Math For Electricity And Magnetism

Give you the power of Mathematics, with 28 illustrated quiz with answers !

What you'll learn
Vector calculus : The definition of a vector, scalar product, vector product and more
Flux of a vector
Using matrices and determinants in vector calculus
Coordinate system: Cartesian, cylindrical and spherical coordinates
Profound details about the coordinate system like relations between the coordinate system and rotation matrix
Application of trigonometry in vector calculus and coordinate system
Recall about: differential of multivariable function
Infinitesimal line element in cartesian, cylindrical and spherical coordinates
Infinitesimal area element in cartesian, cylindrical and spherical coordinates
Infinitesimal volume element in cartesian, cylindrical and spherical coordinates
Gradient operator
Divergence operator
Curl operator
Other tools will come after, such as the Laplacian operator and more details about the operators.
Requirements
Fundamentals of Mathematics
Basic Analysis (like derivative of function of one variable)
Description
 Physics is not hard, but if you don't have the tools for doing Physics, Physics become not just hard but impossible to do it, like a mechanic with not his tools, he can't work! 
 For example, Electricity and Magnetism course is filled with strange symbols like grad, div, curl, partial derivative cos and sin combined…etc, and for this reason, this course maybe appears difficult for the first time, and maybe you can abandon physics…
 Please don't lose hope, because you need first some tools for doing Physics, this beautiful subject.
 Those tools can also help you in mechanics and engineering.
 And for this I represent you some concepts before going in electricity and magnetism course:
Vector calculus: Definition of a vector, scalar product, vector productVector calculus: Flux of a vectorCoordinate system: Cartesian coordinatesCoordinate system: Cylindrical coordinatesCoordinate system: Spherical coordinatesCoordinate system: Relations between Cartesian and cylindrical coordinatesCoordinate system: Relations between Cartesian and spherical coordinatesTrigonometryRotation matrixInfinitesimal line element in the three coordinates systemsInfinitesimal area element in the three coordinates systemsInfinitesimal volume element in the three coordinates systemsGradient operator Divergence operatorCurl operatorI promise you further details about operators
 I hope that this course will be useful for you, pass 8 hours of video with pleasure!

Overview

Section 1: Vector calculus : Intro

Lecture 1 Introduction 1

Lecture 2 Introduction 2

Lecture 3 Example of a vector

Lecture 4 Equality of two vectors

Lecture 5 Unit vector

Lecture 6 Representation of a vector

Lecture 7 The magnitude of a vector

Lecture 8 Addition of vectors

Lecture 9 Addition of vectors, another notation

Lecture 10 Vector multiplication

Section 2: Vector calculus : Scalar product

Lecture 11 The scalar product of two vectors

Lecture 12 The scalar product of two vectors, part 2

Lecture 13 The scalar product in component representation

Lecture 14 Orthonormality relations

Lecture 15 The scalar product in component representation, part 2

Lecture 16 Flux of a vector

Section 3: Vector calculus : Vector product

Lecture 17 Vector product

Lecture 18 The magnitude of the vector product

Lecture 19 Properties of the vector product

Lecture 20 Rules of calculation

Lecture 21 Determinant

Lecture 22 Triple scalar product

Lecture 23 Geometrical interpretation of triple scalar product

Lecture 24 Properties of the triple scalar product

Section 4: Coordinate system : Cartesian coordinates

Lecture 25 Introduction and the expression of position vector in cartesian coordinates

Lecture 26 More details about cartesian basis

Lecture 27 Representation of x=constant, y=constant and z=constant

Section 5: Coordinate system : Cylindrical coordinates

Lecture 28 Introduction

Lecture 29 Cylindrical basis and more

Lecture 30 Remarks

Section 6: Coordinate system : Relations between cartesian and cylindrical coordinates

Lecture 31 The cartesian coordinates in function of cylindrical coordinates

Lecture 32 e_rho and e_phi in function of cartesian basis

Lecture 33 Remark 1 : e_rho in function of cartesian basis, second method

Lecture 34 e_phi in function of cartesian basis, second method

Lecture 35 e_z in function of cartesian basis, second method

Lecture 36 Remark 2

Lecture 37 Remark 3

Lecture 38 Remark 4 : Rotation matrix, part 1

Lecture 39 Remark 4 : Rotation matrix, part 2

Lecture 40 Remark 4 : Rotation matrix, part 3

Section 7: Coordinate system : Spherical coordinates

Lecture 41 Introduction

Lecture 42 Remark

Lecture 43 Spherical basis

Lecture 44 Remark 1

Lecture 45 Remark 1, part 2

Lecture 46 Remark 1, part 3

Lecture 47 Remark 2

Section 8: Coordinate system : Relations between cartesian and spherical coordinates

Lecture 48 The cartesian coordinates in function of spherical coordinates

Lecture 49 The spherical coordinates in function of cartesian coordinates

Lecture 50 The expression of position vector

Lecture 51 Unit vectors for spherical coordinates

Lecture 52 Unit vectors for spherical coordinates, part 2

Lecture 53 Remark 1

Lecture 54 Remark 2

Lecture 55 Remark 3

Lecture 56 Remark 4 : Rotation matrix in spherical coordinates

Section 9: Infinitesimal displacement vector, Area element and Volume element

Lecture 57 Recall : differential of a function of three variables

Lecture 58 Infinitesimal displacement vector in cartesian coordinates, and area element

Lecture 59 Volume element in cartesian coordinates

Lecture 60 Infinitesimal displacement vector in cylindrical coordinates, and area element

Lecture 61 Area element of a cylinder, exactly the lateral area

Lecture 62 Volume element in cylindrical coordinates

Lecture 63 Infinitesimal displacement vector in spherical coordinates

Lecture 64 Area element of a sphere

Lecture 65 Volume element in spherical coordinates

Section 10: The Gradient, Divergence and Curl

Lecture 66 The Gradient operator

Lecture 67 Gradient operator : Example, part 1

Lecture 68 Gradient operator : Example, part 2

Lecture 69 Gradient operator : Example, part 3

Lecture 70 Gradient operator : Example, part 4

Lecture 71 The divergence operator

Lecture 72 The curl operator

Section 11: Bonus Lectures

Lecture 73 Definition of an operator

Lecture 74 Equipotential surfaces

Lecture 75 Divergence

Lecture 76 Circulation

Lecture 77 Circulation, example

Section 12: Introduction to electrostatics

Lecture 78 Electrical constitution of matter

Lecture 79 Elecrtric charge

Lecture 80 What's electrostatics

Lecture 81 Charges distribution, point charge

Lecture 82 Charges distribution, continuous charge distribution, volume distribution

Lecture 83 Charges distribution, continuous charge distribution, surface distribution

Lecture 84 Charges distribution, continuous charge distribution, Linear distribution

If you beginning an electricity and magnetism course, this course is critical,You can also use those tools for mechanics