Courses taught in Autumn Term, 2002

Calculus III MAT- LCU 01	Linear Algebra MAT - NYC 02, 03

New! Pre Exam Office Hours

Tuesday, December   3	12:00pm – 3pm
Tuesday, December 10	12:30pm – 3pm

Calculus III

• Assignments
  • Assignment 1.
  • Assignment 2. and its solution were given out in class.
  • Assignment 3. was given out in class. | Solution to Assignment 3.
  • Assignment 4. was handed out in class.| Solution to Assignment 4.
  • Assignment 5. | Solution to Assignment 5. at the College Library site
  • Assignment 6. | Solution to Assignment 6. at the College Library site
  • Proof of the Lagrange Multiplier equations plus Geometric meaning; case of 3 variables, 1 constraint and 2 constraints - College Library site.
  • Assignment 7. was handed out in class. Due on last day of classes.

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• Goodies
  • If you own Maple: How to recapture the Maple Worksheet on which a web page is based?
  • Online Cal. III course on the Waterloo Maple website (courtesy of University of Wisconsin-Milwaukee Department of Mathematics).
  • Online 'Cal. IV' course on the Waterloo Maple website

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  • Sequences: comparing rates of growth
  • Sequences: Introduction   (Waterloo Maple website)
  • Sequences: Convergence (Waterloo Maple website)
  • Two interesting sequences.
  • The sequence that defines e increases towards e - a rigorous proof.
    
  • Three interesting series.
  • Parametric Curves and Arc Length
  • Practice examples on Space Curves
  • Another practice example: the Astroid curve and its radius of curvature, centers and circles of curvature. Pictures and animation.
    If you own Maple: here is the original Maple worksheet, with the output removed for fast download.
  • Cylindrical and Spherical Coordinates (from the University of Minnesota Geometry Center). This is a good starting point for an exploration of space geometry. The presentations are concise and quite clear.
  • New Oct. 31: Path of Steepest Descent on the Hyperbolic Paraboloid z = x² - y²
  • New Oct. 31: Path of Steepest Descent on the Elliptic Paraboloid z = x² + 2y²
  • Second Partial Derivatives and the Chain rule - a start.
  • Proof of the Second Derivative Test for local extrema in two variables. (MS Word document)
  • Nov.25: Various views of the Viviani Curve - MS Word Document.
  • New Integrative activity: a safe transfer curve between two railroads.
  • Erratum and comment on the Transfer Curve page (minor error due to Maple quirk).

Linear Algebra

• Assignments
  • Assignment 1. | Solution to Assignment 1.
    
  • Assignment 2. | Solution to Assignment 2.
  • Pretest Practice in place of Assignment 3.
  • Additional Practice on Vectors and Matrices.
      There is an update to one of  the solutions (7b) in the Pretest Practice,
    and Erratum to solution (#6) in the Additional Practice sheet.
    
    
  • Assignment 4 was handed out in class. | Solution to Assignment 4.
    Here is a graphic demonstration, to help you with one of the exercises. Rotating an object in 3D.
    If you own Maple, here is the Maple worksheet, with the output removed for fast download. Execute the worksheet (Edit menu), and experiment by changing the angle of rotation (listed near the start; see webpage for first occurrence of "theta").
    
  • Assignment 5. | Solution to Assignment 5.
  • Assignment 6. | Solution to Assignment 6.
  • Assignment 7. MS-Word Document | Web page (HTML)
  • Assignment 7 - Correction to Question 8.

• Goodies
  • Online course in Linear Algebra on the Waterloo Maple website
  • Matrix Algebra Education Pack
  • Cramer's Rule for nXn linear systems with invertible coefficient matrix
  • Notes on Vector Spaces: Basis, dimension. Row Space, Column Space, Null Space of a matrix.
  • Announcement: Office hours for Thursday Nov. 21, Teacher-student day: 1:30 –3:30

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• Examples
• An invertible matrix shown as a product of elementary matrices.
• The Invertibility Theorem, first instalment

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Last updated Thursday, January 16, 2003