Univariate

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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.