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julia代写-MATH50003

时间：2022-03-16

16/03/2022, 08:58 GitHub -
Imperial-MATH50003/MATH50003NumericalAnalysis: Notes and course material
for MATH50003 Numerical Analysis

https://github.com/Imperial-MATH50003/MATH50003NumericalAnalysis 1/6

Imperial-MATH50003 / MATH50003NumericalAnalysis Public

Notes and course material for MATH50003 Numerical Analysis

MIT License

27 stars 77 forks

Code Issues 5 Pull requests 4 Actions Projects Wiki Security Insights

View code

MATH50003NumericalAnalysis

Notes and course material for MATH50003 Numerical Analysis

Lecturer: Dr Sheehan Olver

Problem Classes: 2–4pm Thursdays, Huxley 340–342

Overview lecture: 10–11am Fridays, Clore

Q&A: 9:50–10:30 Mondays, 10:40–11:20 Tuesdays on Teams

Course notes

Background material

1. Introduction to Julia: we introduce the basic features of the Julia language.

2. Asymptotics and Computational Cost: we review Big-O, little-o and asymptotic to

notation, and their usage in describing computational cost.

Part I: Computing with numbers

Star Notifications

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dlfivefifty … 16 hours ago

README.md

16/03/2022, 08:58 GitHub - Imperial-MATH50003/MATH50003NumericalAnalysis: Notes and course material for MATH50003 Numerical Analysis

https://github.com/Imperial-MATH50003/MATH50003NumericalAnalysis 2/6

1. Numbers: we discuss how computers represent integers and real numbers, as well as

their arithmetic operations.

2. Differentiation: we discuss ways of approximating derivatives, including automatic

differentiation, which is essential to machine learning.

Part II: Computing with matrices

1. Structured Matrices: we discuss types of structured matrices (permutations, orthogonal

matrices, triangular, banded).

2. Decompositions: we discuss algorithms for computing matrix decompositions (QR and

PLU decompositions) and their use in solving linear systems.

3. Singular values and condition numbers: we discuss vector and matrix norms, and

condition numbers for matrices, and the singular value decomposition.

4. Differential Equations: we discuss the numerical solution of linear differential equations,

including both time-dependent ordinary differential equations and boundary value

problems, by reduction to linear systems.

Part III: Computing with functions

1. Fourier series: we discuss Fourier series and their usage in numerical computations via

the fast Fourier transform.

2. Orthogonal Polynomials: we discuss orthogonal polynomials—polynomials orthogonal

with respect to a prescribed weight.

3. Interpolation and Gaussian quadrature: we discuss polynomial interpolation, Gaussian

quadrature, and expansions in orthogonal polynomials.

Assessment

1. Practice computer-based exam (Solutions)

2. Computer-based exam (released on Blackboard): 18 March 2022, 3–5pm (1 hour exam,

1 hour upload/download)

3. Practice final exam (pen-and-paper, not for credit): Summer Term (TBC)

4. Final exam (pen-and-paper): Summer Term (TBC)

Problem sheets

1. Week 1 (Solutions): Binary representation, integers, floating point numbers, and interval

arithmetic

2. Week 2 (Solutions): Finite-differences, dual numbers, and Newton iteration

3. Week 3 (Solutions): dense, triangular, banded, permutation, rotation and reflection

matrices

4. Week 4 (Solutions): least squares, QR and PLU decompositions

https://github.com/Imperial-MATH50003/MATH50003NumericalAnalysis 1/6

Imperial-MATH50003 / MATH50003NumericalAnalysis Public

Notes and course material for MATH50003 Numerical Analysis

MIT License

27 stars 77 forks

Code Issues 5 Pull requests 4 Actions Projects Wiki Security Insights

View code

MATH50003NumericalAnalysis

Notes and course material for MATH50003 Numerical Analysis

Lecturer: Dr Sheehan Olver

Problem Classes: 2–4pm Thursdays, Huxley 340–342

Overview lecture: 10–11am Fridays, Clore

Q&A: 9:50–10:30 Mondays, 10:40–11:20 Tuesdays on Teams

Course notes

Background material

1. Introduction to Julia: we introduce the basic features of the Julia language.

2. Asymptotics and Computational Cost: we review Big-O, little-o and asymptotic to

notation, and their usage in describing computational cost.

Part I: Computing with numbers

Star Notifications

main Go to file

dlfivefifty … 16 hours ago

README.md

16/03/2022, 08:58 GitHub - Imperial-MATH50003/MATH50003NumericalAnalysis: Notes and course material for MATH50003 Numerical Analysis

https://github.com/Imperial-MATH50003/MATH50003NumericalAnalysis 2/6

1. Numbers: we discuss how computers represent integers and real numbers, as well as

their arithmetic operations.

2. Differentiation: we discuss ways of approximating derivatives, including automatic

differentiation, which is essential to machine learning.

Part II: Computing with matrices

1. Structured Matrices: we discuss types of structured matrices (permutations, orthogonal

matrices, triangular, banded).

2. Decompositions: we discuss algorithms for computing matrix decompositions (QR and

PLU decompositions) and their use in solving linear systems.

3. Singular values and condition numbers: we discuss vector and matrix norms, and

condition numbers for matrices, and the singular value decomposition.

4. Differential Equations: we discuss the numerical solution of linear differential equations,

including both time-dependent ordinary differential equations and boundary value

problems, by reduction to linear systems.

Part III: Computing with functions

1. Fourier series: we discuss Fourier series and their usage in numerical computations via

the fast Fourier transform.

2. Orthogonal Polynomials: we discuss orthogonal polynomials—polynomials orthogonal

with respect to a prescribed weight.

3. Interpolation and Gaussian quadrature: we discuss polynomial interpolation, Gaussian

quadrature, and expansions in orthogonal polynomials.

Assessment

1. Practice computer-based exam (Solutions)

2. Computer-based exam (released on Blackboard): 18 March 2022, 3–5pm (1 hour exam,

1 hour upload/download)

3. Practice final exam (pen-and-paper, not for credit): Summer Term (TBC)

4. Final exam (pen-and-paper): Summer Term (TBC)

Problem sheets

1. Week 1 (Solutions): Binary representation, integers, floating point numbers, and interval

arithmetic

2. Week 2 (Solutions): Finite-differences, dual numbers, and Newton iteration

3. Week 3 (Solutions): dense, triangular, banded, permutation, rotation and reflection

matrices

4. Week 4 (Solutions): least squares, QR and PLU decompositions