CSC336 Numerical Methods

Fall 2025 Bulletin/discussion board for csc336 Fall 2025 -- course outline --

[Announcements] [Material covered[ [Lectures, Tutorials, Assignments (with pass)]


Announcements, Course information for current students:

Textbook web page (see educational modules)
Material covered or to be covered in the course (with textbook sections in parentheses) (later)
2025-09-03 (2 hours)
0.   What is Scientific Computing? (1.1, 1.2.1)
1.   Computer arithmetic; data and computational errors
1.1  (Human) Representation of nonnegative integers
   - Algorithm for converting base b integers to decimal
   - Algorithm for converting decimal integers to base b
1.2  (Human) Representation of reals
   - Algorithm for converting base b fractions to decimal
   - Algorithm for converting decimal fractions to base b
1.3  Computer representation of numbers (1.3.1-7)
   - floating-point numbers, mantissa, exponent, normalized mantissa,
     significant digits, overflow, underflow, range of representable numbers,
     representable numbers, chopping, rounding
   - The IEEE Standard
1.4  Round-off error (1.3.5)
1.5  Absolute and relative errors (1.2.2)
1.6  Computer arithmetic -- saturation in addition (1.3.8)
1.7  Machine epsilon (1.3.5)
2025-09-05 (1 hour)
1.8  Error propagation in simple arithmetic calculations (1.3.8-9)
   - Multiplication, division, addition/subtraction
   - catastrophic cancellation
1.9  Error propagation in computation: conditioning of problems (1.2.6)
   - condition number of function
1.10 Error propagation in computation: stability of algorithms (1.2.7)
2025-09-10 (2 hours)
1.11 Forward and backward errors (1.2.3-5)
     Propagated data error
     Truncation (discretization) and rounding errors, computational error
     Total error
1.12 Taylor series
1.13 O(n^b) and O(h^a) notations

(more to come)

Notes and handouts:
Note on use of notes: Notes will be available when the course starts. While it may be convenient to study for the course by reading the notes, it should be made clear that the notes are not there to substitute the textbook or any relevant book. Notes are always more condensed and give less overall information than books.
Notes with math notation, etc, are difficult to read online. It may be preferable for some of you to print out the 4-page style notes on paper (preferably double-sided).


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Lecture notes

Tutorial notes Assignments Other