# 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.
Chapter 0
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
Mon
Jan 8
Algorithm properties.
• AG 1.3
• Chapter 1: 4.
08/01/18
• conditioning and stability
• conditioning and stability sheet
Mon
Jan 8
Matlab Tutorial for Beginners.
6-8pm in DMP 301.
Bring your laptop (with Matlab on it).
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
Fri
Jan 12
Roundoff error accumulation.
• AG 2.1, 2.3
• Chapter 2: 3.-4.
Prior Knowledge Quiz 12/01/18 roundoff error accumulation
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
Fri
Jan 19
Lagrange interpolation.
(clicker bonus questions start)
• AG 10.3
• Chapter 3: 3.2
Prior Knowledge Quiz 19/01/18 Lagrange basis
Mon
Jan 22
Divided differences and Newton's form.
• AG 10.4
• Chapter 3: 3.3-3.5
22/01/18 Newton basis
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
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
Fri
Feb 2
Splines.
• AG 11.3-11.4
• Chapter 4: 6.3-8.
Prior Knowledge Quiz 02/02/18
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
Fri
Feb 9
Interpolation-based differentiation.
• AG 14.3
• Chapter 5: 4.
Prior Knowledge Quiz 09/02/18
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
Wed
Feb 28
6. Numerical Integration.
Basic quadrature rules.
• AG 15.1
• Chapter 6: 1.-3.
28/02/18
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
Fri
Mar 9
Adaptive quadrature.
• AG 15.4-15.5
• Chapter 6: 6.-9.
Prior Knowledge Quiz 09/03/18
Mon
Mar 12
7. Ordinary Differential Equation Initial Value Problems.
Motivation. Zombie infection.
• AG 16.1
• Chapter 7: 1.-4.
12/03/18 zombies
Wed
Mar 14
Euler's method.
• AG 16.2
• Chapter 7: 5.-6.
14/03/18 Euler
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
Wed
Mar 21
Multistep methods: Adams Methods.
• AG 16.4
• Chapter 7: 7.2.1-7.2.2
Assignment 4 21/03/18
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
Mon
Mar 26
Absolute stability and stiffness.
• AG 16.5
• Chapter 7: 8.
26/03/18 stiffness
Wed
Mar 28
TA and Course Evaluations. Error control and estimation.
• AG 16.6
• Chapter 7: 9.
28/03/18 adaptivity
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.