Mr. IntegralA PATH, NOT A RACE
Find your way
through mathematics.
Start with what you know. Follow the connections. Return to an earlier idea whenever you need it.
START WHERE YOU ARE
Which sounds like you?
These are suggestions, not a placement test. Open a description to choose a starting unit; every lesson remains available.
I’m building my algebra and graph skills.
Start with coordinates, then work through trigonometry, logarithms and functions. If signed numbers or fractions are unfamiliar, refresh those first.
Start Pre-Calculus →I’m comfortable with functions and algebra.
Start with limits. You should be able to read a piecewise graph, factor a quadratic and work with sine, cosine and logarithms.
Start Calculus I →I know basic derivatives and integrals.
Begin with integration methods. Bring the chain rule, substitution and the Fundamental Theorem; return to Calculus I if any need refreshing.
Start Calculus II →I want to understand systems or fit data.
Start Linear Algebra from vectors and systems. You need basic algebra and coordinates; you can follow this branch alongside calculus.
Start Linear Algebra →THE ENGINEERING FOUNDATION
Two branches. Connected ideas.
The sequence shows what builds on what, not a required timetable.
↓ Use functions to study change
Calculus I
Follow one idea from limits to derivatives and integrals. See how slopes and areas fit together.
Explore course →Builds on Pre-Calculus: limits make instantaneous change precise.
Calculus II
Choose integration methods, study infinite series, and use Taylor polynomials to approximate functions.
Explore course →Builds on Calculus I: accumulation grows into methods and approximations.
Calculus III
Take calculus into space. Explore surfaces, gradients, multiple integrals and vector fields.
Explore course →Builds on Calculus II: extend change and accumulation into space.
↓ Use coordinates to study structure
Linear Algebra
Connect equations with geometry, from vectors and matrices to eigenvalues, least squares and SVD.
Explore course →Branches from Pre-Calculus: study alongside calculus. No calculus prerequisite.
Differential Equations
Bring rates, accumulation and linear systems together to model a changing world.
Explore course →Calculus III is useful context, but is not required before beginning this course.
MAKE EACH VISIT COUNT
A small routine for a deeper understanding.
- Orient
Read the unit’s big question. Check what it builds on.
- Explore
Predict what a diagram will show, then compare it with the explanation.
- Attempt
Try the check before revealing the reasoning. Use one hint at a time.
- Return
Save an uncertain lesson. Come back another day and explain it from memory.