1TEACH ME
Explain [topic] in Calculus I & II to me step by step at a [beginner / intermediate / advanced] level. Use a simple example first, then a harder one, and ask me a question to check I understood.
Sale!
Calculus I & II: Limits, Derivatives and Integrals – AI Tutor-Enabled Course Book
Original price was: $24.00.$14.00Current price is: $14.00.
- AI Tutor-enabled
- Self-paced
- Beginner → Advanced
- Modules
- 10
- Study time
- About 40 hours
- Format
- Digital course book (PDF)
- Projects
- 4 + capstone
Understand calculus, not just memorise it. Solve exam problems step by step with an AI tutor beside you.
TypeNotes & books
DeliveryInstant download after payment
- Instant download after payment
- Lifetime access in My Courses
- Secure checkout
AI Tutor-Enabled Self-Paced Professional Course Book
Understand calculus, not just memorise it. Solve exam problems step by step with an AI tutor beside you.
Calculus I & II is a self-paced course book that takes you from limits and continuity to integration techniques, sequences and series. Every topic is explained in plain language, worked through with examples and backed by practice and AI Tutor prompts, so you can learn at your own pace and check your own work.
Is this you?
- You can follow examples in class but freeze on a new problem
- Limits and the epsilon idea feel abstract
- You mix up the product, quotient and chain rules
- Integration by parts and substitution feel like guesswork
- Word problems on rates and optimisation are hard to set up
- Series convergence tests all blur together
This course book is built to close exactly that gap: clear explanations, worked practice and an AI tutor that guides you instead of just giving answers.
- Learn
- Practise
- Check with your AI Tutor
- Build projects
- Get assessed
What you’ll learn in 10 practical modules
01 Functions and Graphs RefresherRebuild the foundations calculus relies on.
Key concepts
- Domain, range and composition
- Exponential, logarithmic and trigonometric functions
- Transformations of graphs
Sample practice
- Sketch f(x)=2(x−1)²+3 from y=x²
- Find the domain of ln(4−x²)
02 Limits and ContinuityLearn what a limit means and how to evaluate one.
Key concepts
- One-sided limits
- Limit laws and algebraic techniques
- Continuity and the Intermediate Value Theorem
Sample practice
- Evaluate lim(x→2) (x²−4)/(x−2)
- Show x³−x−1=0 has a root in [1,2]
03 The DerivativeDefine the derivative and connect it to rates of change.
Key concepts
- Derivative as a limit
- Tangent lines and instantaneous rate
- Differentiability
Sample practice
- Use the definition to differentiate f(x)=x²
- Find the tangent to y=√x at x=4
04 Differentiation RulesMaster the rules you will use in every later topic.
Key concepts
- Power, product and quotient rules
- Chain rule
- Derivatives of trig, exponential and log functions
Sample practice
- Differentiate y=x²·e^(3x)
- Differentiate y=sin(x²+1)
05 Applications of DerivativesUse derivatives to analyse and optimise.
Key concepts
- Related rates
- Maxima, minima and the first and second derivative tests
- Optimisation problems
Sample practice
- A ladder slides down a wall: find the rate the top falls
- Maximise the area of a rectangle with perimeter 40
06 Integrals and the Fundamental TheoremConnect area, antiderivatives and the Fundamental Theorem.
Key concepts
- Riemann sums
- Definite and indefinite integrals
- Fundamental Theorem of Calculus
Sample practice
- Evaluate ∫₀² (3x²+1) dx
- Use FTC to find d/dx ∫₀^x cos t dt
07 Integration TechniquesBuild a toolkit for harder integrals.
Key concepts
- Substitution
- Integration by parts
- Partial fractions and trigonometric integrals
Sample practice
- Evaluate ∫ x·e^x dx
- Evaluate ∫ 1/(x²−1) dx
08 Applications of IntegrationApply integrals to geometry and science.
Key concepts
- Area between curves
- Volumes by discs and shells
- Work and average value
Sample practice
- Find the area between y=x² and y=x
- Find the volume when y=√x on [0,4] rotates about the x-axis
09 Sequences and SeriesDecide when infinite sums converge.
Key concepts
- Geometric and telescoping series
- Convergence tests
- Absolute and conditional convergence
Sample practice
- Does Σ 1/n² converge?
- Test Σ (−1)ⁿ/n for convergence
10 Power Series and Taylor PolynomialsApproximate functions with polynomials.
Key concepts
- Radius and interval of convergence
- Taylor and Maclaurin series
- Error estimates
Sample practice
- Find the Maclaurin series of e^x
- Approximate sin(0.1) with a third-degree polynomial
Use AI as your personal tutor, not an answer machine
The course book includes ready-to-use prompts for ChatGPT, Copilot, Gemini or any capable AI assistant. Each mode makes the AI teach, guide, check or challenge you, so you build real understanding.
2GUIDE ME
I am working on this problem: [paste problem]. Do not give me the answer. Give me one hint at a time and wait for my next step.
3CHECK MY WORK
Here is my solution: [paste working]. Check each step, tell me exactly where any mistake is and why, but let me correct it myself.
4CHALLENGE ME
Give me three exam-style Calculus I & II questions on [topic], getting harder each time. Wait for my answers, then mark them and explain what I missed.
5HELP ME APPLY IT
Show me how [topic] from Calculus I & II is used in a real situation, then give me a small task to try it myself.
Verify before you trust
- Ask a clear, specific question
- Solve it yourself first
- Test the answer by substituting or estimating
- Check it against the worked examples in the book
- Validate with your teacher if the AI and the book disagree
Don’t just study it. Build evidence you can show.
Project 1
Rates of Change Report
Model a real rate-of-change situation, such as a draining tank, and explain each step.
Project 2
Optimisation Case Study
Choose a business or design problem and find the optimal solution with derivatives.
Project 3
Area and Volume Workbook
Solve a set of geometry problems with integrals and show your working.
Project 4
Series Approximation Investigation
Compare Taylor approximations against true values and discuss the error.
Final capstone
Calculus Problem-Solving Portfolio
Assemble 20 fully worked problems across all modules, with explanations a classmate could follow.
Who this course book is for
- High school students taking AP or A-level calculus
- First-year university students
- Engineering and science students
- Economics and business students
- Adults returning to study
- Self-learners and homeschoolers
Where these skills lead
- Engineering
- Data science
- Economics
- Finance
- Physics
- Teaching
The course builds skills and evidence; it does not guarantee employment or exam results.
What you receive
- 10 progressive learning modules
- Learning objectives, key concepts and practice problems
- Ready-to-use AI Tutor prompts for five learning modes
- Practical projects and a capstone
- Portfolio guide, assessment rubric and completion checklist
- Instant download and lifetime access in My Courses
| Format | Digital course book (PDF) |
|---|---|
| Learning mode | Self-paced + AI Tutor |
| Level | Beginner → Advanced |
| Study time | About 40 hours |
| Created by | NoteStore Academy |
| Certificate | Optional project and portfolio assessment |
| Licence | Personal learning use |
| Updated | November 2, 2026 |
Certificate pathway
Want a certificate? Submit your work for optional assessment by NoteStore Academy. Certificates reflect demonstrated work, so they are not issued automatically with purchase.
Module practice work20%
Projects 1–440%
Capstone project30%
Portfolio and reflection10%
Frequently asked questions
Is this suitable if I struggled with maths before?
Yes. Module 1 rebuilds the algebra and functions you need, and the AI Tutor prompts let you slow down on any step.
Does it cover both Calculus I and Calculus II?
Yes. Modules 1–5 cover differential calculus and modules 6–10 cover integral calculus, sequences and series.
Can I use it alongside my university course?
Yes. The modules follow the order most first-year calculus courses use, so you can study each topic as it comes up in class.
Do I need a graphing calculator?
No. A free graphing tool such as Desmos is helpful for visualising, but all examples can be done by hand.
How do I get the course book after paying?
Your download link appears on the order confirmation page straight away, is emailed to you, and stays in My Courses in your account.
Which AI assistant can I use?
Any capable assistant works, such as ChatGPT, Microsoft Copilot or Google Gemini. The prompts are written to work with all of them.
Start today
Calculus I & II: Limits, Derivatives and Integrals
Self-paced, AI Tutor-enabled and project-based. Download instantly after payment and keep it in My Courses.
Original price was: $24.00.$14.00Current price is: $14.00.
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