School of Computer Science

COMP350 Numerical Computing

 Lecture Content, Notes and Reading

Week 1 (Lecture 1)

   Sept 2014
     S  M Tu W Th  F  S
        1  2  3 4  5  6     
  • Course Outline
  • Introduction
Reading:
Overton: Chap 1; Cheney and Kincaid: 1.1

Week 2 (Lectures 2-3)

   Sept 2014
     S  M Tu  W Th  F  S
     7  8  9 10 11 12 13 
  • Decimal and binary representation
  • Computer representation of numbers
  • IEEE floating point representation
  • Rounding
Reading:
Overton: Chapters 2-5; Cheney and Kincaid: 1.3.

Week 3 (Lectures 4-5)

   Sept 2014
      S  M Tu  W Th  F  S
     14 15 16 17 18 19 20   
  • Floating point operations
  • Exceptional situations
  • Floating point in C
  • Taylor series
  • Approximating a derivative
  • Numerical cancellation
Reading:
Overton: Chapters 6-11; Cheney and Kincaid: 1.2, 4.3 (1st part)

Week 4 (Lectures 6-7)

   Sept 2014
      S  M Tu  W Th  F  S
     21 22 23 24 25 26 27    
  • MATLAB demo
  • Solving a linear system of equations
    • Gaussian elimination with no pivoting
Reading:
  • Overton: Chap 11. Cheney and Kincaid: 1.4, 2.1

Week 5 (Lectures 8-9)

   Sept, Oct 2014
       S  M Tu W Th  F  S
      28 29 30  1 2  3  4    
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: 2.2 & 2.3

Week 6 (Lectures 10-11)

   October 2014
      S  M Tu  W Th  F  S
      5  6  7  8  9 10 11 
Solving a nonlinear equation:
  • Introduction
  • The bisection method
  • Newton's method
Reading:
Cheney and Kincaid: 3.1, 3.2

Week 7 (Midterm)

   October 2014
      S  M Tu  W Th  F  S
     12 13 14 15 16 17 18    
  • In class Midterm on Oct 15.

Week 8 (Lectures 12-13)

   October 2014
      S  M Tu  W Th  F  S
     19 20 21 22 23 24 25  
  • Solving a nonlinear equation:
    • Newton's method, ctd.
    • The secant method
    • Comparsions of the three methods.
  • Polynomial interpolation:
    • Vandermonde form
Reading:
Cheney and Kincaid: 3.3, 4.1.

Week 9 (Lectures 14-15)

   October, Novemebr 2014
      S  M Tu  W Th  F  S
     26 27 28 29 30 31  1      
Polynomial interpolation:
  • Lagrange form
  • Newton form
Reading:
Cheney and Kincaid: 4.2

Week 10 (Lectures 16-17)

   November 2014
      S  M Tu  W Th  F  S
      2  3  4  5  6  7  8    
Spline interpolation:
  • Linear spline
  • Cubic spline
Reading:
Cheney and Kincaid: 6.1, 6.2

Week 11 (Lectures 18-19)

   November 2014
      S  M Tu  W Th  F  S
      9 10 11 12 13 14 15 
  • Least squares approximation
  • Numerical integration:
    • Rectangle rule
    • Midpoint rule
Reading:
Cheney and Kincaid: 9.1, 5.1

Week 12 (Lectures 20-21)

   November 2014
      S  M Tu  W Th  F  S
     16 17 18 19 20 21 22 
Numerical integration:
  • Trapezoid rule
  • Simpson's rule
  • Adaptive Simpson's rule
  • Gaussian quadrature rules
Reading:
Cheney and Kincaid: 5.3, 5.4.

Week 13 (Lectures 22-23)

   November, December 2014
      S  M Tu  W Th  F  S
     23 24 25 26 27 28 29 
  • 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: 7.1

Week 14 (Lectures 24-25)

   December 2014
      S  M Tu  W Th  F  S
      30 1  2  3  4  5  6  
  • General Taylor series methods
  • Runge Kutta Mathods
  • Review
Reading:
Cheney and Kincaid: 7.2


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