ENGI 2422 Engineering Mathematics 2
Table of Contents for the Lecture Notes

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The lecture notes for this course are available for purchase in the University bookstore.   Please bring these notes with you to every class.   There are intentional gaps in the notes, which will be filled in during the lectures.

After each chapter is completed, the completed version of the lecture notes will become available as a Word document, from this page.

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Gapped Version of the Lecture Notes

Chapter 1   Fundamentals         + Addenda for Parametric Curves,   1.2 Polar Curves
Chapter 2   Partial Differentiation
Chapter 3   First Order ODEs
Chapter 4   Second Order ODEs
Chapter 5   Laplace Transforms
Chapter 6   Multiple Integration

Completed Version of the Lecture Notes

Chapter 1   Fundamentals     (PDF version)
        + Addenda for 1.A Parametric Curves, 1.B Tangents & Normals,   1.2 Polar Curves
Chapter 2   Partial Differentiation     (PDF version)
    [+ solution to Example 2.8.3]
Chapter 3   First Order ODEs     (PDF version)
      Examples of Partial Fractions       More Examples of ODEs  (from a tutorial during February 27-29)
Chapter 4   Second Order ODEs     (PDF version)
      Example of Second Order ODE (from the tutorial cancelled on March 13)
Chapter 5   Laplace Transforms     (PDF version)     [Note: sections 5.09-5.11 are not examinable]
      Examples of Second Order ODE using Laplace transforms (from a tutorial in the week of March 24 - 28)
Chapter 6   Multiple Integration     (PDF version)
Appendix   Suggestions for Formula Sheets     (PDF version)

ENGI 2422 Engineering Mathematics 2
Table of Contents for the Brief Notes

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Also available here is a very condensed older version of the course notes, (with very few examples), as used until 2004 Winter.

Chapter 1:	Fundamentals	[HTML version]	[Word version]
Chapter 2:	Partial Differentiation	[XML version]	[Word version]
Chapter 3:	First Order Ordinary Differential Equations	[XML version]	[Word version]
Chapter 4:	Linear Ordinary Differential   Equations of Higher Order	[XML version]	[Word version]
Chapter 5:	Laplace Transforms	[XML version]	[Word version]
Chapter 6:	Multiple Integration	[HTML version]	[No Word version yet]

Chapter 1:       Fundamentals

1.1       Lines and planes
1.2       Polar coordinates and curve sketching;   (not in 2004)
1.2       Radial and transverse components of velocity and acceleration   (not in 2004)
1.3       Arc length and curvature
1.4       Classification of conic sections
1.5       Classification of quadric surfaces
1.6       Generating the equation of a surface of revolution
1.7       Hyperbolic functions and their comparison to trigonometric functions
1.8       Integration by parts
1.9       Leibnitz differentiation of an integral

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Chapter 2:       Partial Differentiation

2.1       Partial derivatives
2.2       Higher derivatives
2.3       Differentials and the chain rule
2.4       The Jacobian
2.5       The gradient vector
2.6       Maximum and minimum values of functions of several variables
2.7       Lagrange multipliers
Appendix 1:   Example of Jacobian in multiple integration
Appendix 2:   Example: absolute extrema of V(x, y) in a finite domain

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Chapter 3:       First Order Ordinary Differential Equations (1^st Order O.D.E.'s)

3.1       Classification; separation of variables
3.2       Exact first order ODEs
3.3       Integrating factor
3.4       First order linear ODEs
3.5       Reduction of order
3.6       applications (including orthogonal trajectories)
Appendix:   General checklist for first order ODEs

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Chapter 4:       Linear Ordinary Differential Equations of Higher Order

4.1       Complementary function; mass-spring system; operator method
4.2       Particular solutions by undetermined coefficients
4.3       Particular solutions by variation of parameters
4.4       Higher order linear ODEs

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Chapter 5:       Laplace Transforms

5.1       Definitions
5.2       Properties and theorems
5.3       Convolution
5.4       Table of inverse Laplace transforms
5.5       Miscellaneous examples
5.6       Additional details on inhomogeneous ODEs with discontinuities
Appendix 1:   Example of ODE with discontinuity
Appendix 2:   Two examples of partial fractions
Appendix 3:   Four derivations of the Laplace transform of cos ωt

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Chapter 6:       Multiple Integration

6.1       Double Integrals (Cartesian Coordinates)
6.2       Double Integrals (Plane Polar and Other Coordinates)
6.3       Triple Integrals

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