Vector Calculus for Electromagnetism
Video Lectures
Displaying all 45 video lectures.
Lecture 1![]() Play Video |
Vector Components In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I discuss the components which we use as a basis in the rectangular coordinate system. |
Lecture 2![]() Play Video |
Scalar Dot Product In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I discuss the dot or scalar product which is an essential quantity for simplifying mathematical expressions. |
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Vector Cross Product (1/2) In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I discuss the vector produce which is an essential quantity for simplifying complicated mathematical expressions. Furthermore, it's physical interpretation aides in the analysis of the physics! |
Lecture 4![]() Play Video |
Vector Cross Product (2/2) In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I discuss the vector produce which is an essential quantity for simplifying complicated mathematical expressions. Furthermore, it's physical interpretation aides in the analysis of the physics! |
Lecture 5![]() Play Video |
Law of Cosines In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I derive the Law of Cosines. This is a very useful quantity when analysing vector function using two separate vectors. In the study of electrodynamics, many vector functions involve two separate vectors (usually the separation vector) and thus this expression greatly simplifies the analysis! |
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Separation Vector In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I discuss the separation vector. This vector is the vector difference between the a vector to the sources of a field and the vector to our detector. It is used in every expression in electrodynamics. |
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Nabla Operator (1/2) In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I introduce arguably the most important operator in vector calculus. |
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The Gradient Grad In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in introduce the first of the uses of the Nable operator. The gradient is fundamental to vector calculus and any studies of electromagnetism. |
Lecture 9![]() Play Video |
The Normal Vector In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss how we calculate the vector which is perpendicular to or 'normal' to a function. This is important for Lagrange Multipliers and our studies of electromagnetism. |
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Why the Gradient is Perpendicular to Functions In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I build upon video number 8 where I discussed the normal vector. In fact we see that the gradient calculates the normal vector for us. |
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Directional Derivative In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I discuss how we calculate the vector which calculates the rate of change of a function in a specific direction. |
Lecture 12![]() Play Video |
The Nabla Operator (2/2) In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I summarise our knowledge of the Nabla operator and prepare for its use in our studies of electromagnetism. |
Lecture 13![]() Play Video |
The Divergence In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss the divergence of a vector field. This mathematical construct is used both because it has a very interesting physical interpretation and that it simplifies complicated mathematical expressions. |
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The Curl of a Vector Field In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss the curl of a vector field both because it has a very important physical interpretation that it greatly simplifies complicated mathematical expressions. |
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Product Rules for Grad Div Curl In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss the vector produce rules for the gradient, divergence and curl. These allow us to write Maxwell's Equations in a simpler fashion than would other wise be possible. |
Lecture 16![]() Play Video |
Vector Product Rule 2 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I discuss the divergence of a function which is the product of a scalar and a vector. |
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Vector Product Rule 3 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when we take the curl of a function which is a product of both a vector and a scalar. |
Lecture 18![]() Play Video |
Vector Product Rule 4 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when we take the divergence of a cross product. |
Lecture 19![]() Play Video |
Vector Product Rule 5 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when we take the curl of a cross product. |
Lecture 20![]() Play Video |
Vector Product Rule 6 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when we take the gradient of a scalar dot product. |
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Vector Quotient Rule 1 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when we take the gradient of a scalar quotient. |
Lecture 22![]() Play Video |
Vector Quotient Rule 2 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when we take the divergence of a function which is a quotient of a vector and a scalar. |
Lecture 23![]() Play Video |
Vector Quotient Rule 3 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when we take the curl of a function which is the quotient of a vector and a scalar. |
Lecture 24![]() Play Video |
The Laplacian In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I introduce yet another important operator for our studies of electromagnetism. |
Lecture 25![]() Play Video |
Curl of the Gradient In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when we take the curl of the grad of a vector field. |
Lecture 26![]() Play Video |
Divergence of the Curl In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when we take the divergence of the curl of a vector field. |
Lecture 27![]() Play Video |
Curl of the Curl In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss what happens when you take the double curl of a vector function. |
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Fundamental Theorem of Calculus In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. |
Lecture 29![]() Play Video |
Fundamental Theorem for Gradients In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I extend the Fundamental Theorem of Calculus to three dimensions. |
Lecture 30![]() Play Video |
Green's Divergence Theorem In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss the fundamental theorem for divergences. |
Lecture 31![]() Play Video |
Stokes' Theorem In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss the fundamental theorem for curls. |
Lecture 32![]() Play Video |
Integration by Parts Rule 1 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss an extremely powerful technique in mathematics known as integration by parts. We shall see in the future that it can be done in many may ways on very many expressions! |
Lecture 33![]() Play Video |
Integration by Parts Example In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss an extremely powerful technique in mathematics known as integration by parts. We shall see in the future that it can be done in many may ways on very many expressions! |
Lecture 34![]() Play Video |
Integration by Parts Rule 2 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss an extremely powerful technique in mathematics known as integration by parts. We shall see in the future that it can be done in many may ways on very many expressions! |
Lecture 35![]() Play Video |
Integration by Parts Rule 3 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss an extremely powerful technique in mathematics known as integration by parts. We shall see in the future that it can be done in many may ways on very many expressions! |
Lecture 36![]() Play Video |
Integration by Parts Rule 4 In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss an extremely powerful technique in mathematics known as integration by parts. We shall see in the future that it can be done in many may ways on very many expressions! |
Lecture 37![]() Play Video |
Spherical Polar Co-ordinates In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss transforming from rectangular to spherical polar co-ordinates. This greatly simplifies calculations when there exists spherical symmetry. |
Lecture 38![]() Play Video |
Helmholtz Theorem (No Derivation) In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically in this video I discuss but I don't derive the Helmholtz Theorem. This theorem allows the use of scalar and vector potentials which are the backbone of the study of electromagnetism. See later videos in this section for its derivation (numbers 44 and 45). |
Lecture 39![]() Play Video |
Dirac Delta Function (1/2) In this video I continue my videos on Vector Calculus For Electromagnetism. Specifically I discuss the Dirac Delta Function (part 2 is the next video). This is vital for Electromagnetism as it permits the use of the Helmholtz Theorem and therefore the electric and magnetic potentials (vector and scalar). |
Lecture 40![]() Play Video |
Dirac Delta Function (2/2) In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I discuss the Dirac Delta Function (part 2 is the next video). This is vital for Electromagnetism as it permits the use of the Helmholtz Theorem and therefore the electric and magnetic potentials (vector and scalar). |
Lecture 41![]() Play Video |
Gradient of One Over the Separation Vector In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I work out the gradient of the inverse of the magnitude of the separation vector. This is required in order to prove the Helmholtz Theorem The Helmholtz theorem is vital to simplify the study of electric and magnetic fields; permitting the introduction of a scalar and magnetic potential. The proof of which is often overlooked, or in my opinion it's just shown to be true. The proof follows from the Dirac Delta Function (or distribution) which is how I do it. I prove all the necessary machinery required for the proof (which is quite involved in that regard). |
Lecture 42![]() Play Video |
Laplacian of One Over the Separation Vector In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I work out the Laplacian of the inverse of the magnitude of the separation vector. This is required in order to prove the Helmholtz Theorem The Helmholtz theorem is vital to simplify the study of electric and magnetic fields; permitting the introduction of a scalar and magnetic potential. The proof of which is often overlooked, or in my opinion it's just shown to be true. The proof follows from the Dirac Delta Function (or distribution) which is how I do it. I prove all the necessary machinery required for the proof (which is quite involved in that regard). Thanks to Andrew Weatherbee for pointing out a serious error in a previous version of this video. |
Lecture 43![]() Play Video |
Helmholtz Theorem Proof (Part 1) In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I derive the scalar potential for the Helmholtz Theorem. The Helmholtz theorem is vital to simplify the study of electric and magnetic fields; permitting the introduction of a scalar and magnetic potential. The proof of which is often overlooked, or in my opinion it's just shown to be true. The proof follows from the Dirac Delta Function (or distribution) which is how I do it. I prove all the necessary machinery required for the proof (which is quite involved in that regard). |
Lecture 44![]() Play Video |
Helmholtz Theorem Proof (Part 2) In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I derive the vector potential for the Helmholtz Theorem. The Helmholtz theorem is vital to simplify the study of electric and magnetic fields; permitting the introduction of a scalar and magnetic potential. The proof of which is often overlooked, or in my opinion it's just shown to be true. The proof follows from the Dirac Delta Function (or distribution) which is how I do it. I prove all the necessary machinery required for the proof (which is quite involved in that regard). |
Lecture 45![]() Play Video |
Derivation Biot and Savart Law In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I derive the Biot and Savart Law for magnetism. In many textbooks it's noted as a law derived from experiment. However, it's a consequence of Maxwell's equations (as is everything in this regard too!). It requires some tricky vector calculus and that's why it's in my vector calculus tutorials and not my magnetostatics section. |