School of Computer Science

COMP350 Numerical Computing

 Lecture Content, Notes and Reading

Week 1 (Lecture 1)

   Sept 2013
     S  M Tu W Th  F  S
     1  2  3 4  5  6  7   
  • Course Outline
  • Introduction
Reading:
Overton: Chap 1.

Notes:

Week 2 (Lectures 2-3)

   Sept 2013
     S  M Tu  W Th  F  S
     8  9 10 11 12 13 14
  • Decimal and binary representation
  • Computer representation of numbers
  • IEEE floating point representation
  • Rounding
Reading:
Overton: Chapters 2-5; Cheney and Kincaid: 2.1.

Notes:

Week 3 (Lectures 4-5)

   Sept 2013
      S  M Tu  W Th  F  S
     15 16 17 18 19 20 21  
  • 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 2013
      S  M Tu  W Th  F  S
     22 23 24 25 26 27 28  
  • 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

Notes:

Week 5 (Lectures 8-9)

   Sept, Oct 2013
       S  M Tu W Th  F  S
      29 30  1 2  3  4  5  
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 (Lectures 10-11)

   October 2013
      S  M Tu  W Th  F  S
      6  7  8  9 10 11 12 
Solving a nonlinear equation:
  • Introduction
  • The bisection method
  • Newton's method
Reading:
Cheney and Kincaid: 3.1, 3.2

Notes:
Solving a nonlinear equation (Lecs 10-12)

Week 7 (Midterm)

   October 2013
      S  M Tu  W Th  F  S
     13 14 15 16 17 18 19   
  • In class Midterm on Oct 16.

Week 8 (Lectures 12-13)

   October 2013
      S  M Tu  W Th  F  S
     20 21 22 23 24 25 26 
  • Solving a nonlinear equation:
    • Newton's method, ctd.
    • 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)

   October, Novemebr 2013
      S  M Tu  W Th  F  S
     27 28 29 30 31  1  2    
Polynomial interpolation:
  • Lagrange form
  • Newton's approach
Reading:
Cheney and Kincaid: 4.2

Week 10 (Lectures 16-17)

   November 2013
      S  M Tu  W Th  F  S
      3  4  5  6  7  8  9  
Spline interpolation:
  • Linear spline
  • Cubic spline
Reading:
Cheney and Kincaid: 9.1, 9.2

Notes:

Week 11 (Lectures 18-19)

   November 2013
      S  M Tu  W Th  F  S
     10 11 12 13 14 15 16 
  • Least squares approximation
  • Numerical integration:
    • Rectangle rule
    • Midpoint rule
Reading:
Cheney and Kincaid: 12.1, 5.1

Notes:

Week 12 (Lectures 20-21)

   November 2013
      S  M Tu  W Th  F  S
     17 18 19 20 21 22 23  
Numerical integration:
  • Trapezoid rule
  • Simpson's rule
  • Adaptive Simpson's rule
  • Gaussian quadrature rules
Reading:
Cheney and Kincaid: 5.2, 6.1, 6.2

Week 13 (Lectures 22-23)

   November, December 2013
      S  M Tu  W Th  F  S
     24 25 26 27 28 29 30    
  • Gaussian quadrature rules, ctd.
  • 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:

Week 14 (Lectures 24-25)

   December 2013
      S  M Tu  W Th  F  S
      1  2  3  4  5  6  7  
  • General Taylor series methods
  • Runge Kutta Mathods
  • Review
Reading:
Cheney and Kincaid: 10.2


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