This mathematics sheet would be helpful for quick revision of most of maths formulas needed before class 11 and 12 physics examination. It covers quick and much needed formulas on differentiation , integration, trigonometry, AP, GP etc.
Full notes on vector Differentiation is now available at the website physicscatalyst.com covering following topics
1. Differentiation of vectors
2. Scalar and vector fields
3. Gradient of a scalar field
In this post we’ll discuss about Divergence and curl of vector fields. Here get a short synopsis of what is divergence and curl of a vector field along with their geometrical interpretation.
Here in this post we will revise our concept of Vector Calculas (differentiation of vectors). This mathematical tool would help us in expressing certain basic ideas with a great convenience while studying electrodynamics.
DIFFERENTIATION OF VECTORS
Consider a vector function f(u) such that
Complex numbers are the numbers of the form a+ib where a and b are real numbers.
Definition:- Complex numbers are defined as an ordered pair of real numbers like (x,y) where
and both x and y are real numbers and x is known as real part of complex number and y is known as imaginary part of the complex number.
In this post we’ll lern Vector algebra in component form.
Component of any vector is the projection of that vector along the three coordinate axis X, Y, Z.
In component form addition of two vectors is
We know that many physical quantities like temperature, electric or gravitational field etc. have different values at different points in space for example electric field of a point charge is large near the charge and it decreases as we go farther away from the charge. So we can say that electric field here is the physical quantity that varies from point to in space and it can be expressed as a continuous function of position of point in that region of space .
Here in this post we will go through a quick recap of vector algebra keeping in mind that reader already had detail knowledge and problem solving skills related to the topic being discussed. Here we are briefing Vector Algebra because concepts of electrostatics , electromagnetism and many more physical phenomenon can best be conveniently expressed using this tool.