Foundations of calculus
Limits → Derivative → Mean value theorem → Integral → Taylor expansion
- 01
Limits
Saying “arbitrarily close” precisely with ε–δ.
about 7 min · 0 Interactive experiments · 2 Exercises
- 02
The derivative
The limit of a rate of change, and why eˣ is its own derivative.
about 9 min · 2 Interactive experiments · 2 Exercises
- 03
Mean value theorem
The overall average rate of change is attained at some instant; Rolle → Lagrange, and why no hypothesis can be dropped.
about 5 min · 1 Interactive experiments · 2 Exercises
- 04
The integral
The limit of Riemann sums and the fundamental theorem.
about 5 min · 1 Interactive experiments · 2 Exercises
- 05
Taylor expansion
Approximating functions by polynomials, with error control.
about 9 min · 1 Interactive experiments · 2 Exercises
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Foundations of calculus
Foundations of linear algebra
Introduction to differential equations
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