Help Center

Everything you need to get the most out of NumericaLTI — from your first solve to full Canvas LTI integration.

Getting Started

Creating your account

Visit /auth/signup and register with your email address. After confirming your email you will be automatically placed on the Free tier, which gives you 5 interactive solves per day.

Choosing a plan

From your dashboard, click Billing in the left sidebar. Three tiers are available:

Free — 5 solves/day, access to all solver methods, read-only problem sets.
Student ($9/mo) — Unlimited solves, AI tutor hints, personal problem set history, study groups.
Classroom ($29/mo) — Everything in Student, plus instructor analytics, problem set management, Canvas LTI grade passback.

Navigating the dashboard

After login you land on your personal dashboard. The left sidebar gives you access to:

Dashboard — recent activity and quick stats.
Interactive Solver — choose a method, enter an equation, and visualize convergence.
Problem Sets — guided exercises assigned by your instructor or available publicly.
Study Groups — collaborative sessions with classmates.
Billing — manage your subscription and view invoices.
Help — you are here.

Interactive Solver

The solver supports seven numerical methods. Each method requires different inputs — the form adapts automatically when you select a method.

Newton-Raphson

Root Finding

Use when: You have a smooth, differentiable function and a reasonable initial guess near the root.

Required Inputs

EquationA function of one variable, e.g. x^3 - 2*x - 5

VariableThe variable letter (typically x)

Initial GuessA number close to the root

Tips

•Derivatives are computed automatically via symbolic differentiation.
•If the derivative is zero at your guess, the method may fail — try a different guess.
•Use e for Euler's number (e.g. e^x), pi for π.
•Trig functions: sin(x), cos(x), tan(x). Log: log(x) or ln(x).

Example:Find root of x³ − 2x − 5 — x^3 - 2*x - 5 (Guess: 2)

Bisection

Root Finding

Use when: You know two points a and b where the function has opposite signs (a sign change guarantees a root between them by the Intermediate Value Theorem).

Required Inputs

EquationFunction equal to zero, e.g. x^2 - 4

VariableThe variable letter

aLeft endpoint (f(a) and f(b) must have opposite signs)

bRight endpoint

Tips

•Guaranteed to converge as long as f(a) and f(b) have opposite signs.
•Slower than Newton-Raphson but always safe — good for initial bracketing.
•Each iteration halves the interval, so you get about one decimal digit of accuracy every 3–4 iterations.

Example:Root of x² − 4 on [1, 3] — x^2 - 4 (a=1, b=3)

Secant

Root Finding

Use when: You want Newton-Raphson speed without computing a derivative — the secant method approximates the derivative from two prior iterates.

Required Inputs

EquationFunction of one variable

VariableThe variable letter

Initial GuessA starting point; the solver uses x₀ and x₀+1 as the two seed points

Tips

•Superlinear convergence (order ≈ 1.618) — faster than bisection, slightly slower than Newton.
•May diverge if the two seed points have a very flat slope between them.
•Good choice when symbolic differentiation fails (e.g. piecewise or externally-defined functions).

Example:Root of cos(x) − x — cos(x) - x (Guess: 0.5)

Fixed-Point Iteration

Root Finding

Use when: Your equation is already expressed as x = g(x), or you can rearrange it that way. Convergence requires |g′(x)| < 1 near the root.

Required Inputs

Equation (g(x))The right-hand side of x = g(x), e.g. sqrt(2 + x)

VariableThe variable letter

Initial GuessStarting point

Tips

•Enter g(x) only — the solver iterates xₙ₊₁ = g(xₙ).
•If the sequence diverges, try rearranging the equation into a different g(x) form.
•A cobweb diagram is rendered showing convergence toward y = x.

Example:x = √(2 + x) — sqrt(2 + x) (Guess: 1)

Gaussian Elimination

Linear Systems

Use when: You have a system of linear equations Ax = b to solve exactly.

Required Inputs

Matrix (augmented)Enter as a JSON 2D array: the first n columns are A, the last column is b. Example for 2×2: [[2,1,5],[1,-1,1]]

Tips

•Maximum size is 8×8 (8 equations, 8 unknowns).
•The system must be square and non-singular.
•Partial pivoting is applied automatically for numerical stability.
•The solution vector x is shown in the results panel.

Example:Solve 2x+y=5, x−y=1 — [[2,1,5],[1,-1,1]]

Lagrange Interpolation

Interpolation

Use when: You have a set of data points (xᵢ, yᵢ) and want to find the polynomial that passes through all of them.

Required Inputs

PointsEnter as a JSON array of [x, y] pairs: [[x₁,y₁],[x₂,y₂],…]. Minimum 2 points, maximum 15.

Tips

•The degree of the interpolating polynomial is n−1 where n is the number of points.
•Evenly-spaced points can cause Runge's phenomenon at high degrees — consider Chebyshev nodes for better behaviour.
•The polynomial is displayed in expanded form and rendered on the canvas.

Example:Interpolate (0,1),(1,3),(2,7) — [[0,1],[1,3],[2,7]]

Simpson's Rule

Numerical Integration

Use when: You want to estimate a definite integral ∫ₐᵇ f(x) dx numerically.

Required Inputs

EquationThe integrand f(x)

VariableIntegration variable

aLower bound

bUpper bound

nNumber of sub-intervals (must be even; default 4, max 100)

Tips

•Higher n gives more accurate results — try n=10 or n=20 for smoother curves.
•Error decreases as O(h⁴) — much faster than the Trapezoidal Rule.
•The shaded area under the curve is visualized on the canvas.
•The integrand is shaded in the canvas visualizer between a and b.

Example:∫₀¹ e^(−x²) dx, n=10 — e^(-x^2) (a=0, b=1, n=10)

Canvas visualizer — zoom & pan

After solving, an interactive canvas renders your function and the solver's path. You can:

Scroll to zoom in and out.
Click and drag to pan.
The curve is re-sampled at full resolution for the current viewport — no pixelation at any zoom level.
Extra equations can be overlaid in a second colour by entering them in the "Additional curves" field.

Equation syntax reference

You want	Type this	Notes
x²	`x^2`	Caret for exponentiation
√x	`sqrt(x)`
eˣ	`e^x or exp(x)`
ln x	`log(x) or ln(x)`	Natural log
log₁₀ x	`log10(x)`
sin, cos, tan	`sin(x), cos(x), tan(x)`	In radians
π	`pi`
e	`e`	Euler's number ≈ 2.718
Multiplication	`2x (explicit )`	2x without * may fail
\|x\|	`abs(x)`	Absolute value

Problem Sets

For students — working through a problem set

Navigate to Problem Sets in the sidebar.
Click on a set to expand it and view the individual problems.
Each problem shows the method, equation, and any required parameters.
Click Open in Solver to pre-fill the Interactive Solver with that problem's parameters.
Submit your result — it is automatically saved and (if graded via Canvas LTI) sent to your course gradebook.

For instructors — creating a problem set

Go to Problem Sets under the Instructor section of the sidebar.
Click New Problem Set and give it a name and topic.
Use the Add Problem button to add problems one at a time.
For each problem specify: title, method, equation, and the method-specific parameters (initial guess, bounds, etc.).
Problems can be reordered, edited, or deleted at any time.
Entire sets can be deleted from the set header using the trash icon.

Supported problem methods

Problem sets support all seven solver methods: Newton-Raphson, Bisection, Secant, Fixed-Point, Gaussian Elimination, Lagrange Interpolation, and Simpson's Rule. When a student opens a problem in the solver, all pre-set parameters are automatically populated.

Study Groups

Creating and joining groups

Study groups let you collaborate with classmates. Navigate to Study Groups in the sidebar to create a new group or browse existing ones. Share your group's link with classmates to invite them.

What you can do in a group

Share solve results and canvas screenshots with group members.
Discuss problem set questions in the group thread.
Track who has completed which problems (if your instructor enables it).

For Instructors

Getting the Classroom plan

Instructor features require the Classroom plan ($29/mo). After upgrading via Billing, your account is automatically promoted to instructor status and the instructor sidebar appears with Analytics, Problem Sets, Canvas LTI, and Solver.

Analytics dashboard

The Analytics page shows real-time data from your students' activity:

Overview cards — total solvers, total solves, activity today and this week, convergence rate, at-risk count.
14-day solve volume chart — daily bar chart of solve activity to spot engagement trends.
Method usage — which algorithms your students use most, with convergence rates per method.
Problem set engagement — submission counts and average scores per set.
Student activity table — per-student solve counts, last-active timestamp, study streak, and convergence rate.
At-risk students — count of students active in the last 14 days who have not solved in the past 5 days.

Canvas LTI 1.3 integration

NumericaLTI supports the LTI 1.3 standard for seamless Canvas integration with automatic grade passback.

Go to Canvas LTI in the instructor sidebar.
Copy the Tool URL, Client ID, and JWKS URL shown on that page.
In Canvas, go to Settings → Apps → View App Configurations → + App and choose By Client ID.
Paste the Client ID. Canvas will auto-fetch the configuration.
Add NumericaLTI as an External Tool in any Canvas assignment to enable grade passback.

LTI launches require the student to be logged into NumericaLTI with the same email address as their Canvas account.

Billing & Plans

Plan comparison

Feature	Free	Student $9	Classroom $29
Solver access	5/day	Unlimited	Unlimited
All 7 methods	✓	✓	✓
Canvas visualizer	✓	✓	✓
AI tutor hints	—	✓	✓
Problem sets (view)	✓	✓	✓
Problem sets (create)	—	—	✓
Study groups	—	✓	✓
Instructor analytics	—	—	✓
Canvas LTI grade passback	—	—	✓

How billing works

Plans are billed monthly via Stripe. Your card is charged on the same date each month.
You can upgrade or downgrade at any time from the Billing page.
Cancellation takes effect at the end of the current billing period — you retain access until then.
No refunds are issued for partial months.
Invoices are emailed automatically and available in the Stripe customer portal (click Manage Subscription on the Billing page).

Upgrading or downgrading

Go to Billing in the sidebar. Each plan card shows your current relationship — Active Plan, Upgrade, or Downgrade (disabled). Click the Upgrade button and you will be redirected to Stripe Checkout. Your plan is updated automatically within seconds of payment confirmation.

Classroom plan and instructor access

When the Classroom plan payment is confirmed your account role is automatically set to instructor. You do not need to contact support — the sidebar updates on your next page load. If cancellation occurs, your role reverts to student and instructor-only pages are no longer accessible.

Frequently Asked Questions

I hit the daily solve limit on the Free plan — what do I do?

The Free plan allows 5 solves per day. The limit resets at midnight UTC. To remove the limit entirely, upgrade to the Student plan ($9/mo) from the Billing page.

My Canvas grade didn't update after submitting a problem. What's wrong?

Ensure: (1) the LTI tool was launched from inside Canvas (not opened directly), (2) your NumericaLTI account email matches your Canvas email, (3) your instructor has a Classroom plan active. If all three are true and grades still aren't passing back, contact support with your course name and the problem set title.

The solver says 'did not converge' — is that a bug?

No. Some methods fail to converge for certain inputs. For Newton-Raphson, try a different initial guess closer to the root. For Bisection, verify that f(a) and f(b) have opposite signs. For Fixed-Point, try rearranging the equation into a form where |g′(x)| < 1.

Can I use NumericaLTI without Canvas?

Absolutely. Canvas LTI is optional. You can use the full solver, problem sets, and study groups directly through the NumericaLTI dashboard without any Canvas integration.

I upgraded to Classroom but I still see the Student sidebar.

Try signing out and signing back in to force a session refresh. If the problem persists, clear your browser cache. Your subscription status is read on every page load from Stripe, so if payment succeeded it should appear within 30 seconds.

Are my solve results stored? Can my instructor see them?

Yes — all solves are logged and visible on the instructor analytics page (aggregate counts). Individual equations you enter are not shown to instructors; only metadata like method used, convergence status, and timestamp.

Can I enter equations in LaTeX format?

Not currently. The solver uses mathjs expression syntax — see the Equation Syntax Reference in the Interactive Solver section above. LaTeX input is on our roadmap.

How do I cancel my subscription?

Go to Billing and click the Manage Subscription button on your current plan card. This opens the Stripe customer portal where you can cancel. You will retain access until the end of the current billing period.

I forgot my password. How do I reset it?

Click 'Forgot password?' on the Sign In page and enter your email. A reset link will be sent. Links expire after 60 minutes.

Is there a mobile app?

NumericaLTI is a progressive web app and works in mobile browsers. The solver and canvas visualizer are best experienced on a desktop or tablet for full interaction. A dedicated mobile app is planned for a future release.

Contact Support

Can't find what you're looking for? Send us a message and we'll get back to you within one business day. You can also email us directly at support@numericalti.com.