MAT215

Complex Variables and Laplace Transformations

[PSD, EMNH, MASZ, Azmir, Math Crafters]86 Videos

Complex numbers, complex functions, analyticity, Cauchy-Riemann equations, elementary functions, complex integration, Cauchy’s theorems, Taylor & Laurent series, residue theorem, and Laplace transforms.

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86 Videos

Complex Numbers (Modulus, Argument, Polar Form & nth Roots)

13
1
Complex Number, Modulus, Argument, Polar Form - Part 1 [PSD]

Complex Number, Modulus, Argument, Polar Form - Part 1 [PSD]

1:52:43
2
nth Roots, Graphing - Part 2 [PSD]

nth Roots, Graphing - Part 2 [PSD]

1:38:16
3
Complex Variable: Polar Form, Examples and nth Roots [EMNH]

Complex Variable: Polar Form, Examples and nth Roots [EMNH]

1:23:58
4
Find nth Roots and Visualize Them in Riemann Surfaces [EMNH]

Find nth Roots and Visualize Them in Riemann Surfaces [EMNH]

1:00:46
5
Complex Equations and Inequalities [EMNH]

Complex Equations and Inequalities [EMNH]

50:35
6
Complex Numbers and Their Arithmetic [MASZ]

Complex Numbers and Their Arithmetic [MASZ]

1:44:17
7
Introduction & Complex Number - Part 1 [Azmir]

Introduction & Complex Number - Part 1 [Azmir]

1:49:53
8
Complex Number - Part 2 [Azmir]

Complex Number - Part 2 [Azmir]

1:43:01
9
Complex Number - Part 3 [Azmir]

Complex Number - Part 3 [Azmir]

1:27:00
10
Introduction to Complex Numbers [Math Crafters]

Introduction to Complex Numbers [Math Crafters]

1:08:18
11
Complex Numbers (Continued) [Math Crafters]

Complex Numbers (Continued) [Math Crafters]

47:32
12
Finding Roots [Math Crafters]

Finding Roots [Math Crafters]

59:01
13
Sketching Complex Equations [Math Crafters]

Sketching Complex Equations [Math Crafters]

1:13:50

Complex Functions, Limit & Continuity

7
1
Complex Valued Functions [PSD]

Complex Valued Functions [PSD]

1:26:33
2
Limit & Continuity [PSD]

Limit & Continuity [PSD]

1:38:05
3
Limit [EMNH]

Limit [EMNH]

54:03
4
Complex Variables, Mapping [MASZ]

Complex Variables, Mapping [MASZ]

40:48
5
Limit and Derivative of Functions of Complex Variables [MASZ]

Limit and Derivative of Functions of Complex Variables [MASZ]

1:16:20
6
Function, Mapping and Limits (Epsilon-Delta) [Azmir]

Function, Mapping and Limits (Epsilon-Delta) [Azmir]

2:53:55
7
Complex Functions, Limit and Continuity - Full Lecture [Math Crafters]

Complex Functions, Limit and Continuity - Full Lecture [Math Crafters]

1:58:05

Differentiability, Cauchy-Riemann Equations & Harmonic Functions

12
1
Differentiability of Complex Valued Functions [PSD]

Differentiability of Complex Valued Functions [PSD]

1:12:54
2
Cauchy-Riemann Equations & Analytic Functions [PSD]

Cauchy-Riemann Equations & Analytic Functions [PSD]

1:46:35
3
Harmonic Functions & Harmonic Conjugate [PSD]

Harmonic Functions & Harmonic Conjugate [PSD]

1:32:17
4
Differentiability in Higher Dimensions and Complex Planes [EMNH]

Differentiability in Higher Dimensions and Complex Planes [EMNH]

1:15:23
5
Continuity and Complex Differentiation [EMNH]

Continuity and Complex Differentiation [EMNH]

1:26:56
6
Harmonic Function [EMNH]

Harmonic Function [EMNH]

1:18:27
7
Complex Differentiation: Example and Formula [EMNH]

Complex Differentiation: Example and Formula [EMNH]

42:08
8
Cauchy-Riemann Equations, Analytic and Harmonic Functions [MASZ]

Cauchy-Riemann Equations, Analytic and Harmonic Functions [MASZ]

1:05:08
9
Limits and Derivative [Azmir]

Limits and Derivative [Azmir]

3:03:34
10
Analytic Functions [Azmir]

Analytic Functions [Azmir]

1:55:53
11
Definition of Derivatives, Cauchy-Riemann Equations, L'Hopital's Rule [Math Crafters]

Definition of Derivatives, Cauchy-Riemann Equations, L'Hopital's Rule [Math Crafters]

2:04:33
12
Harmonic Function, Analytic Function [Math Crafters]

Harmonic Function, Analytic Function [Math Crafters]

44:58

Elementary Functions (Exponential, Log & Trigonometric)

3
1
Exponential and Log Function [MASZ]

Exponential and Log Function [MASZ]

35:49
2
Complex Exponent, Trigonometric Functions [MASZ]

Complex Exponent, Trigonometric Functions [MASZ]

33:18
3
Elementary Functions [Azmir]

Elementary Functions [Azmir]

2:49:37

Complex Integration & Cauchy-Goursat Theorem

10
1
Complex Integration [PSD]

Complex Integration [PSD]

2:05:50
2
Cauchy-Goursat Theorem [PSD]

Cauchy-Goursat Theorem [PSD]

1:26:47
3
Complex Integration [EMNH]

Complex Integration [EMNH]

24:19
4
Contour Integral of Complex Functions [MASZ]

Contour Integral of Complex Functions [MASZ]

48:13
5
Contour Integral of Complex Functions (Continued) [MASZ]

Contour Integral of Complex Functions (Continued) [MASZ]

24:51
6
Cauchy-Goursat Theorem, Principle of Continuous Deformation, Cauchy's Integral Formula [MASZ]

Cauchy-Goursat Theorem, Principle of Continuous Deformation, Cauchy's Integral Formula [MASZ]

52:32
7
Complex or Contour Integral - Part 1 [Azmir]

Complex or Contour Integral - Part 1 [Azmir]

2:01:31
8
Complex or Contour Integral - Part 2 [Azmir]

Complex or Contour Integral - Part 2 [Azmir]

2:06:49
9
Complex Line Integration - Part 1 [Math Crafters]

Complex Line Integration - Part 1 [Math Crafters]

53:49
10
Complex Line Integration - Part 2 [Math Crafters]

Complex Line Integration - Part 2 [Math Crafters]

58:15

Cauchy Integral Formula

3
1
Cauchy Integral Formula [PSD]

Cauchy Integral Formula [PSD]

1:21:40
2
Cauchy's Integral Formula - Part 1 [Math Crafters]

Cauchy's Integral Formula - Part 1 [Math Crafters]

55:11
3
Cauchy's Integral Formula - Part 2 [Math Crafters]

Cauchy's Integral Formula - Part 2 [Math Crafters]

1:03:52

Taylor & Laurent Series

3
1
Laurent's Series [PSD]

Laurent's Series [PSD]

1:22:13
2
Extension of Cauchy's Integral Formula, Taylor and Laurent Series [MASZ]

Extension of Cauchy's Integral Formula, Taylor and Laurent Series [MASZ]

48:59
3
Complex/Contour Integral and Laurent Series - Part 3 [Azmir]

Complex/Contour Integral and Laurent Series - Part 3 [Azmir]

2:30:52

The Residue Theorem

6
1
The Residue Theorem [PSD]

The Residue Theorem [PSD]

1:10:29
2
Laurent Series (Continued), Pole, Residue, Cauchy's Residue Theorem [MASZ]

Laurent Series (Continued), Pole, Residue, Cauchy's Residue Theorem [MASZ]

39:17
3
Solving Improper Integrals using Cauchy's Residue Theorem [MASZ]

Solving Improper Integrals using Cauchy's Residue Theorem [MASZ]

36:04
4
Solving Improper Integrals using Cauchy's Residue Theorem (Continued) [MASZ]

Solving Improper Integrals using Cauchy's Residue Theorem (Continued) [MASZ]

26:04
5
Cauchy's Residue Theorem - Part 1 [Math Crafters]

Cauchy's Residue Theorem - Part 1 [Math Crafters]

49:35
6
Cauchy's Residue Theorem - Part 2 [Math Crafters]

Cauchy's Residue Theorem - Part 2 [Math Crafters]

48:37

Laplace Transform: Definition, Table & Translation Properties

13
1
Laplace Transformations Using Definition, Formula Proofs [PSD]

Laplace Transformations Using Definition, Formula Proofs [PSD]

1:12:30
2
Use of Table, First Translation & Laplace of t^n f(t) [PSD]

Use of Table, First Translation & Laplace of t^n f(t) [PSD]

1:06:59
3
Unit Step Function, Second Translation Formula [PSD]

Unit Step Function, Second Translation Formula [PSD]

56:34
4
Laplace Transform - Motivation [EMNH]

Laplace Transform - Motivation [EMNH]

39:34
5
Laplace Transform Definition and Basic Properties [EMNH]

Laplace Transform Definition and Basic Properties [EMNH]

1:00:39
6
Laplace Transform - Common Function Types [EMNH]

Laplace Transform - Common Function Types [EMNH]

1:16:57
7
Second Translation Property [EMNH]

Second Translation Property [EMNH]

54:29
8
Laplace Transformation [Azmir]

Laplace Transformation [Azmir]

2:05:20
9
Laplace Transform - Part 1 [Math Crafters]

Laplace Transform - Part 1 [Math Crafters]

37:23
10
Laplace Transform - Part 2 [Math Crafters]

Laplace Transform - Part 2 [Math Crafters]

32:11
11
Laplace Transform - Part 3 [Math Crafters]

Laplace Transform - Part 3 [Math Crafters]

30:49
12
Laplace Transform - Part 4 [Math Crafters]

Laplace Transform - Part 4 [Math Crafters]

22:56
13
Laplace Transform - Part 5 [Math Crafters]

Laplace Transform - Part 5 [Math Crafters]

43:05

Inverse Laplace Transform

8
1
Inverse Laplace Transform [PSD]

Inverse Laplace Transform [PSD]

54:51
2
Inverse Laplace using Partial Fraction Method [PSD]

Inverse Laplace using Partial Fraction Method [PSD]

1:13:58
3
Inverse Laplace Transformation [EMNH]

Inverse Laplace Transformation [EMNH]

1:08:02
4
Inverse Laplace Transform [Azmir]

Inverse Laplace Transform [Azmir]

1:34:29
5
Inverse Laplace Transform - Part 1 [Math Crafters]

Inverse Laplace Transform - Part 1 [Math Crafters]

23:27
6
Inverse Laplace Transform - Part 2 [Math Crafters]

Inverse Laplace Transform - Part 2 [Math Crafters]

21:29
7
Inverse Laplace Transform - Part 3 [Math Crafters]

Inverse Laplace Transform - Part 3 [Math Crafters]

22:22
8
Inverse Laplace Transform - Part 4 [Math Crafters]

Inverse Laplace Transform - Part 4 [Math Crafters]

29:29

Solving Differential Equations using Laplace Transform

7
1
Solving Differential Equations - Part 1 [PSD]

Solving Differential Equations - Part 1 [PSD]

1:02:27
2
Solving Differential Equations - Part 2 [PSD]

Solving Differential Equations - Part 2 [PSD]

1:03:54
3
Solving ODEs using Laplace Transform [EMNH]

Solving ODEs using Laplace Transform [EMNH]

1:24:48
4
Solving ODE by Laplace Transformations [Azmir]

Solving ODE by Laplace Transformations [Azmir]

16:20
5
Solving ODE (Initial Value Problem) - Part 1 [Math Crafters]

Solving ODE (Initial Value Problem) - Part 1 [Math Crafters]

35:15
6
Solving ODE (Initial Value Problem) - Part 2 [Math Crafters]

Solving ODE (Initial Value Problem) - Part 2 [Math Crafters]

51:59
7
Solving ODE (Boundary Value Problem) - Part 3 [Math Crafters]

Solving ODE (Boundary Value Problem) - Part 3 [Math Crafters]

27:15

Exam & Quiz Guidance

1
1
Question Pattern for Quiz [EMNH]

Question Pattern for Quiz [EMNH]

13:03