# Univariate

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## Text

Univariate Calculus at NKU is taught using Stewart's *Calculus*.

## Calculus I

[Several of us use an on-line homework program (IMathAS).] You will need to enroll in a class to use it, however.

- A Quick Overview of the course
- Three Problems with One Solution, or, How Calculus Works in a Straight-line World.
- From secant lines to tangents, slopes of curved graphs and instantaneous velocity
- One Application of the Tangent Line
- Limits: An Intuitive Approach
- Linearity: when you see it, it's a big help!
- The most important definition in calculus
- Hand-wavy proof of the Chain Rule
- How does calculus inform the graph of a function?
- Using the most important definition in calculus and linearization to derive the Fundamental Theorem of Calculus
- Substitution is Just the Chain Rule Backwards
- There's always more than one way to do it: an integral (a volume integral)
- Compound Interest (and L'Hopital's rule)

## Calculus II

Andy Long's Fall 2009 MAT228 section

- In MAT229 Andy covers the following sections of Rogawski: Rogawski CalcII Coverage

- Some topic pages:
- Tangent Lines as Approximation
- Taylor Series as Approximations
- Convergent Alternating Series may have simple error structure
- A proof by induction that the dominoes will overhang by an infinite amount
- Manipulating series to solve Differential Equations -- some examples
- A parametric equation plotter, with vector velocity
- An example to motivate integration by parts

## Resources

- The UBC Calculus Online Homepage (and especially their applet collection)
- Comic Book Calculus -- vignettes that illustrate what calculus is in few words.
- MAT128 Mathematica Resources -- pdfs from Mathematica files.