Talk:Calculus pre-test
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Latest comment: 4 years ago by Dave Braunschweig in topic Course Outline
I am currently a first year mathematics student at Wollongong University Australia.
Whilst I am fully aware that courses do differ in content, I thought I would give another prespective on how we approach calculus in its various levels.
Pre-Calculus
[edit source]Algebra
- Algebra comes first
- What is a logarithm?
- What is a slope-intercept equation?
Trig
- What is a radian?
- What is a trigonometric function?
- Name a trigonometric identity.
Functions
- What is a function?
- What is an inverse function?
- What is a parametric equation?
I have not even covered these things
- What does it mean for something to be proportional?
- What does injective, surjective, and bijective mean?
Calculus I
[edit source]Limits
- I will accept an intuitive or formal answer for this, although a formal answer is obviously preferred, what is a limit?
- What is a one-sided limit?
- What does it mean for a function to be continuous? Is it possible for a function to be discontinuous everywhere?
Differentiation
- What is a derivative?
- What is the product rule?
- What is the relation between differentiability and continuity?
- What is the chain rule?
I have not even covered these things
- What is the relation between a local extrema and a derivative of a function?
- What is the mean value theorem?
- What is L'Hôpital's rule?
Calculus II
[edit source]Integration
- What is the Fundamental Theorem of Calculus?
- What is an integral?
- What is the substitution method?
- What is the difference between a definite and indefinite integral?
I have not even covered these things
- What is a Riemann Sum?
My Outline
[edit source]It seems clear below that
Pre Calculus covers
- Algebra
- Trigonometry
- Functions
Calculus I or Differentiation covers
- Limits
- Differentiation rules
Calculus II or Integration covers
- Integration rules
there should be
Calculus III or Advanced Calculus covers
- What is the relation between a local extrema and a derivative of a function?
- What is the mean value theorem?
- What is L'Hôpital's rule?
- What is a Riemann Sum?
Course Outline
[edit source]Precalculus should probably follow an outline similar to OpneStax: Precalculus. -- Dave Braunschweig (discuss • contribs) 00:33, 2 May 2020 (UTC)