Assignments

Assignment 1:  3076, due 14 April  (Solutions) 
 3976, due 14 April  (Solutions) 
Assignment 2:  3076/3976, due 16 May  (Solutions) 
Assignment 3:  3076/3976, due 6 June  (Solutions) 
3976 Project:  Draft due 6 June

 Final due 1 July

Lecture notes

Lecture 1:  Integers and Bits

Lecture 2:  Strings and Vectors 
Lecture 3:  Types and Functions 
Lecture 4:  IEEE Floating Point Arithmetic 
Lecture 5:  Rounding and Arithmetic in IEEE Floating Point 

Lecture 6:  Linear Algebra

Lecture 7:  Interpolation

Lecture 8:  Abstract Types

Lecture 9:  Norms

Lecture 10:  Permutation, Orthogonal and Triangular Matrices

Lecture 11:  Matrix Factorizations

Lecture 12:  PLU Decomposition

Lecture 13:  Givens' Rotations

Lecture 14:  QR Factorization and Least Squares


Lecture 15:  Computational Cost and Complexity

Lecture 16:  Matrix Norms

Lecture 17:  Problems and Absolute Condition Numbers

Lecture 18:  Relative and Matrix Condition Numbers

Lecture 19:  Error Analysis

Lecture 20:  Backward Error Analysis For Dot Products


Lecture 21:  Images

Lecture 22:  The Singular Value Decomposition (SVD)

Lecture 23:  The SVD and Condition Numbers, Matrix Exponentials

Lecture 24:  Schur decomposition, The QR Algorithm and Companion Matrices


Lecture 25:  Continuous Problems

Lecture 26:  Numerical Integration/Quadrature

Lecture 27:  Error of Quadrature Rules

Lecture 28:  Bernoulli Polynomials

Lecture 29:  The Euler–Maclaurin Formula

Lecture 30:  The Trapezium Rule and Fourier Modes

Lecture 31:  The Discrete Fourier Expansion

Lecture 32:  The Discrete Fourier Transform


Lecture 33:  Linear ODEs

Lecture 34:  Discretizing Derivatives

Lecture 35:  Forward Euler, Backward Euler and Midpoint Methods

Lecture 36:  Boundary Value Problems

Lecture 37:  Timeevolution PDEs with Periodic Boundary Conditions

Lecture 38:  Nonlinear Problems

Lecture 39:  CFL Condition, Nonlinear Boundary Value Problems

Tutorials

Lab 1:  REPL, Jupyter and Plotting
 (Solutions)

Lab 2:  Creating a Rational Type
 (Solutions)

Lab 3:  Structures
 (Solutions)

Lab 4:  Linear Systems for Structures
 (Solutions)

Lab 5:  Stable Structures
 (Solutions)

Lab 6:  QR Decomposition using Householder Reflections
 (Solutions)

Lab 7:  Conditioning and Error Analysis
 (Solutions)

Lab 8:  Function Compression and the SVD
 (Solutions)

Lab 9:  Simpson's Rule
 (Solutions)

Lab 10:  Romberg Quadrature
 (Solutions)

Lab 11:  The Discrete Cosine Transform
 (Solutions)

Lab 12:  Timeevolution PDEs with Boundary Conditions
 (Solutions)

Reading list

Lecture 1:  Overton, Chapters 1–3 
Introduction,
The Real Numbers,
Computer Representation of Numbers 
 Julia Documentation 
Variables,
Mathematical Operations and Elementary Functions

Lecture 2:  Julia Documentation 
Integers and Floating Point Numbers,
Strings

Lecture 3:  Overton, Chapter 4 
IEEE Floating Point Representation

 Julia Documentation 
Functions,
Types

Lecture 4:  Overton, Chapter 5–6 
Rounding,
Correctly Rounded Floating Point Operations 
Lecture 5:  Overton, Chapter 11 
Cancellation

Lecture 6:  Julia Documentation 
Multidimensional Arrays,
Linear Algebra 
 Quantitative Economics 
Vectors, Arrays and Matrices,
Linear Algebra

Lecture 7:  Trefethen & Bau, Lecture 1–2 
MatrixVector Multiplication,
Orthogonal Vectors and Matrices

 Wikipedia 
Interpolation,
Least squares

Lecture 9:  Trefethen & Bau, Lecture 3 
Norms (Section Vector Norms) 
Lecture 10:  Corless & Fillon, Sections 4.2–4.3 
Solving Unitary or Orthogonal Systems, Solving Triangular Systems

Lecture 11:  Wikipedia 
LU Decomposition,
QR Decomposition

 Corless & Fillon, Sections 4.4–4.5 
Factoring as a Step Toward Solution, The QR Factoring

Lecture 12:  Corless & Fillon, Sections 4.7 
Solving Ax=b with the LU Factoring

Lecture 13:  Corless & Fillon, Sections 4.5.3 
Householder Reflections

Lecture 14:  Corless & Fillon, Sections 4.5.5 
Solving Overspecified Systems with the QR Factoring

Lecture 15:  Corless & Fillon, Section 1.5 
Complexity and Cost of Algorithms

Lecture 16:  Trefethen & Bau, Lecture 3 
Norms (Section Matrix Norms Induced by Vector Norms) 
Lecture 17:  Overton, Chapter 12 
Conditioning of Problems

 Corless & Fillon, Sections 1.1 
Mathematical Problems and Computability of Solutions

Lecture 18:  Corless & Fillon, Sections 1.4 
Perspectives on Error Analysis

Lecture 19:  Overton, Chapter 13 
Stability of Algorithms

Lecture 20:  Corless & Fillon, Sections 1.3 
Error Accumulation and Catastrophic Cancellation

Lecture 22:  Trefethen & Bau, Lecture 4 
The Singular Value Decomposition

Lecture 23:  Trefethen & Bau, Lecture 5 
More on the SVD

 Wikipedia 
Matrix Exponential

Lecture 24:  Wikipedia 
Schur Decomposition ,
Companion Matrix ,
QR Algorithm

Lecture 25:  18.330 Notes  Numerical Integration, Part 1

Lecture 30:  18.330 Notes  The FFT and its Applications

Lecture 33:  18.330 Notes  Integration of Ordinary Differential Equations

Lecture 36:  18.330 Notes  Boundary Value Problems

Lecture 38:  18.330 Notes  Nonlinear Root Finding and a Glimpse at Optimization
