Courses taught in Autumn Term, 2007

Calculus I Science MAT - NYA 06, NYA 22	Linear Algebra Arts MAT- 105 01

Pre-exam office hours

• To be updated

Calculus I, Science

The contents are identical to the Autumn 2005 page, except for material that has been removed.
The site has not been updated since Winter 2006 due to the introduction of the Omnivox system.

• Asgts 4 and 5
• Asgt 6

Practice Sheets

• Review: Analytic Geometry, Functions
• Limits : Definition and first examples.
• Tricky limits at infinity : a function may have two horizontal asymptotes.
• Professor C. Garneau's Lab Sheets on the College Library Reserves site. Highly recommended for extra practice!
• First practice sheet on derivatives
• Second practice sheet on derivatives
  

  Jump to Notes further down this page:

  • Definitions of the Derivative; first examples (presented with Maple)
  • Table of Derivatives, continued.
  • "0/0" type Trigonometric Limits; Derivative of sin x
  • (Enriched section) Newton's Method shown with Maple

Assignments

• Assignment 1. [PDF file, requires Acrobat Reader] | Solution to Assignment 1. [PDF file, requires Acrobat Reader]
• Assignment 2.| Solution to Assignment 2. [ZIP file]
• Assignment 3 | Solution to Assignment 3. [ PDF file]
  • Solution to Assignment 3. (PDF file)
  • Solution in a Maple worksheet (If you own Maple: download this file, open it with Maple, click on Edit/Execute/Worksheet)
• Assignment 4.[PDF] |  Assignment 4 Solution[ZIP] Solution[Maple worksheet]
• Assignment 5. [PDF] | Solution to Assignment 5 (PDF file)
• Assignment 6. [PDF]| Solution to Assignment 6.[PDF]
• Assignment 7. | Solution to Asgt.7.[PDF]
• Assignment 8.
• Assignment 9.
• New! Solutions to Asgt. 9:
  • Simple Harmonic Motion | Error, corrected on Dec. 11.
  • Optimization
  • Curve Sketching

     

Goodies

• Continuity of a Piecewise defined Function: an Animation. [PowerPoint document on College Library site | ZIP file containing the same Powerpoint, at my other site.]
  
• Exponential Growth (University of Illinois at Urbana-Champaign)
Exponential Decay and Archeology – an amazing example. [Ref: Calculus with Analytic Geometry, by H. Flanders and J. Price, Academic Press, 1978, page 176.]

• Exponential Functions: Tangents and Slopes.
• The number e and its meaning (University of Toronto)
• The number e to one million digits, computed by Robert Nemiroff (George Mason University and NASA Goddard Space Flight Center)
• The number e - history
• Lessons in basic Maple, as applied to Calculus I - North Carolina State University (link updated September 2004)
• Newton's Method illustrated in Maple.
• New! Differentials -Tangent line approximations. [PDF] [ZIP]
  
• Maple worksheets for the Computer Lab:
  The amazing Astroid -1 | The amazing Astroid -2| The natural exponential function and its derivative| Newton's Method
• Implicit Equations: Curves and Tangents
  
  
• The MacTutor History of Mathematics archive, University of St.Andrews, Scotland. Great biographies, imaginative cross-references.
• Online Derivative Calculator. Use it wisely.
  

  Time out: fun stuff

• Deep Thoughts by Great Minds (not all of them mathematicians.)
• Find your birthday or phone number among the digits of Pi!

Notes

• Definitions of the Derivative; example worked out in Maple; a graphic animation showing the derivative function as moving tangents.
• Table of Derivatives, continued.
• Proof of the Product Rule for Derivatives.
• Trigonometric limits of 0/0 type; the derivative of sin x — proof of the Rule.
• Implicit Equations: Curves and Tangents
• New! Two excellent handouts courtesy of Professor. J. Osborne
  • Simple Harmonic Motion (Integrative Activity) [PDF file]: Physics background and equations
  • Curve Sketching (a.k.a. Complete Analysis of a Function): summary and examples

 

Maple syrup

• If you own Maple: How to recapture the Maple Worksheet on which a webpage (HTML) is based?

Examples

• A function may have two Horizontal Asymptotes: 2 examples showing tricky limits at infinity involving radicals.
• First Practice Sheet on derivatives. (.pdf document.)
• Second Practice sheet on derivatives. (.pdf document.)
• ------------------------------------------------------------------------
• Practice examples on: extrema, concavity, points of inflection: PDF file | ZIP
file
• Another Curve Sketching Example; using the Summary Chart [.PDF file]

Linear Algebra

• Examples

  • Gaussian Elimination without fractions; two nice graphics [HTML file, produced from Maple]
  • Input Output Analysis example shown in class, Sept. 21
  • Applications of the Determinant [PDF]. Note: you will understand Page 2 better after studying the Cross Product of vectors and its properties.
  • The Cross Product - Fact Sheet
  • Dot Product, Cross Product, Triple Scalar Product
  • New! Pre-test 2 Review Guide

• Assignments

  • Assignment 1.
  • Assignment 2. | Solution to Assignment 2 [PDF file]
  • Assignment 3. | Solution to Assignment 3. [PDF file]
  • Assignment 4.
  • Assignment 5. [PDF file]
  • Assignment 6. | Selected Solutions to Assignment 6.
  • Assignment 7. | Solution to Assignment 7.
  • Assignment 8, solution .

    Goodies

    • Online Matrix Algebra Calculator. Use it wisely.
    • New! Online Simplex Method Calculator. Use it wisely.

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