General course description
Instructor: Da Kuang
TA: Wei Zhu

Syllabus

• Floating-point system
• Nonlinear equations with one variable
• Interpolation methods
• Numerical integration
• Linear systems / LU factorization
• Matlab/Octave programming

Textbooks and references

• (Officially) Required: R. L. Burden and J. D. Faires, Numerical analysis, 9th or 10th edition.
• Recommended: Michael Heath, Scientific Computing, 2nd edition.


• A good summary (or cheat-sheet) of the required textbook in slides: [link]
• A more practical treatment: Cleve Moler, Numerical Computing with Matlab.
• Matlab tutorial: [link]


• Additional references (posted here as the course proceeds):
• Floating-point system: [Slides from EE103]
• Nonlinear equations with one variable: [Slides from EE103]
• LU factorization: [Slides from EE103]
• Cholesky factorization: [Slides from EE103]
• Vector norms: [Slides from EE103]
• Matrix norms: [Slides from EE103]
• Conditioning and stability: [Slides from EE103]

Grading

• 60% Homework
• 20% Midterms
• 20% Final exam

Late Submissions Policy

• No late homework allowed. However, there are no penalties for medical reasons or emergencies. You must submit a doctor's note or an official letter explaining the emergency.

Programming Environments

• We will use Matlab or Octave for programming assignments.

Homework

Please note that while discussion is allowed and encouraged, individual students must write up their own answers and computer programs.
All the students must observe the conduct code.

• [10%] HW1
• [10%] HW2
• [10%] HW3
• [10%] HW4
• [10%] HW5
• [10%] HW6

Exercise Sets

• Exercise Set 1
• Exercise Set 2

Schedule

Date	Mon	Wed	Fri
Sep 25			Course overview / Logistics
Sep 28 Sep 30 Oct 2	Nonlinear equations (bisection, fixed-point) Reading: BF 2.1, 2.2 / MH 5.2.1, 5.2.2	Matlab/Octave introduction (example data set) HW1 out	Nonlinear equations (convergence order and rates) Reading: BF 2.4 / MH 5.1.2
Oct 5 Oct 7 Oct 9	Nonlinear equations (Newton's method) Reading: BF 2.3 / MH 5.2.3	Nonlinear equations (secant method) Reading: BF 2.3 / MH 5.2.4 HW1 due; HW2 out	Nonlinear equations (summary, pitfalls) Reading: BF 2.4 / MH 5.1.1
Oct 12 Oct 14 Oct 16	Conditioning and stability Reading: BF 7.1 / MH 1.2, 2.3.1	Floating-point numbers Reading: BF 1.2 / MH 1.3 HW2 due	Case study Midterm review
Oct 19 Oct 21 Oct 23	Midterm I [10%]	Linear systems (Gaussian elimination) Reading: BF 6.1 / MH 2.2.1, 2.2.2 HW3 out	Linear systems (LU factorization) Reading: BF 6.5 / MH 2.2.3
Oct 26 Oct 28 Oct 30	Linear systems (LU factorization) Reading: BF 6.5 / MH 2.2.3	Linear systems (pivoting) Reading: BF 6.2 / MH 2.2.4 HW3 due; HW4 out	Linear systems (Cholesky factorization) Reading: BF 6.6 / MH 2.4
Nov 2 Nov 4 Nov 6	Linear systems (Jacobi, Gauss-Seidel) Reading: BF 7.3 / MH 11.5.2, 11.5.3	Matrix norms Reading: BF 7.1 / MH 2.3.2, 2.3.3 HW4 due	Singular value decomposition (very briefly) Midterm review Reading: BF 9.6 / MH 4.5
Nov 9 Nov 11 Nov 13	Midterm II [10%]	(Veterans Day holiday)	Examples for SVD Principal component analysis (Data) (Script)
Nov 16 Nov 18 Nov 20	Matrix condition number Reading: BF 7.5 / MH 2.3.3 HW5 out	Interpolation (monomial, Lagrange) Demo Reading: BF 3.1 / MH 7.1 - 7.2.2	Interpolation (Newton, cubic spline) Reading: BF 3.3, 3.5 / MH 7.2.3, 7.3.2
Nov 23 Nov 25 Nov 27	Numerical integration (Newton-Cotes, composite rules) Reading: BF 4.3, 4.4 / MH 8.2, 8.4.1 HW5 due; HW6 out	(Cancelled)	(Thanksgiving)
Nov 30 Dec 2 Dec 4	Numerical integration (error analysis)	Numerical integration (extrapolation methods) HW6 due	Demos for PCA and cubic splines Course review
Dec 7	Final exam [20%] 3pm-6pm

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