CSE330

Numerical Methods

[RRH, ALB, NLH]81 Videos

Floating-point arithmetic, polynomial interpolation, numerical differentiation, root finding, linear systems, least squares, and numerical integration.

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81 Videos

Floating Point Arithmetic

12
1
Floating Point Representation [RRH]

Floating Point Representation [RRH]

42:52
2
Floating-3 [RRH]

Floating-3 [RRH]

13:35
3
Rounding Error [RRH]

Rounding Error [RRH]

1:01:50
4
Introductory Class [ALB]

Introductory Class [ALB]

36:46
5
Chapter 1: IEEE Standard (1985) for Double Precision [ALB]

Chapter 1: IEEE Standard (1985) for Double Precision [ALB]

1:16:41
6
Chapter 1: Rounding Error & Machine Epsilon Derivation [ALB]

Chapter 1: Rounding Error & Machine Epsilon Derivation [ALB]

1:40:18
7
Chapter03: Upper Bound of Truncation Error, Rounding Error & Relative Error [ALB]

Chapter03: Upper Bound of Truncation Error, Rounding Error & Relative Error [ALB]

1:10:48
8
Rounding Error, Truncation Error & Richardson Extrapolation [ALB]

Rounding Error, Truncation Error & Richardson Extrapolation [ALB]

1:18:30
9
Lecture 1.1 Floating Point Arithmetic 1 [NLH]

Lecture 1.1 Floating Point Arithmetic 1 [NLH]

1:17:26
10
Lecture 1.2 Floating Point Arithmetic 2 [NLH]

Lecture 1.2 Floating Point Arithmetic 2 [NLH]

1:07:18
11

Floating Point Arithmetic - 1

1:14:23
12

Floating Point Arithmetic - 2

1:11:57

Polynomial Interpolation

24
1
Polynomial [RRH]

Polynomial [RRH]

48:00
2
Vandermonde Matrix [RRH]

Vandermonde Matrix [RRH]

36:56
3
Lagrange [RRH]

Lagrange [RRH]

55:09
4
Newton's Divided Difference & Cauchy's Theorem [RRH]

Newton's Divided Difference & Cauchy's Theorem [RRH]

1:05:03
5
Hermite Practice [RRH]

Hermite Practice [RRH]

55:49
6
Runge Practice [RRH]

Runge Practice [RRH]

11:09
7
Chapter 2: Vandermonde Matrix [ALB]

Chapter 2: Vandermonde Matrix [ALB]

1:10:48
8
Chapter 2: Lagrange Interpolation Method [ALB]

Chapter 2: Lagrange Interpolation Method [ALB]

1:28:59
9
Chapter 2: Runge Phenomenon & Chebyshev Nodes [ALB]

Chapter 2: Runge Phenomenon & Chebyshev Nodes [ALB]

1:14:07
10
Chapter 2: Chebyshev Nodes Example & Chapter 3: Numerical Differentiation [ALB]

Chapter 2: Chebyshev Nodes Example & Chapter 3: Numerical Differentiation [ALB]

1:47:20
11
Chapter 7: Cauchy's Theorem & Final Syllabus Review Session [ALB]

Chapter 7: Cauchy's Theorem & Final Syllabus Review Session [ALB]

58:59
12
Lecture 2.1 Polynomials and Taylor Series [NLH]

Lecture 2.1 Polynomials and Taylor Series [NLH]

1:08:57
13
Lecture 2.2 Polynomial Interpolation & Vandermonde Matrix [NLH]

Lecture 2.2 Polynomial Interpolation & Vandermonde Matrix [NLH]

32:42
14
Lecture 2.3 Lagrange Interpolation [NLH]

Lecture 2.3 Lagrange Interpolation [NLH]

28:55
15
Lecture 2.4 Newton's Divided Difference Form [NLH]

Lecture 2.4 Newton's Divided Difference Form [NLH]

29:47
16
Lecture 2.5 Cauchy's Theorem [NLH]

Lecture 2.5 Cauchy's Theorem [NLH]

29:56
17
Lecture 2.6 Hermite Interpolation [NLH]

Lecture 2.6 Hermite Interpolation [NLH]

54:45
18
Lecture 2.7 Convergence, Runge Phenomenon, Chebyshev's Node [NLH]

Lecture 2.7 Convergence, Runge Phenomenon, Chebyshev's Node [NLH]

51:01
19

Polynomial Interpolation - 1

1:10:37
20

Polynomial Interpolation - 2

1:06:35
21

Polynomial Interpolation - 3

1:01:33
22

Polynomial Interpolation - 4

50:47
23

Polynomial Interpolation - 5

50:51
24

Polynomial Interpolation - 6

41:27

Numerical Differentiation

10
1
Numerical Differentiation [RRH]

Numerical Differentiation [RRH]

22:42
2
Richardson Extrapolation - Derivation [RRH]

Richardson Extrapolation - Derivation [RRH]

15:01
3
Richardson Extrapolation - 2 [RRH]

Richardson Extrapolation - 2 [RRH]

31:34
4
Upper Bound of Truncation Error in Differentiation [RRH]

Upper Bound of Truncation Error in Differentiation [RRH]

17:06
5
Chapter 3: Richardson Extrapolation [ALB]

Chapter 3: Richardson Extrapolation [ALB]

55:55
6
Lecture 3.1 Numerical Differentiation 1 [NLH]

Lecture 3.1 Numerical Differentiation 1 [NLH]

1:13:47
7
Lecture 3.2 Numerical Differentiation 2 | Richardson Extrapolation Theory [NLH]

Lecture 3.2 Numerical Differentiation 2 | Richardson Extrapolation Theory [NLH]

48:53
8
Lecture 3.3 Numerical Differentiation 3 Examples [NLH]

Lecture 3.3 Numerical Differentiation 3 Examples [NLH]

57:24
9

Differentiation - 1

41:11
10

Differentiation - 2

56:28

Root Finding

12
1
Bisection Method [RRH]

Bisection Method [RRH]

44:30
2
Fixed Point Iteration [RRH]

Fixed Point Iteration [RRH]

55:12
3
Newton Raphson Method [RRH]

Newton Raphson Method [RRH]

48:58
4
Aitken and Secant [RRH]

Aitken and Secant [RRH]

28:40
5
Chapter-04: Fixed Point Iteration [ALB]

Chapter-04: Fixed Point Iteration [ALB]

1:07:24
6
Chapter 4: Contraction Mapping Theorem [ALB]

Chapter 4: Contraction Mapping Theorem [ALB]

52:53
7
Chapter 4: Newton's Method [ALB]

Chapter 4: Newton's Method [ALB]

1:10:33
8
Newton Raphson Method [ALB]

Newton Raphson Method [ALB]

1:12:38
9
Lecture 4.1 Root Finding: Bisection Method [NLH]

Lecture 4.1 Root Finding: Bisection Method [NLH]

1:17:13
10
Lecture 4.2 Root Finding: Fixed Point Iteration [NLH]

Lecture 4.2 Root Finding: Fixed Point Iteration [NLH]

1:11:30
11
Lecture 4.4 Root Finding: Newton-Raphson Method [NLH]

Lecture 4.4 Root Finding: Newton-Raphson Method [NLH]

57:53
12
Lecture 4.7 Root Finding: Quasi-Newton / Secant Method [NLH]

Lecture 4.7 Root Finding: Quasi-Newton / Secant Method [NLH]

21:02

Linear Systems

8
1
Example Problem - Gaussian Elimination [RRH]

Example Problem - Gaussian Elimination [RRH]

23:55
2
Example Problem - LU Decomposition [RRH]

Example Problem - LU Decomposition [RRH]

39:42
3
Chapter-05: Gaussian Elimination, No. of Operations, Pivoting [ALB]

Chapter-05: Gaussian Elimination, No. of Operations, Pivoting [ALB]

1:09:00
4
Chapter-05: Gaussian Elimination, Pivoting, No. of Operations - 2 [ALB]

Chapter-05: Gaussian Elimination, Pivoting, No. of Operations - 2 [ALB]

55:33
5
Chapter 05: LU Decomposition [ALB]

Chapter 05: LU Decomposition [ALB]

1:04:58
6
Lecture 5.1 Linear Systems: Basics & Triangular Systems [NLH]

Lecture 5.1 Linear Systems: Basics & Triangular Systems [NLH]

45:38
7
Lecture 5.2 Linear Systems: Gaussian Elimination [NLH]

Lecture 5.2 Linear Systems: Gaussian Elimination [NLH]

42:55
8
Lecture 5.3 Linear Systems: LU Decomposition [NLH]

Lecture 5.3 Linear Systems: LU Decomposition [NLH]

1:08:44

Least Squares & QR Decomposition

7
1
Problem Solving Using Least Squares [RRH]

Problem Solving Using Least Squares [RRH]

1:00:48
2
Problem Solving - QR Decomposition [RRH]

Problem Solving - QR Decomposition [RRH]

1:01:18
3
Chapter 6: QR Decomposition [ALB]

Chapter 6: QR Decomposition [ALB]

1:23:57
4
Chapter 6: QR Decomposition - 2 [ALB]

Chapter 6: QR Decomposition - 2 [ALB]

1:34:53
5
Lecture 6.1.1 Least Squares: Discrete Least Squares [NLH]

Lecture 6.1.1 Least Squares: Discrete Least Squares [NLH]

47:13
6
Lecture 6.1.2 Least Squares: Orthonormality [NLH]

Lecture 6.1.2 Least Squares: Orthonormality [NLH]

14:52
7
Lecture 6.2 Least Squares: QR Decomposition [NLH]

Lecture 6.2 Least Squares: QR Decomposition [NLH]

1:03:07

Numerical Integration

8
1
Numerical Integration Part 1 [RRH]

Numerical Integration Part 1 [RRH]

54:06
2
Numerical Integration Part 2 [RRH]

Numerical Integration Part 2 [RRH]

28:07
3
Chapter 7: Numerical Integration Basics, Trapezium Rule [ALB]

Chapter 7: Numerical Integration Basics, Trapezium Rule [ALB]

1:12:32
4
Chapter 07: Simpson's Rule [ALB]

Chapter 07: Simpson's Rule [ALB]

47:54
5
Chapter 7: Composite Newton's Cotes [ALB]

Chapter 7: Composite Newton's Cotes [ALB]

1:14:07
6
Lecture 7.1.1 Numerical Integration Part 1 [NLH]

Lecture 7.1.1 Numerical Integration Part 1 [NLH]

1:06:47
7
Lecture 7.1.2 Numerical Integration Part 2 [NLH]

Lecture 7.1.2 Numerical Integration Part 2 [NLH]

31:53
8
Lecture 7.2 Numerical Integration Part 3 [NLH]

Lecture 7.2 Numerical Integration Part 3 [NLH]

36:12