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Advanced Complex Analysis - Part 1 (NPTEL):- The Mean-Value Property, Harmonic Functions and the Maximum Principle

Advanced Complex Analysis - Part 1 (NPTEL):- The Mean-Value Property, Harmonic Functions and the Maximum Principle

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Advanced Complex Analysis - Part 1 (NPTEL):- Proofs of Maximum Principles and Introduction to Schwarz's Lemma

Advanced Complex Analysis - Part 1 (NPTEL):- Proofs of Maximum Principles and Introduction to Schwarz's Lemma

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Advanced Complex Analysis - Part 1 (NPTEL):- Proof of Schwarz's Lemma and Uniqueness of Riemann Mappings

Advanced Complex Analysis - Part 1 (NPTEL):- Proof of Schwarz's Lemma and Uniqueness of Riemann Mappings

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Advanced Complex Analysis - Part 1 (NPTEL):- Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-domains

Advanced Complex Analysis - Part 1 (NPTEL):- Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-domains

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Advanced Complex Analysis - Part 1 (NPTEL):- Differential or Infinitesimal Schwarz's Lemma, Pick's Lemma, Hyperbolic

Advanced Complex Analysis - Part 1 (NPTEL):- Differential or Infinitesimal Schwarz's Lemma, Pick's Lemma, Hyperbolic

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Advanced Complex Analysis - Part 1 (NPTEL):- Hyperbolic Geodesics for the Hyperbolic Metric on the Unit Disc

Advanced Complex Analysis - Part 1 (NPTEL):- Hyperbolic Geodesics for the Hyperbolic Metric on the Unit Disc

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Advanced Complex Analysis - Part 1 (NPTEL):- Schwarz-Pick Lemma for the Hyperbolic Metric on the Unit Disc

Advanced Complex Analysis - Part 1 (NPTEL):- Schwarz-Pick Lemma for the Hyperbolic Metric on the Unit Disc

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Advanced Complex Analysis - Part 1 (NPTEL):- Arzela-Ascoli Theorem: Under Uniform Boundedness, Equicontinuity and Uniform

Advanced Complex Analysis - Part 1 (NPTEL):- Arzela-Ascoli Theorem: Under Uniform Boundedness, Equicontinuity and Uniform

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Advanced Complex Analysis - Part 1 (NPTEL):- Completion of the Proof of the Arzela-Ascoli Theorem and Introduction

Advanced Complex Analysis - Part 1 (NPTEL):- Completion of the Proof of the Arzela-Ascoli Theorem and Introduction

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Advanced Complex Analysis - Part 1 (NPTEL):- The Proof of Montel's Theorem

Advanced Complex Analysis - Part 1 (NPTEL):- The Proof of Montel's Theorem

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Advanced Complex Analysis - Part 1 (NPTEL):- The Candidate for a Riemann Mapping

Advanced Complex Analysis - Part 1 (NPTEL):- The Candidate for a Riemann Mapping

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Advanced Complex Analysis - Part 1 (NPTEL):- Completion of Proof of The Riemann Mapping Theorem - 1

Advanced Complex Analysis - Part 1 (NPTEL):- Completion of Proof of The Riemann Mapping Theorem - 1

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Advanced Complex Analysis - Part 1 (NPTEL):- Completion of Proof of The Riemann Mapping Theorem - 2

Advanced Complex Analysis - Part 1 (NPTEL):- Completion of Proof of The Riemann Mapping Theorem - 2

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Ex: Determine a Value in a 3x3 Matrix To Make the Matrix Singular

Ex: Determine a Value in a 3x3 Matrix To Make the Matrix Singular

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Ex: Determine a Value in a 2x2 Matrix To Make the Matrix Singular

Ex: Determine a Value in a 2x2 Matrix To Make the Matrix Singular

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Ex: Determine if a 3x3 Matrix is Invertible (nonsingular) Using a Determinant

Ex: Determine if a 3x3 Matrix is Invertible (nonsingular) Using a Determinant

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Ex: Determine if a 2x2 Matrix is Invertible (nonsingular) Using a Determinant

Ex: Determine if a 2x2 Matrix is Invertible (nonsingular) Using a Determinant

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Ex: Find the Area of a Triangle on the Coordinate Plane Using a Determinant

Ex: Find the Area of a Triangle on the Coordinate Plane Using a Determinant

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Area Using Determinants

Area Using Determinants

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Ex: Solve a System of Three Equations Using Cramer's Rule

Ex: Solve a System of Three Equations Using Cramer's Rule

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Ex: Solve a System of Two Equations Using Cramer's Rule

Ex: Solve a System of Two Equations Using Cramer's Rule

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Cramer’s Rule

Cramer’s Rule

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Determinants on the Graphing Calculator

Determinants on the Graphing Calculator

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Ex: Find the Value of a 4x4 Determinant Using Cofactor Expansion (with Zeros)

Ex: Find the Value of a 4x4 Determinant Using Cofactor Expansion (with Zeros)

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Ex: Find a 3x3 Determinant using Cofactor Expansion on Row 3

Ex: Find a 3x3 Determinant using Cofactor Expansion on Row 3

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Ex: Find a 3x3 Determinant using Cofactor Expansion on Row 2

Ex: Find a 3x3 Determinant using Cofactor Expansion on Row 2

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Ex 2: Determinant of 3x3 Matrix - Cofactor Method

Ex 2: Determinant of 3x3 Matrix - Cofactor Method

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Ex 1: Determinant of 3x3 Matrix - Cofactor Method

Ex 1: Determinant of 3x3 Matrix - Cofactor Method

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Ex 2: Determinant of 3x3 Matrix - Diagonal Method

Ex 2: Determinant of 3x3 Matrix - Diagonal Method

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Ex 1: Determinant of 3x3 Matrix - Diagonal Method

Ex 1: Determinant of 3x3 Matrix - Diagonal Method

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Ex: Solve an Equation Involving a Determinant

Ex: Solve an Equation Involving a Determinant

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Ex: Determinant of a 2x2 Matrix

Ex: Determinant of a 2x2 Matrix

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Determinants

Determinants

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Perform Linear Regression Using Matrices

Perform Linear Regression Using Matrices

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Solve a System of Linear Equations Using LU Decomposition

Solve a System of Linear Equations Using LU Decomposition

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LU Decomposition - Shortcut

LU Decomposition - Shortcut

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LU Decomposition Using Elementary Matrices

LU Decomposition Using Elementary Matrices

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Ex: Solve a System of Three Equations Using a Matrix Equation

Ex: Solve a System of Three Equations Using a Matrix Equation

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Ex 2: Solve a System of Two Equations Using a Matrix Equation

Ex 2: Solve a System of Two Equations Using a Matrix Equation

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Ex 1: Solve a System of Two Equations Using a Matrix Equation

Ex 1: Solve a System of Two Equations Using a Matrix Equation

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Matrix Equations

Matrix Equations

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Ex: Solve the Matrix Equation AX=B (3x3)

Ex: Solve the Matrix Equation AX=B (3x3)

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Ex 2: Solve the Matrix Equation AX=B (2x2)

Ex 2: Solve the Matrix Equation AX=B (2x2)

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Ex 1: Solve the Matrix Equation AX=B (2x2)

Ex 1: Solve the Matrix Equation AX=B (2x2)

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Inverse Matrices on the Graphing Calculator

Inverse Matrices on the Graphing Calculator

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Ex 2: Inverse of a 3x3 Matrix Using an Augmented Matrix

Ex 2: Inverse of a 3x3 Matrix Using an Augmented Matrix

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Ex 1: Inverse of a 3x3 Matrix Using an Augmented Matrix

Ex 1: Inverse of a 3x3 Matrix Using an Augmented Matrix

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Ex: Inverse of a 2x2 Matrix Using an Augmented Matrix

Ex: Inverse of a 2x2 Matrix Using an Augmented Matrix

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Ex: Find the Inverse of a 2x2 Matrix Using a Formula

Ex: Find the Inverse of a 2x2 Matrix Using a Formula

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Inverse Matrices Using Augmented Matrices

Inverse Matrices Using Augmented Matrices

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2 x 2 Inverse Matrix Formula

2 x 2 Inverse Matrix Formula

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LU Decomposition - Shortcut

LU Decomposition - Shortcut

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LU Decomposition Using Elementary Matrices

LU Decomposition Using Elementary Matrices

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Elementary Matrices

Elementary Matrices

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The Identity Matrix

The Identity Matrix

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Ex: Inverse of a 2x2 Matrix Using an Augmented Matrix

Ex: Inverse of a 2x2 Matrix Using an Augmented Matrix

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Ex: Find the Inverse of a 2x2 Matrix Using a Formula

Ex: Find the Inverse of a 2x2 Matrix Using a Formula

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Inverse Matrices Using Augmented Matrices

Inverse Matrices Using Augmented Matrices

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2 x 2 Inverse Matrix Formula

2 x 2 Inverse Matrix Formula

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LU Decomposition - Shortcut

LU Decomposition - Shortcut

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LU Decomposition Using Elementary Matrices

LU Decomposition Using Elementary Matrices

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Elementary Matrices

Elementary Matrices

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The Identity Matrix

The Identity Matrix

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Animation: Matrix Multiplication

Animation: Matrix Multiplication

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Ex Applicaton of Matrix Multiplication - Transformation

Ex Applicaton of Matrix Multiplication - Transformation

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Ex 3: Matrix Multiplication (3x2)*(2x3)

Ex 3: Matrix Multiplication (3x2)*(2x3)

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Ex 2: Matrix Multiplication (2x3)*(3x2)

Ex 2: Matrix Multiplication (2x3)*(3x2)

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Ex 1: Matrix Multiplication (Basic)

Ex 1: Matrix Multiplication (Basic)

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Matrix Multiplication on the Graphing Calculator

Matrix Multiplication on the Graphing Calculator

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Ex: Square a 2x2 Matrix

Ex: Square a 2x2 Matrix

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Ex: Matrix Multiplication (2x3)*(3x4)

Ex: Matrix Multiplication (2x3)*(3x4)

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Ex: Matrix Multiplication (2x2)*(2x2)

Ex: Matrix Multiplication (2x2)*(2x2)

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Ex: Solve a Basic Matrix Equation (No Inverse)

Ex: Solve a Basic Matrix Equation (No Inverse)

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Ex: Determine if Matrix Multiplication is Possible

Ex: Determine if Matrix Multiplication is Possible

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Matrix Multiplication

Matrix Multiplication

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Ex: Matrix Scalar Multiplication Application - Dilation

Ex: Matrix Scalar Multiplication Application - Dilation

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Ex: Use Matrices to Dilate and Translate a Triangle

Ex: Use Matrices to Dilate and Translate a Triangle

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Ex 2: Matrix Application: Translation / Dilation

Ex 2: Matrix Application: Translation / Dilation

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Ex 1: Matrix Application: Translation / Dilation

Ex 1: Matrix Application: Translation / Dilation

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Ex: Matrix Addition Application - Translation

Ex: Matrix Addition Application - Translation

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Ex: Matrix Operations - Scalar Multiplication, Addition, and Subtraction

Ex: Matrix Operations - Scalar Multiplication, Addition, and Subtraction

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Ex: Matrix Scalar Multiplication

Ex: Matrix Scalar Multiplication

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Ex: Perform Matrix Scalar Multiplication and Matrix Addition

Ex: Perform Matrix Scalar Multiplication and Matrix Addition

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Ex: Perform Matrix Scalar Multiplication

Ex: Perform Matrix Scalar Multiplication

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Ex: Matrix Addition and Subtraction

Ex: Matrix Addition and Subtraction

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Ex: Subtract Two 2x3 Matrices

Ex: Subtract Two 2x3 Matrices

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Ex: Add Two 2x2 Matrices

Ex: Add Two 2x2 Matrices

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Matrix Addition, Subtraction and Scalar Multiplication

Matrix Addition, Subtraction and Scalar Multiplication

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Write a Matrix as a Product of Elementary Matrices

Write a Matrix as a Product of Elementary Matrices

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Use Elementary Matrices to Perform Row Operations to Solve a System

Use Elementary Matrices to Perform Row Operations to Solve a System

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Write a Matrix as a Product of Elementary Matrices

Write a Matrix as a Product of Elementary Matrices

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Use Elementary Matrices to Perform Row Operations to Solve a System

Use Elementary Matrices to Perform Row Operations to Solve a System

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Augmented Matrices on the Graphing Calculator

Augmented Matrices on the Graphing Calculator

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Ex: Write a 4x4 Matrix in Reduced Row Echelon Form (Not Identity)

Ex: Write a 4x4 Matrix in Reduced Row Echelon Form (Not Identity)

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Ex: Write a 3x3 Matrix in Reduced Row Echelon Form (Not Identity)

Ex: Write a 3x3 Matrix in Reduced Row Echelon Form (Not Identity)

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Ex: Write a 3x3 Matrix in Reduced Row Echelon Form (Identity)

Ex: Write a 3x3 Matrix in Reduced Row Echelon Form (Identity)

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Ex: Solve a System of Equation By Writing an Augmented Matrix in RREF (3x3 Infinite Sol)

Ex: Solve a System of Equation By Writing an Augmented Matrix in RREF (3x3 Infinite Sol)

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Ex: Solve a System of Three Equations Using an Augmented Matrix (Reduced Row Echelon Form)

Ex: Solve a System of Three Equations Using an Augmented Matrix (Reduced Row Echelon Form)

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Ex 3: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)

Ex 3: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)

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Ex 2: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)

Ex 2: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)

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