Resources on Conics for H2 Further Maths
In Service Course Oct 2016
JCMTC sharing 17 Feb 2016
References for Conics
The following are some books that I had used. My comments in italics pertain to the specific edition of the books that I had access to.
The following is a list of articles from the College Mathematics Journal that are related to conics.
- College Trigonometry - Richard Aufmann, Vernon Barker and Richard Nation
The most comprehensive reference I could find. I believe other books by the same authors contain similar material if you cannot find this title.
- College Algebra: Concepts through functions - Sullivan and Sullivan
More elementary, D-E-F is relegated to exercises.
- Calulus - James Stewart
Two short sections but contains the polar form and applications.
- Explorations in Geometry - Bruce Shawyer
Only one short chapter on conics but well written.
- Conics and Cubics - Robert Bix
Too advanced for A levels, but useful to view conics using projective plane. Proves that five points (no three of which collinear) lie on exactly one conic.
- Practical Conic Sections - J. W. Downs
Available at a reasonable price from BookDepository. This book really emphasizes the practical aspects. There are no proofs but lots of examples of how to actually draw conics and practical applications.
- Pure Mathematics for Advanced Level - B.D. Bunday and H. Mulholland
Chapter 20 is on Conics. Lots of problems and examples related to tangents and normals.
- Analytical Geometry (Two and Three Dimensions) - D. Chatterjee
Chapters 4 and 5 are on Conics. Contains many useful examples/problems that are quite appropriate for A-Levels, including the clever proof of the director circle for ellipses and hyperbolas.
- An Imaginary Tale, The Story of Sqrt(-1) - Paul J. Nahin
This is a book about complex numbers, not conics. But Section 5.3 (pp 109-120) is about Kepler's Laws and contains a very nice and understandable proof of the laws via complex differentiation. This section is highly recommended.
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Updated Oct 2016