:00+01:00" +close_at: "2026-12-31T23:59:59+01:00" +retakes_enabled: true +max_attempts: 999 +grade_max: 100 +--- + +# Unit 01 — Limits and Derivatives + +## T1 +Type: essay +Points: 20 +Prompt: Explain in your own words what a limit means and how it is used to define the derivative. +Refs: +- mat-01-limits-continuity#what-is-a-limit +- mat-02-derivatives#derivative-definition +Rubric: +- Clear conceptual explanation (10) +- Mentions difference quotient and limiting process (10) + +## T2 +Type: essay +Points: 25 +Prompt: Compute the limit of (sin x)/x as x approaches 0 and briefly justify your result. +Refs: +- mat-01-limits-continuity#special-limits +Rubric: +- Correct limit value (15) +- Justification is mathematically coherent (10) + +## T3 +Type: essay +Points: 30 +Prompt: Differentiate f(x)=x^3-2x+sin x and simplify the result. +Refs: +- mat-02-derivatives#derivative-rules +- mat-02-derivatives#derivatives-of-common-functions +Rubric: +- Applies power rule correctly (15) +- Differentiates sin x correctly (10) +- Simplifies correctly (5) + +## T4 +Type: file +Points: 25 +Prompt: Create a small Python script @solutions/numerical_derivative.py that approximates the derivative using a finite difference and prints the approximate derivative of x^3 at x=2 with step h=1e-5. +Refs: +- mat-02-derivatives#tangent-line-approximation +Rubric: +- Script runs and prints a numeric result (10) +- Uses finite difference correctly (10) +- Code is readable (5) diff --git a/activities/02-integrals-and-applications-homework.md b/activities/02-integrals-and-applications-homework.md new file mode 100644 index 0000000..b9d4a90 --- /dev/null +++ b/activities/02-integrals-and-applications-homework.md @@ -0,0 +1,55 @@ +--- +id: act-02-integrals-and-applications-homework +title: "Unit 02 — Integrals and Applications" +mode: homework +open_at: "2026-02-01T00:00:00+01:00" +close_at: "2026-12-31T23:59:59+01:00" +retakes_enabled: true +max_attempts: 999 +grade_max: 100 +--- + +# Unit 02 — Integrals and Applications + +## T1 +Type: essay +Points: 25 +Prompt: Explain the difference between an antiderivative and a definite integral (interpretation). +Refs: +- mat-04-integrals#antiderivative +- mat-04-integrals#definite-integral +Rubric: +- Correct distinction (15) +- Meaning/interpretation is clear (10) + +## T2 +Type: essay +Points: 25 +Prompt: Compute the definite integral from 0 to 1 of 3x^2 dx. +Refs: +- mat-04-integrals#basic-integration-rules +- mat-04-integrals#definite-integral +Rubric: +- Correct antiderivative and evaluation (20) +- Clear presentation (5) + +## T3 +Type: essay +Points: 25 +Prompt: State the fundamental theorem of calculus in your own words and explain what it connects. +Refs: +- mat-04-integrals#fundamental-theorem-of-calculus +Rubric: +- Correct statement at a high level (15) +- Explains connection between differentiation and accumulation (10) + +## T4 +Type: essay +Points: 25 +Prompt: Optimization mini-task: For f(x)=x^2-4x+1, find the x that minimizes f(x) and the minimum value. +Refs: +- mat-03-derivative-applications#optimization-workflow +- mat-02-derivatives#critical-points +Rubric: +- Computes derivative and critical point correctly (15) +- Correct minimum value and interpretation (10) diff --git a/activities/03-limits-derivatives-test.md b/activities/03-limits-derivatives-test.md new file mode 100644 index 0000000..32a1d35 --- /dev/null +++ b/activities/03-limits-derivatives-test.md @@ -0,0 +1,51 @@ +--- +id: act-03-limits-derivatives-test +title: "Test 01 — Limits and Derivatives Quiz" +mode: test +open_at: "2026-02-05T00:00:00+01:00" +close_at: "2026-12-31T23:59:59+01:00" +retakes_enabled: true +max_attempts: 5 +grade_max: 100 +time_limit_seconds: 1500 +--- + +# Test 01 — Limits and Derivatives Quiz + +## T1 +Type: mcq +Points: 25 +Prompt: The derivative of a function at a point is defined as: +Refs: +- mat-02-derivatives#derivative-definition +Choices: +- [ ] The area under the curve from 0 to x +- [x] The limit of the difference quotient as the step approaches 0 +- [ ] The average rate of change over an interval + +## T2 +Type: short +Points: 25 +Prompt: Compute d/dx of x^4. +Refs: +- mat-02-derivatives#derivative-rules +Answer: 4x^3 + +## T3 +Type: mcq +Points: 25 +Prompt: What is the limit of (sin x)/x as x approaches 0? +Refs: +- mat-01-limits-continuity#special-limits +Choices: +- [ ] 0 +- [x] 1 +- [ ] Does not exist + +## T4 +Type: short +Points: 25 +Prompt: Differentiate sin x. +Refs: +- mat-02-derivatives#derivatives-of-common-functions +Answer: cos x diff --git a/activities/04-integrals-test.md b/activities/04-integrals-test.md new file mode 100644 index 0000000..f49ca4b --- /dev/null +++ b/activities/04-integrals-test.md @@ -0,0 +1,53 @@ +--- +id: act-04-integrals-test +title: "Test 02 — Integrals Quiz" +mode: test +open_at: "2026-02-12T00:00:00+01:00" +close_at: "2026-12-31T23:59:59+01:00" +retakes_enabled: true +max_attempts: 5 +grade_max: 100 +time_limit_seconds: 1500 +--- + +# Test 02 — Integrals Quiz + +## T1 +Type: mcq +Points: 25 +Prompt: A definite integral is best interpreted as: +Refs: +- mat-04-integrals#definite-integral +Choices: +- [x] Accumulated change / signed area under the curve +- [ ] The slope of the tangent line +- [ ] A function that undoes differentiation only in indefinite form + +## T2 +Type: short +Points: 25 +Prompt: Compute the integral from 0 to 1 of 2x dx. +Refs: +- mat-04-integrals#basic-integration-rules +- mat-04-integrals#definite-integral +Answer: 1 + +## T3 +Type: mcq +Points: 25 +Prompt: The fundamental theorem of calculus connects: +Refs: +- mat-04-integrals#fundamental-theorem-of-calculus +Choices: +- [ ] Limits and continuity +- [x] Differentiation and integration +- [ ] Optimization and related rates + +## T4 +Type: short +Points: 25 +Prompt: An antiderivative of 3x^2 is: +Refs: +- mat-04-integrals#antiderivative +- mat-04-integrals#basic-integration-rules +Answer: x^3 diff --git a/materials/01-limits-and-continuity.md b/materials/01-limits-and-continuity.md new file mode 100644 index 0000000..af79984 --- /dev/null +++ b/materials/01-limits-and-continuity.md @@ -0,0 +1,23 @@ +--- +id: mat-01-limits-continuity +title: "Limits and continuity" +--- + +# Limits and continuity + +## What is a limit +A limit describes the value that a function approaches as the input approaches a point. + +## Basic limit laws +If limits exist, they follow linearity, product, quotient, and power laws. + +## Special limits +Two important special limits are: +- sin x / x as x approaches 0 +- (1 + 1/n)^n as n grows + +## Continuity +A function is continuous at a point if the limit equals the function value. + +## One sided and infinite limits +Sometimes we consider limits from the left or right, or limits that diverge to infinity. diff --git a/materials/02-derivatives-rules.md b/materials/02-derivatives-rules.md new file mode 100644 index 0000000..6193bc8 --- /dev/null +++ b/materials/02-derivatives-rules.md @@ -0,0 +1,28 @@ +--- +id: mat-02-derivatives +title: "Derivatives: definition and rules" +--- + +# Derivatives + +## Derivative definition +The derivative at a point is the limit of the difference quotient. + +## Derivative rules +Key rules include: +- constant and power rule +- sum and product rule +- quotient rule +- chain rule + +## Derivatives of common functions +Examples: +- derivative of x^n +- derivative of sin x and cos x +- derivative of e^x and ln x + +## Tangent line approximation +A derivative gives the slope of the tangent line and supports local linear approximation. + +## Critical points +Critical points occur where the derivative is zero or undefined (within the domain). diff --git a/materials/03-derivative-applications.md b/materials/03-derivative-applications.md new file mode 100644 index 0000000..92a64bd --- /dev/null +++ b/materials/03-derivative-applications.md @@ -0,0 +1,23 @@ +--- +id: mat-03-derivative-applications +title: "Applications of derivatives" +--- + +# Applications of derivatives + +## Increasing decreasing and extrema +Use the sign of the derivative to determine where a function increases or decreases, and locate maxima or minima. + +## Optimization workflow +Typical steps: +1) define the objective function +2) compute derivative +3) find critical points +4) test candidates (including endpoints if relevant) +5) interpret the solution + +## Related rates idea +Differentiate an equation relating variables with respect to time to connect their rates of change. + +## Error and sensitivity +Derivatives quantify sensitivity: how much output changes per unit input. diff --git a/materials/04-integrals-basics.md b/materials/04-integrals-basics.md new file mode 100644 index 0000000..10c2595 --- /dev/null +++ b/materials/04-integrals-basics.md @@ -0,0 +1,25 @@ +--- +id: mat-04-integrals +title: "Integrals: basics and the fundamental theorem" +--- + +# Integrals + +## Antiderivative +An antiderivative is a function whose derivative is the integrand. + +## Definite integral +A definite integral measures accumulated change and is interpreted as signed area under a curve. + +## Fundamental theorem of calculus +The fundamental theorem connects derivatives and integrals: +- differentiation and accumulation are inverse operations (under suitable conditions) + +## Basic integration rules +Rules include: +- linearity +- power rule for integrals (with n not equal to -1) +- integral of 1/x is ln|x| + +## Substitution idea +Substitution changes variables to simplify the integrand when a composition structure appears.