School of Computer Science

COMP350 Numerical Computing

 Lecture Content, Notes and Reading

Week 1 (Lecture 1)

   Sept 2015
     S  M Tu W Th  F  S
    30 31  1 2  3  4  5      
  • Course Outline
  • Introduction
Reading:
Overton: Chap 1; Cheney and Kincaid: 1.1

Week 2 (Lectures 2)

   Sept 2015
     S  M Tu  W Th  F  S
     6  7  8  9 10 11 12  
  • Decimal and binary representation
  • Computer representation of numbers
Reading:
Overton: Chapters 2-3.

Week 3 (Lectures 3-4)

   Sept 2015
      S  M Tu  W Th  F  S
     13 14 15 16 17 18 19  
  • IEEE floating point representation
  • Rounding
  • Floating point operations
  • Exceptional situations
Reading:
Overton: Chapters 4-7; Cheney and Kincaid: 1.3

Week 4 (Lectures 6-7)

   Sept 2015
      S  M Tu  W Th  F  S
     20 21 22 23 24 25 26     
  • Floating point in C
  • Taylor series
  • Approximating a derivative
  • Numerical cancellation
  • MATLAB demo
  • Solving a linear system of equations
    • Gaussian elimination with no pivoting
Reading:
  • Overton: Chapters 10-11. Cheney and Kincaid: 1.2, 1.4, 2.1

Week 5 (Lectures 8-9)

   Sept, Oct 2015
       S  M Tu W Th  F  S
      27 28 29 30  1 2  3  
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 2015
      S  M Tu  W Th  F  S
      4  5  6  7  8  9 10 
Solving a nonlinear equation:
  • Introduction
  • The bisection method
  • Newton's method
Reading:
Cheney and Kincaid: 3.1, 3.2

Week 7 (Midterm)

   October 2015
      S  M Tu  W Th  F  S
     11 12 13 14 15 16 17 
  • In class Midterm on Oct 14.

Week 8 (Lectures 12-13)

   October 2015
      S  M Tu  W Th  F  S
     18 19 20 21 22 23 24 
Solving a nonlinear equation:
  • Newton's method
  • The secant method
  • Comparsions of the three methods.
Reading:
Cheney and Kincaid: 3.2, 3.3

Week 9 (Lectures 14-15)

   October, Novemebr 2015
      S  M Tu  W Th  F  S
     25 26 27 28 29 30 31        
Polynomial interpolation:
  • Vandermonde form
  • Lagrange form
  • Newton form
Reading:
Cheney and Kincaid: 4.1, 4.2

Week 10 (Lectures 16-17)

   November 2015
      S  M Tu  W Th  F  S
      1  2  3  4  5  6  7     
  • Polynomial interpolation: Newton form, contd.
  • Spline interpolation:
    • Linear spline
    • Cubic spline
Reading:
Cheney and Kincaid: 6.1, 6.2

Week 11 (Lectures 18-19)

   November 2015
      S  M Tu  W Th  F  S
      8  9 10 11 12 13 14  
  • Cubic spline
  • Least squares approximation
Reading:
Cheney and Kincaid: 6.3, 9.1

Week 12 (Lectures 20-21)

   November 2015
      S  M Tu  W Th  F  S
     15 16 17 18 19 20 21 
Numerical integration:
  • Rectangle rule
  • Midpoint rule
  • Trapezoid rule
  • Simpson's rule
  • Adaptive Simpson's rule
Reading:
Cheney and Kincaid: 5.1, 5.3.

Week 13 (Lectures 22-23)

   November 2015
      S  M Tu  W Th  F  S
     22 23 24 25 26 27 28 
  • Gaussian quadrature rules
Numerical solutions of ordinary differential equations:
  • Introduction
  • Euler's method
  • Types of errors
  • Trapezoid-Euler method and Midpoint-Euler method
Reading:
Cheney and Kincaid: 5.4, 7.1

Week 14 (Lectures 24-25)

   November, December 2015
      S  M Tu W Th  F  S
     29 30 1  2  3  4  5   
  • General Taylor series methods
  • Runge Kutta Methods
  • Review
Reading:
Cheney and Kincaid: 7.2

Week 15 (Lectures 26)

   December 2015
      S  M Tu  W Th  F  S
      6  7  8  9 10 11 12
    Class time will be office hours

 


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