ENGI 9420 Engineering Analysis – Course Notes

The gapped lecture notes are available (from September) at cost price at the University Bookstore.

In the event that there are not enough copies at the bookstore for the number of students in this course, the PDF files of the gapped lecture notes are available as follows:

1. Chapter 1   (Ordinary Differential Equations)
2. Chapter 2   (Matrix Algebra)
3. Chapter 3   (Numerical Methods)
4. Chapter 4   (Stability Analysis)
5. Chapter 5   (Gradient Operators)
6. Chapter 6   (Calculus of Variations)
7. Chapter 7   (Fourier Series)
8. Chapter 8   (Partial Differential Equations)

PDF files for the completed version of each lecture will be added here after that lecture has taken place.

Initial Course Handout:   List of Topics, Evaluation Scheme, etc.

Sep. 10 Mon.:   Lecture 01   (Separable ODEs; Integrating factor; Linear ODEs)
Sep. 11 Tue.:   Lecture 02   (Tabular integration by parts; Bernoulli ODEs)
[Note:   the University was closed on Tue. Sep. 11.]

Sep. 17 Mon.:   Lecture 03   (2nd Order ODEs)
Sep. 18 Tue.:   Lecture 04   (Laplace transforms; series solutions of ODEs)

Sep. 24 Mon.:   Lecture 05   (Series Solutions of ODEs)
Sep. 25 Tue.:   Lecture 06   (2.   Linear systems, Gaussian elimination)

Oct. 01 Mon.:   Lecture 07   (Matrix algebra, eigenvalues; 3.   Numerical Methods)
Oct. 02 Tue.:   Lecture 08   (4.   Motion of a Pendulum, singular points)

Oct. 10 Wed.:   Lecture 09   (Stability Analysis - types of singularities)
Oct. 11 Thu.:   Lecture 10   (Stability Analysis - example of focus)   [+ review for the mid term test]

Oct. 15 Mon.:   [mid term test]
Oct. 16 Tue.:   Lecture 11   (Stability Analysis - linear approximation)

Oct. 22 Mon.:   Lecture 12   (Stability Analysis - limit cycles, van der Pol’s equation)
Oct. 23 Tue.:   Lecture 13   (Stability Analysis - Duffing’s equation;   5.   gradient operator)

Oct. 29 Mon.:   Lecture 14   (review of assignment 4 & chapter 5;   6. Calculus of Variations introduction)
Oct. 30 Tue.:   Lecture 15   (Calculus of Variations)

Nov. 05 Mon.:   Lecture 16   (7.   Orthogonal functions, Fourier series)
              + supplementary note on trigonometric identities
Nov. 06 Tue.:   Lecture 17   (Fourier half-range series, frequency spectra)

Nov. 12 Mon.:   [Remembrance Day Holiday]
Nov. 13 Tue.:   Lecture 18   (8.   Partial differential equations - waves on finite strings)
Nov. 16 Fri.:   Lecture 19   (PDEs - Fourier and d’Alembert solutions)

Nov. 19 Mon.:   Lecture 20   (PDEs - d’Alembert solutions)
Nov. 20 Tue.:   Lecture 21   (PDEs - d’Alembert solutions, harmonic functions, heat PDE)

PDF files of the complete
Chapter 1   (Ordinary Differential Equations)
Chapter 2   (Matrix Algebra)
Chapter 3   (Numerical Methods)
Chapter 4   (Stability Analysis)
Chapter 5   (Gradient Operator)
Chapter 6   (Calculus of Variations)
Chapter 7   (Fourier Series)
Chapter 8   (Partial Differential Equations)

Formula sheets that will be supplied with the final examination.