PURE AND APPLIED > VECTOR INTEGRAL CALCULUS
Vector integral calculus used in analyzing
quantities in 3-dimensional space
The big brother of the vector differential calculus, the vector integral calculus. Where previously we were talking about tangent vectors and how they relate to a given curve, we will now seek the understanding of areas formed by such curve.
Unlike normal single-variable calculus where areas are easily calculated by setting boundaries of the integral, in vector integration, areas can be calculated in a variety of ways. The method depends on factors such as the parameter, direction and the conditions set.
I would like to tell the student that the difficulty of understanding, more so the teaching, the integral calculus is about double of that of differential calculus. Hence, I ask for your forgiveness should the video lectures contain mistakes especially in the conditions and accuracy of the theorems. If anything, it helps to focus more closely in the written lessons.
NOTE: While vector fields and the del operator are actually in the differential calculus, I thought it would be better that I place those topics here because they are vital in understanding the rest of the theorems in the integral calculus.
Oliver Heaviside
Line Integral
Green's theorem
Stokes' theorem
Magnetic Fields
Vector integral calculus used in analyzing
quantities in 3-dimensional space
Unlike normal single-variable calculus where areas are easily calculated by setting boundaries of the integral, in vector integration, areas can be calculated in a variety of ways. The method depends on factors such as the parameter, direction and the conditions set.
I would like to tell the student that the difficulty of understanding, more so the teaching, the integral calculus is about double of that of differential calculus. Hence, I ask for your forgiveness should the video lectures contain mistakes especially in the conditions and accuracy of the theorems. If anything, it helps to focus more closely in the written lessons.
NOTE: While vector fields and the del operator are actually in the differential calculus, I thought it would be better that I place those topics here because they are vital in understanding the rest of the theorems in the integral calculus.
CONCEPT CONTENTS
> VECTOR FIELDS AND LINES OF FORCE
> FINDING THE LINES OF FORCE
> GENERAL AND PARTICULAR SOLUTION
> THE GRADIENT VECTOR FIELD
> DEFINING THE DIRECTIONAL DERIVATIVE
> DIRECTIONAL DERIVATIVE AND THE DEL OPERATOR
> MAXIMUM AND MINIMUM RATE OF CHANGE
> TANGENT PLANE
> THE NORMAL LINE
> TERMS OF A CURVE
> DEFINITION OF THE LINE INTEGRAL
> LINE INTEGRAL EXAMPLE
> LINE INTEGRAL OF A PIECEWISE SMOOTH CURVE
> PIECEWISE SMOOTH CURVE EXAMPLE
> INTERPRETATION OF THE LINE INTEGRAL
> GREEN'S THEOREM
> USES OF GREEN'S THEOREM
> PROOF OF GREEN'S THEOREM
Notable Mathematicians
J. Willard GibbsOliver Heaviside
Important Theorems
Vector Field Line Integral
Green's theorem
Stokes' theorem
Applications
StreamlinesMagnetic Fields
