借势AI系列：从教材到练习题-AIGC助力教育资源的智能化生成

pip install openai

import openai

# 设置API密钥
openai.api_key = 'your-api-key'

def generate_study_outline(topic):
    prompt = f"Generate a study outline for the topic '{topic}' in Calculus. The outline should include key concepts, definitions, and example problems."
    
    response = openai.Completion.create(
        engine="text-davinci-003",
        prompt=prompt,
        max_tokens=500
    )
    
    outline = response.choices[0].text.strip()
    return outline

# 生成微积分学习提纲
topic = "Calculus"
study_outline = generate_study_outline(topic)
print(study_outline)

1. Introduction to Calculus
   - Definition of calculus
   - Importance of calculus in real-world applications

2. Limits and Continuity
   - Definition of a limit
   - How to compute limits
   - Continuous functions

3. Derivatives
   - Definition of a derivative
   - Rules of differentiation
   - Chain rule and product rule

4. Applications of Derivatives
   - Finding maxima and minima
   - Optimization problems
   - Related rates

5. Integrals
   - Definition of an integral
   - Fundamental theorem of calculus
   - Techniques of integration

def generate_exercise_questions(topic):
    prompt = f"Generate practice problems for the topic '{topic}' in Calculus. Include solutions to the problems."
    
    response = openai.Completion.create(
        engine="text-davinci-003",
        prompt=prompt,
        max_tokens=600
    )
    
    questions = response.choices[0].text.strip()
    return questions

# 生成微积分练习题
questions = generate_exercise_questions(topic)
print(questions)

1. Compute the limit: lim (x -> 0) (sin(x) / x).
   Solution: 1.

2. Differentiate the following function: f(x) = 3x^2 + 2x + 5.
   Solution: f'(x) = 6x + 2.

3. Find the critical points of the function f(x) = x^3 - 3x^2 + 2.
   Solution: Critical points occur at x = 1 and x = 2.

4. Compute the integral of f(x) = 5x^4.
   Solution: ∫5x^4 dx = x^5 + C.

def generate_multimedia_lesson(topic):
    prompt = f"Generate a multimedia lesson outline for the topic '{topic}', including references to diagrams, animations, and videos for better understanding."
    
    response = openai.Completion.create(
        engine="text-davinci-003",
        prompt=prompt,
        max_tokens=800
    )
    
    multimedia_lesson = response.choices[0].text.strip()
    return multimedia_lesson

# 生成包含多媒体的微积分课件提纲
topic = "Calculus"
lesson_plan = generate_multimedia_lesson(topic)
print(lesson_plan)

1. Introduction to Limits
   - Concept of limits with a diagram showing the limit of a function as x approaches a value.
   - Video: Explanation of limits using real-world examples (include a link to a video).

2. Derivatives
   - Animation: Visualizing the slope of a tangent line.
   - Diagram: Derivative rules (product rule, quotient rule) in a flowchart.
   
3. Applications of Derivatives
   - Video: Optimization problems in physics and economics.
   - Interactive simulation: Changing parameters and observing changes in maximum/minimum values.

def generate_personalized_study_plan(student_level, topic):
    prompt = f"Create a personalized study plan for a student at {student_level} level on the topic '{topic}'. Include daily tasks, exercises, and resource recommendations."
    
    response = openai.Completion.create(
        engine="text-davinci-003",
        prompt=prompt,
        max_tokens=800
    )
    
    study_plan = response.choices[0].text.strip()
    return study_plan

# 为中级水平学生生成个性化的微积分学习路径
student_level = "intermediate"
topic = "Calculus"
personalized_plan = generate_personalized_study_plan(student_level, topic)
print(personalized_plan)

Day 1: Introduction to Limits
   - Read: Chapter 1 of the textbook.
   - Watch: Video on "Introduction to Limits."
   - Exercise: Complete problems 1-5 from Section 1.1.

Day 2: Exploring Derivatives
   - Read: Chapter 2, Section 2.1.
   - Practice: Solve exercises 10-15 (derivative rules).
   - Interactive: Use an online derivative calculator to explore different functions.

Day 3: Advanced Derivatives and Applications
   - Watch: Advanced lesson on "Applications of Derivatives."
   - Practice: Solve optimization problems and submit for feedback.
   - Extra resources: Review online simulation on related rates.

def virtual_teacher_interaction(question):
    prompt = f"As a virtual teacher, answer the following question from a student: '{question}'"
    
    response = openai.Completion.create(
        engine="text-davinci-003",
        prompt=prompt,
        max_tokens=300
    )
    
    answer = response.choices[0].text.strip()
    return answer

# 虚拟教师回答学生关于导数的疑问
student_question = "What is the chain rule in calculus, and how do I use it?"
answer = virtual_teacher_interaction(student_question)
print(answer)

The chain rule is a method for finding the derivative of a composite function. If you have two functions, f(x) and g(x), and you want to differentiate the composite function f(g(x)), the chain rule states that:

d/dx [f(g(x))] = f'(g(x)) * g'(x)

To use the chain rule, first take the derivative of the outer function (f) with respect to the inner function (g), and then multiply it by the derivative of the inner function (g). For example:

If f(x) = (2x + 3)^2, then f'(x) = 2(2x + 3) * 2.