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Basic command of college-level mathematics (linear algebra and calculus). Basic level of programming proficiency: python programming language.

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자막: 영어
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지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.
유동적 마감일
일정에 따라 마감일을 재설정합니다.
중급 단계

Basic command of college-level mathematics (linear algebra and calculus). Basic level of programming proficiency: python programming language.

완료하는 데 약 18시간 필요
영어
자막: 영어

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강의 계획 - 이 강좌에서 배울 내용

1

1

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Machine arithmetics. Systems of linear algebraic equations.

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11개 동영상 (총 61분), 3 개의 읽기 자료, 2 개의 테스트
11개의 동영상
Introduction.56
A simple worked example.5m
Machine arithmetics. Representation of real numbers.6m
Machine epsilon. Over- and underflow.8m
A crude estimate of the machine epsilon.2m
Systems of linear equations. Cramer's rule.5m
Gaussian elimination.10m
LU decomposition: the matrix form of the Gaussian elimination.9m
When does the Gaussian elimination work?2m
LU decomposition with pivoting. Permutation matrices.8m
3개의 읽기 자료
About the University10m
About the course10m
Slides10m
2

2

완료하는 데 3시간 필요

Numerical linear algebra.

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12개 동영상 (총 72분), 2 개의 읽기 자료, 1 개의 테스트
12개의 동영상
Sensitivity of a linear system.3m
Vector norms.5m
Matrix norms.3m
Common matrix norms.4m
Sensitivity of a linear system. Condition number.11m
Cholesky decomposition.7m
Banded matrices. Thomas algorithm.3m
Shermann-Morrison formula.8m
QR decomposition.6m
Constructing the QR decomposition: Householder reflections.13m
Constructing the QR decomposition: Givens rotations3m
2개의 읽기 자료
Slides10m
Slides10m
3

3

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Non-linear algebraic equations.

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11개 동영상 (총 71분), 1 개의 읽기 자료, 1 개의 테스트
11개의 동영상
Localization of roots. Bisection.4m
Fixed-point iteration.4m
Aside: convergence rates and related technicalities.7m
Back to the fixed-point iteration.11m
Fine-tuning the fixed-point iteration.5m
Newton's iteration.16m
Multiple roots. Modified Newton's method.3m
Inverse quadratic interpolation.4m
Roots of polynomials.3m
Roots of polynomials: the companion matrix.3m
1개의 읽기 자료
Slides10m
4

4

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Iterative method for linear systems.

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8개 동영상 (총 55분), 1 개의 읽기 자료, 1 개의 테스트
8개의 동영상
Simple iteration for a linear system. Jacobi iteration.8m
Convergence criteria for simple iteration.4m
Seidel's iteration.9m
Successive over-relaxation.3m
Canonic form of two-step iterative methods for linear systems.10m
Variational approaches: minimum residual method.5m
Copy of Simple iteration for a linear system. Jacobi iteration.8m
1개의 읽기 자료
Slides10m

검토

INTRODUCTION TO NUMERICAL ANALYSIS의 최상위 리뷰

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