CPSC 303: Numerical Approximation and Discretization

2017/2018 Winter Term 2 (January-April 2018)

Mon/Wed/Fri 14:00-15:00, DMP 110

Tentative Lecture and Pre-Reading Schedule

The schedule is tentative, and materials will be updated as we go. Pre-class materials will be posted several days before class. Clicker questions and in-class exercises will be posted after class.
Readings are from
- notes uploaded on Canvas,
- the course textbook Ascher & Greif (AG), or
- the book Heath, 2nd edition (H). (optional)
Required Pre-Reading: It is important to complete the pre-class reading.
Due Date: This column shows the due dates of the weekly out-of-class quizzes (in Canvas), bi-weekly homework assignments, and surveys.
For the students on the waiting list, I will copy the material into Piazza until January 17.

Date	Topic	Required Pre-Reading	Due Date (2pm)	Clickers and Exercises	Relevant Files	Optional Reading
Wed Jan 3	Introduction to CPSC 303.	Syllabus Sign up for Piazza Register iClicker/REEF (bonus questions start Jan 19) Get access to Matlab		Chapter 0		Crashing waves, awesome explosions, turbulent smoke and beyond: applied mathematics and scientific computing in the visual effects industry Using the Force: Star Wars in the Classroom Bending a Soccer Ball with CFD Sports ball aerodynamics: A numerical study of the erratic motion of soccer balls Qualitative Analysis of Insect Outbreak Systems: The Spruce Budworm and Forest
Fri Jan 5	1. Numerical Algorithms. Scientific computing. Numerical algorithms and errors.	AG 1.1-1.2 Chapter 1: 1.-3.	Interest Inventory	05/01/18	computational error	H 1.2.1-1.2.2, 1.2.4 Roundoff vs. Discretization Error
Mon Jan 8	Algorithm properties.	AG 1.3 Chapter 1: 4.		08/01/18	conditioning and stability conditioning and stability sheet	H 1.2.3, 1.2.6-1.2.7 Accuracy and Stability of Numerical Algorithms Towards a formal definition of numerical stability
Mon Jan 8	Matlab Tutorial for Beginners. 6-8pm in DMP 301. Bring your laptop (with Matlab on it).	Getting Started with Matlab Introduction to Matlab				Introductions to Matlab Origins of Matlab
Wed Jan 10	2. Roundoff Errors. Floating point systems. The IEEE standard.	AG 2.1-2.2, 2.4 Chapter 2: 1.-2.	Assignment 0	10/01/18	roundoff error	H 1.3.1.-1.3.8 Numerical Computing with IEEE Floating Point Arithmetic Patriot Missile Failure Video Patriot Missile Failure Collection of Software Bugs Floating Point Systems Rounding Rules Base Conversion
Fri Jan 12	Roundoff error accumulation.	AG 2.1, 2.3 Chapter 2: 3.-4.	Prior Knowledge Quiz	12/01/18	roundoff error accumulation	H 1.3.9 Quadratic Formula Infinite Series
Mon Jan 15	Review numerical algorithms and errors: In-class group exercise.	AG 1-2 Chapter 1-2
Wed Jan 17	3. Polynomial Interpolation. Monomial interpolation.	AG 10.1-10.2 Chapter 3: 1.-3.1		17/01/18	monomial basis	H 7.1-7.3.1 A Chronology of Interpolation: From Ancient Astronomy to Modern Signal and Image Processing Six Myths of Polynomial Interpolation and Quadrature How to Share a Secret Polynomial interpolation in several variables On multivariate polynomial interpolation Polynomial Bases Basis Functions Taylor Polynomial Interpolation
Fri Jan 19	Lagrange interpolation. (clicker bonus questions start)	AG 10.3 Chapter 3: 3.2	Prior Knowledge Quiz	19/01/18	Lagrange basis	H 7.3.2 Barycentric Lagrange Interpolation The numerical stability of barycentric Lagrange interpolation The Lagrange Interpolation Polynomial for Neural Network Learning The Reconstruction of the Compressed Digital Signal using Lagrange Polynomial Interpolation Application of the polynomial interpolation method for determining performance characteristics of a diesel engine
Mon Jan 22	Divided differences and Newton's form.	AG 10.4 Chapter 3: 3.3-3.5		22/01/18	Newton basis	H 7.3.3 Newton Interpolation
Wed Jan 24	Polynomial interpolation error.	AG 10.5 Chapter 3: 4.	Assignment 1	24/01/18
Fri Jan 26	Chebychev interpolation.	AG 10.6 Chapter 3: 5.	Prior Knowledge Quiz	26/01/18		H 7.3.4-7.3.5 Approximation Theory and Approximation Practice Chebyshev Polynomials Convergence of Polynomial Interpolants
Mon Jan 29	Osculating interpolation.	AG 10.7 Chapter 3: 6.		29/01/18
Wed Jan 31	4. Piecewise Polynomial Interpolation. Local interpolants.	AG 11.1-11.2 Chapter 4: 1.-6.2		31/01/18	polynomial vs piecewise polynomial interpolation	H 7.4 Subdivision Surfaces in Character Animation Shape Optimization Using Reflection Lines Polynomial-Spline Comparison
Fri Feb 2	Splines.	AG 11.3-11.4 Chapter 4: 6.3-8.	Prior Knowledge Quiz	02/02/18		H 7.4 The Extensive Use of Splines at Boeing Curves and Surfaces in Computer Aided Geometric Design 3D Computer Graphics and CAD Application Software Smoothing by spline functions Smoothing by spline functions. II Spline Functions: Basic Theory Spline Functions: Computational Methods Interpolating Cubic Splines Piecewise Cubic Interpolation B-Splines
Mon Feb 5	Review polynomial and piecewise polynomial interpolation: In-class group exercise.	AG 10-11 Chapter 3-4
Wed Feb 7	5. Numerical Differentiation. Finite difference formulas using Taylor series.	AG 14.1 Chapter 5: 1.-3.	Assignment 2	07/02/18		H 8.6 Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Second Edition Finite Difference Approximations
Fri Feb 9	Interpolation-based differentiation.	AG 14.3 Chapter 5: 4.	Prior Knowledge Quiz	09/02/18		H 8.6.1 Numerical Differentiation
Mon Feb 12	Family Day.
Wed Feb 14	Roundoff and data errors in numerical differentiation.	AG 14.4 Chapter 5: 5.	Mid-Course Feedback	14/02/18
Fri Feb 16	Midterm Exam.	Location: FRDM 153 Be on time: Exam starts at 14:00. Bring your student ID. One side of a letter-sized (216mm × 279mm) sheet.
Mon Feb 26	Richardson extrapolation.	AG 14.2 Chapter 5: 6.		26/02/18		H 8.7 Extrapolation methods: theory and practice Survey of Extrapolation Processes in Numerical Analysis Richardson Extrapolation
Wed Feb 28	6. Numerical Integration. Basic quadrature rules.	AG 15.1 Chapter 6: 1.-3.		28/02/18		H 8.1-8.3.1 Computational Integration Newton-Cotes Quadrature Cancellation of Errors An encyclopaedia of cubature formulas Numerical Evaluation of Multiple Integrals A survey of numerical cubature over triangles Lattice methods for multiple integration A Primer on Integral Equations of the First Kind: The Problem of Deconvolution and Unfolding Computational Methods for Integral Equations
Fri Mar 2	Composite quadrature rules.	AG 15.2 Chapter 6: 4.	Prior Knowledge Quiz	02/03/18		H 8.3.5
Mon Mar 5	Review numerical differentiation: In-class group exercise.	AG 14 Chapter 5
Wed Mar 7	Gaussian quadrature.	AG 15:3 Chapter 6: 5.	Assignment 3	07/03/18		H 8.3.2-8.3.3 Is Gauss Quadrature Better than Clenshaw-Curtis?
Fri Mar 9	Adaptive quadrature.	AG 15.4-15.5 Chapter 6: 6.-9.	Prior Knowledge Quiz	09/03/18		H 8.3.6, 8.7 Adaptive Quadrature - Revisited QUADPACK: A Subroutine Package for Automatic Integration Improving QUADPACK automatic integration routines When Not to Use an Automatic Quadrature Routine Comments on the Nature of Automatic Quadrature Routines Double Integration Using One-Dimensional Adaptive Quadrature Routines: A Software Interface Problem Adaptive Quadrature Romberg Integration
Mon Mar 12	7. Ordinary Differential Equation Initial Value Problems. Motivation. Zombie infection.	AG 16.1 Chapter 7: 1.-4.		12/03/18	zombies	H 9.1-9.2 When Zombies attack! The MATLAB ODE Suite Test Set for IVP Solvers A History of Algorithms Numerical Solution of Ordinary Differential Equations: Is There Anything Left to Do? Solving Ordinary Differential Equations I Solving Ordinary Differential Equations II Numerical Methods for Evolutionary Differential Equations Numerical Solution of Two Point Boundary Value Problems Numerical Solution of Boundary Value Problems for Ordinary Differential Equations Finite Difference Methods for Ordinary and Partial Differential Equations
Wed Mar 14	Euler's method.	AG 16.2 Chapter 7: 5.-6.		14/03/18	Euler	H 9.3.1-9.3.3 Euler's Method Backward Euler Method
Fri Mar 16	Review numerical integration: In-class group exercise.	AG 15 Chapter 6	Prior Knowledge Quiz
Mon Mar 19	Runge-Kutta methods.	AG 16.3 Chapter 7: 7.1		19/03/18	Runge-Kutta	H 9.3.6 Numerical Methods for Ordinary Differential Equations Runge-Kutta Methods Trapezoid Method
Wed Mar 21	Multistep methods: Adams Methods.	AG 16.4 Chapter 7: 7.2.1-7.2.2	Assignment 4	21/03/18		H 9.3.8 An attempt to test the theories of capillary action by comparing the theoretical and measured forms of drops of fluid Adams-Bashforth Methods Predictor-Corrector Methods
Fri Mar 23	Multistep methods: BDF Methods. ODE stability.	AG 16.4 Chapter 7: 7.2.3-8.1.1	Prior Knowledge Quiz	23/03/18		H 9.3.7-9.3.9 Integration of Stiff Equations BDF Methods
Mon Mar 26	Absolute stability and stiffness.	AG 16.5 Chapter 7: 8.		26/03/18	stiffness	H 9.3.4 Stiff ODE solvers: A review of current and coming attractions A user's view of solving stiff ordinary differential equations Stability Regions of ODE Formulas Stiff ODEs
Wed Mar 28	TA and Course Evaluations. Error control and estimation.	AG 16.6 Chapter 7: 9.		28/03/18	adaptivity	H 9.3.2 Error Estimation
Fri Mar 30	Good Friday.
Mon Apr 2	Easter Monday.
Wed Apr 4	Review ordinary differential equation initial value problems: In-class group exercise.	AG 16 Chapter 7
Fri Apr 6	Review. Questions.		Prior Knowledge Quiz, Assignment 5
Mon Apr 9			Teaching Evaluation Survey
Wed Apr 18			Assignment 6 (Bonus)
Wed Apr 25	Final Exam.	Location: CHBE 101 Be on time: Exam starts at 15:30. Bring your student ID. One letter-sized (216mm × 279mm) sheet.