Understand calculus, don't just memorize it
8 topic modules. 360+ practice problems — each with step-by-step solutions. Free to read. No account required.
Compute lim(x→4) of (x² − 16) / (x − 4)
Every problem includes a full walkthrough. Read the Limits module →
Curriculum
Eight modules covering Calculus I–III. Each module is free to read with worked examples.
Limits & Continuity
What does it mean for a function to approach a value? Build intuition for limits through direct substitution, factoring, the squeeze theorem, and L'Hôpital's rule.
IIDerivatives
The derivative measures instantaneous rate of change. Master the power rule, product and quotient rules, chain rule, and implicit differentiation.
IIIApplications of Derivatives
Solve optimization problems, related rates, and curve sketching. Understand how derivatives describe the physical world.
IVIntegrals
Integration is the reverse of differentiation — and much more. Master substitution, integration by parts, and the Fundamental Theorem of Calculus.
VSeries & Sequences
When does an infinite sum converge? Study convergence tests, power series, and Taylor expansions that underpin modern mathematics.
VIDifferential Equations
Equations involving derivatives model growth, decay, and change. Solve separable and first-order linear equations with real applications.
VIIApplications of Integration
Use integrals to compute areas between curves, volumes of revolution, arc lengths, and work done by a force.
VIIIMultivariable & Vector Calculus
Extend calculus to multiple dimensions with partial derivatives, double and triple integrals, and vector fields.
How we teach
Not shortcuts. Not tricks. Understanding.
Intuition before formulas
Each module builds understanding of why a concept works before introducing the formal machinery.
Worked examples throughout
Detailed examples solved step by step — you see the thinking process, not just the answer.
Immediate feedback
Practice problems check your answer instantly. When you're wrong, hints come first — then the full solution.
Progressive difficulty
Problems go from straightforward to challenging. Easy problems build confidence; hard problems build depth.
Questions
What background do I need?+
Algebra and basic trigonometry. If you're comfortable with functions, factoring, and solving equations, you're ready to start.
Is this free?+
Yes — everything is completely free. Modules, practice problems, topic tests, and learning paths are all available at no cost. You can create a free account to track your progress.
How is this different from a textbook?+
You get the same rigor, but with instant feedback. Every practice problem checks your answer immediately and walks through the solution step by step.
What topics are covered?+
Limits, derivatives, applications of derivatives, integrals, series & sequences, and differential equations. This covers a standard Calculus I–II curriculum.
Can I try the practice problems first?+
Yes. All practice problems are free. Visit the practice page to start — no account needed.
Who made this?+
CalcPath is an independent project built to make calculus more accessible. Every explanation is written to build understanding, not just get you through an exam.
Start with Limits
The foundation of all calculus. Read at your own pace.