CPSC 303: Numerical Approximation and Discretization

2016/2017 Winter Term 2 (January-April 2017)

MWF 12-1pm, Dempster (DMP) 301

Schedule


Date Topic Slides Required Reading Optional Reading
Jan 4 Introduction to CPSC 303.
Process & strategies of scientific computing. Course details.
  • AG 1.1
  • H 1.1
Jan 6 Numerical algorithms and errors.
Review process & strategies of scientific computing.
  • AG 1.2-1.3
  • H 1.2
Jan 9 Introduction to Matlab.
Jan 11 Problem conditioning and algorithm stability.
  • AG 1.3
  • H 1.2.6
  • H 1.3.1-1.3.8
Jan 13 Floating point arithmetic. Roundoff erros.
  • AG 2.1-2.4
  • H 1.3.9
Jan 16 Polynomial interpolation.
Monomial basis.
  • AG 10.1-10.2
  • H 7.1-7.3.1
Jan 18 Lagrange interpolation.
  • AG 10.3
  • Deadline Assignment 0
  • H 7.3.2
Jan 20 Divided Differences and Newton basis.
  • H 7.3.3
Jan 23 Review basis functions. Interpolation error.
  • AG 10.5
Jan 25 Chebychev interpolation.
  • AG 10.6
  • Deadline Assignment 1
  • H 7.3.4
Jan 27 Osculating interpolation.
  • AG 10.7
Jan 30 Piecewise polynomial interpolation.
  • AG 11.0-11.2
Feb 1 Cubic splines.
  • AG 11.3
  • Deadline Assignment 2
  • H 7.4.2
Feb 3 Hat function and B-splines.
  • AG 11.4
  • H 7.4.3
Feb 6 Parametric interpolation.
  • AG 11.5
Feb 8 Discrete least squares data fitting.
Discrete best fit.
  • AG 6.1
Feb 10 Least squares formulation.
  • AG 6.1
Feb 15 Midterm exam.
  • Location: FRDM 153
  • Be on time: Exam starts at 12:00.
  • Bring your student ID.
  • One side of a letter-sized (216mm × 279mm) sheet with handwritten notes.
Feb 17 Midterm discussion.
Feb 27 Numerical differentiation.
Finite difference formulas using Taylor series.
  • AG 14.1
Mar 1 Interpolation-based differentiation.
  • AG 14.3
  • Deadline Assignment 3
  • H 8.6.1
Mar 3 Roundoff and data errors in numerical differentiation. (lecture by Mike Gelbart)
  • AG 14.4
Mar 6 Richardson extrapolation.
  • AG 14.2
Mar 8 Numerical integration.
Basic quadrature rules.
  • AG 15.0-15.1
  • Deadline Assignment 4
  • H 8.1-8.3.0
Mar 10 Composite quadrature rules.
  • AG 15.2
  • H 8.3.5
Mar 13 Gaussian quadrature rules.
  • AG 15.3
  • H 8.3.3
Mar 15 Adaptive quadrature.
  • AG 15.4
  • Deadline Assignment 5
  • H 8.3.6
Mar 17 Numerical solution of initial value ordinary differential equations.
Differential equations - Motivation. Example: Zombie infection.
  • AG 16.1
Mar 20 Initial value ordinary differential equations. Existence, uniqueness, and conditioning.
  • H 9.2
Mar 22 Euler's method.
  • AG 16.2
  • H 9.3.1
Mar 24 Runge-Kutta methods.
  • AG 16.3
  • Deadline Assignment 6
  • H 9.3.6
Mar 27 Multistep methods.
  • AG 16.4
  • H 9.3.8
Mar 29 Absolute stability and stiffness.
  • AG 16.5
  • H 9.3.4
Mar 31 Error estimation.
  • AG 16.6
  • Deadline Assignment 7
  • H 9.3.2
Apr 3 Fun with PDEs.
Apr 5 Review. Questions.
Apr 7 No lecture.
  • Deadline Extra Assignment
Apr 9 No lecture.
Apr 26 Final exam.
  • Location: DMP 310
  • Be on time: Exam starts at 8:30 AM.
  • Bring your student ID.
  • One letter-sized (216mm × 279mm) sheet (both sides) with handwritten notes.