Introduction

This is a refresher mathematics and modelling course to get you ready for the UNENE courses. UNENE students come from a wide variety of science and engineering background and may have been away from academia for a number of years. Unused math skills fade quickly. This course is intended to get students up to speed quickly in key mathematical areas that commonly arise in this program. It is NOT intended for first-time learners.

THIS REFRESHER COURSE IS HIGHLY RECOMMENDED PREPARATION FOR THE UNENE JOINT MASTER'S OF ENGINEERING DEGREE COURSES

Administration

• Format: Two day compressed workshop containing lectures and hands-on sessions.
• Prerequisite: Undergraduate degree in engineering or science.
• Lecturer: Bill Garland, Email: garlandw@mcmaster.ca, general nuclear engineering web site: www.nuceng.ca.
• The first offering of this course - September 19-20, 2009 weekend, approximately 9:00 am to 4:30 pm Saturday and Sunday.
• Location: Room 1-2, Durham College - Whitby Campus, 1610 Champlain Avenue, Whitby, Ontario. See Campus Maps.
• For students at remote locations, it is planned that this course will be offered as a live distance education course via MacLive. You will need a high speed internet connection outside corporate firewalls, an inexpensive headset with microphone and, optionally, a webcam.
• Evaluation: An individual informal assessment and recommendation will be made and provided to the student.
• Your comments and suggestions are welcome.
• Note: Handouts will not be provided at the sessions. You are advised to bring a printout of the lecture notes at the very least. Depending on the particular interests of the class, discussions and exercises may take unexpected turns. So to ensure maximum flexibility bring a laptop and a memory stick if you can.

Course Material

• Lecture Notes: Mathematics and Modelling (pdf 1.0Mb) containing notes on [revised 2009-08-06]
  1. Introduction. See also:
     1. Learning 101 and Mastery, www.nuceng.ca
  2. Engineering Concepts, Equations and Context. See also:
     1. Summary of the book The Evolution of Physics
  3. Vectors (Div, Curl, Grad and all that). See also:
     1. Vector Math Review (pdf 146kb)from http://epsc.wustl.edu/classwork/454/syllabus.html
  4. Linear Algebra. See also:
     1. Matrix Algebra Review (pdf 60kb) from www.cse.unr.edu/~bebis/MathMethods
  5. Calculus. See also:
     1. www.mathcentre.ac.uk for detailed refresher notes and exercises on basic differentiation (pdf 128kb) and differentiation integration (pdf 400kb).
     2. Table of derivatives (pdf 56kb) from www.math.ubc.ca/~feldman/m120
     3. Table of integrals (pdf 89kb) from www.integral-table.com.
     4. Solve integrals on-line.
  6. Ordinary Differential Equations
  7. Boundary-Value and Eigenvalue Problems
  8. Partial Differential Equations
  9. Data Analysis (Statistics and Least Squares Regression). See also:
     1. T-Test notes (pdf 90kb) from www.socialresearchmethods.net
     2. Statistical tables (pdf 153kb) from www.statsoft.com/textbook/sttable.html
  10. Laplace Transforms
      1. Reference: Kells, Elementary Differential Equations, McGraw-Hill, 1965, Chapter 7
      2. Table of common Laplace transforms (pdf 42kb) from stanford.edu/~boyd/ee102/
  11. Control Theory
      1. Reference: George Stephanopoulos, Chemical Process Control: An Introduction to Theory and Practice, Prentice Hall, 1984, ISBN 0-13-128629-3
• Reference Text: [C&C] Chapra and Canale, Numerical Methods for Engineers, 5th edition, Publishers: McGraw Hill, ISBN 0-07-291873-X, TK345.C47, Year: 2006. You might be able to get a used copy at www.alibris.com.
• Solutions to exercises in notes (pdf 165 kb) [password protected]

Course Plan

• Session 1 Saturday 9:00-10:15
  • Introduction
  • Engineering Concepts, Equations and Context
  • Vectors (Div, Curl, Grad and all that)
• Session 2 Saturday 10:30-12:00
  • Linear Algebra
  • Calculus
• Session 3 Saturday 1:00-2:30
  • Ordinary Differential Equations
• Session 4 Saturday 3:00-4:30
  • Boundary-Value and Eigenvalue Problems
  • Partial Differential Equations
• Session 5 Sunday 9:00-10:15
  • Data Analysis (Statistics and Least Squares Regression)
• Session 6 Sunday 10:30-12:00
  • Data Analysis (Distributions and Probability)
• Session 7 Sunday 1:00-2:30
  • Laplace Transforms
  • Control Theory
• Session 8 Sunday 3:00-4:30
  • Review and Discussion

Class Recordings

• Chapter 1 - Introduction & Chapter 2 - Concepts (exe 43Mb)
• Chapter 3 - Vectors (exe 31Mb)
• Chapter 4 - Linear algebra (exe 32Mb)
• Chapter 5 - Calculus (exe 21Mb)
• Chapter 6 - ODEs (exe 19Mb)
• Chapter 7 - Boundary Value & Eigenvalue problems - recording unavailable
• Chapter 8 - PDEs (exe 29MB)
• Chapter 9 - Data Analysis - this section was skipped
• Chapter 10 - Laplace Transforms - recording unavailable
• Chapter 11 - Control Theory - this section was skipped
• Review of reactor physics concepts and equation in relation to the math - part 1 (exe 8.5Mb), part 2 (exe 33Mb)

Supplementary Material

• DYNASY control theory, block diagrams, animations and more [link broken].