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COMP350 Numerical Computing

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Week 1 (Lecture 1)
   Sept 2011
     S  M Tu W Th  F  S
     4  5  6 7  8  9 10   
Course Outline
Introduction
Reading:
Overton: Chap 1.
Notes:

Outline (Lec 1)
Introduction (Lec 1)
Week 2 (Lectures 2-3)
   Sept 2011
     S  M Tu  W Th  F  S
    11 12 13 14 15 16 17
Decimal and binary representation
Computer representation of numbers
IEEE floating point representation
Rounding
Reading:
Overton: Chapters 2-5; Cheney and Kincaid: 2.1.
Notes:

IEEE floating point arithmetic (Lecs 2-5)
Week 3 (Lectures 4-5)
   Sept 2011
      S  M Tu  W Th  F  S
     18 19 20 21 22 23 24  
Floating point operations
Exceptional situations
Floating point in C
Taylor series
Approximating a derivative
Reading:
Overton: Chapters 6-10; Cheney and Kincaid: 2.2.
Week 4 (Lectures 6-7)
   Sept 2011
      S  M Tu  W Th  F  S
     25 26 27 28 29 30  1
Numerical cancellation
MATLAB demo
Solving a linear system of equations

Gaussian elimination with no pivoting

Reading:

Overton: Chap 11. Cheney and Kincaid: 1.2, 2.2, 7.1
Sigmon "MATLAB Primer" on this site.

Notes:

MATLAB
Solving linear equations (Lecs 7-9)
Week 5 (Lectures 8-9)
   Oct 2011
       S  M Tu  W Th  F  S
       2  3  4  5  6  7  8
Solving a linear system of equations

Gaussian elimination with partial pivoting
Some theoretical results about GEPP
Solving tridiagonal systems by GENP
Reading:
Cheney and Kincaid: 7.2 & 7.3
Week 6 (Lecture 10)
   October 2011
      S  M Tu  W Th  F  S
      9 10 11 12 13 14 15 
Solving a nonlinear equation:

Introduction
The bisection method
Reading:
Cheney and Kincaid: 3.1
Notes:
Solving a nonlinear equation (Lecs 10-12)
Week 7 (Lecture 11, Midterm)
   October 2011
      S  M Tu  W Th  F  S
     16 17 18 19 20 21 22  
Solving a nonlinear equation: Newton's method
In class Midterm on Oct 19.
Reading:
Cheney and Kincaid: 3.2
Week 8 (Lectures 12-13)
   October 2011
      S  M Tu  W Th  F  S
     23 24 25 26 27 28 29 
Solving a nonlinear equation:

The secant method
Comparsions of the three methods.

Polynomial interpolation:

Vandermonde's approach

Reading:
Cheney and Kincaid: 3.3, 4.1.
Notes:
Polynomial interpolation (Lecs 13-15)
Week 9 (Lectures 14-15)
   Novemebr 2011
      S  M Tu  W Th  F  S
     30 31  1  2  3  4  5  
Polynomial interpolation:

Lagrange form
Newton's approach
Reading:
Cheney and Kincaid: 4.2
Week 10 (Lectures 16-17)
   November 2011
      S  M Tu  W Th  F  S
      6  7  8  9 10 11 12 
Spline interpolation:

Linear spline
Cubic spline
Reading:
Cheney and Kincaid: 9.1, 9.2
Notes:
Spline interpolation (Lecs 16-17)
Week 11 (Lectures 18-19)
   November 2011
      S  M Tu  W Th  F  S
     13 14 15 16 17 18 19 
Least squares approximation
Numerical integration:

Rectangle rule
Midpoint rule

Reading:
Cheney and Kincaid: 12.1, 5.1
Notes:

Least squares approximation (Lec 18)
Numerical integration (Lecs 19-21)
Week 12 (Lectures 20-21)
   November 2011
      S  M Tu  W Th  F  S
     20 21 22 23 24 25 26 
Numerical integration:

Trapezoid rule
Simpson's rule
Gaussian quadrature rules
Reading:
Cheney and Kincaid: 5.2, 6.1, 6.2
Week 13 (Lectures 22-23)
   November, December 2011
      S  M Tu  W Th  F  S
     27 28 29 30  1  2  3  
Numerical solutions of ordinary differential equations:

Introduction
Euler's method
Types of errors
Trapezoid-Euler method and Midpoint-Euler method
Reading:
Cheney and Kincaid: 10.1
Notes:

Numerical methods for ODE (Lecs 22-24)
Week 14 (Lectures 24-25)
   December 2011
      S  M Tu  W Th  F  S
      4  5  6  7  8  9 10
General Taylor series methods
Runge Kutta Mathods
Review
Reading:
Cheney and Kincaid: 10.2