Vector Calculus Part 1: Gradient Divergence & Curl of vector

Gradient , Divergence and Curl of a Vector, Tangent and Normal plane, vector calculus, Laplacian operator, Del Operator

Last updated 2/2025

English

What you'll learn

3 sections • 26 lectures • 7h 59m total length

Introduction13:41
Concept of Scalar and Vector Function , Scalar function of a scalar variable , Vector function of a scalar variable , Single Valued Function , Limit of a Vector Function , Algebra of limits , Variable Function , Diffrentiability of the Vector Function
Basic Concepts Lesson 216:42
Some Important Results and Theorems
Theorem : Every Diffrentiable Vector Function is Continous.
Constant Vectors Lesson 118:55
Definition of Constant vector and some Important Theorems.
Constant Vectors Lesson 213:33
Introduction of a Null Vector and Important Theorem.
Constant Vectors Lesson 322:10
Some more Theorems and Geometrical Significance of df/dt .

Geometrical Significance of Scalar And Vector Point Function10:36
Geometrical Significance of Velocity and Accelaration
Scalar and Vector Point Functions
Limits and Continuity
Directional Derivatives19:35
Cartesian Representation of Point Function and their Directional Derivatives.
Directional Derivative of Scalar Point Function along Coordinate Axes.
Directional Derivative along any Line.
Gradient of a Scalar Point Function. and Gradient of a Constant.
Introduction of Del Operator18:17
Important Expected Theorem and some Examples.
Geometrical Interpretation of a Gradient of a Scalar Point Function25:31
Basic concept of Direction Cosines and Level Surfaces.
Greometrical Interpretation of a Gradient of a Scalar Point Function.
Gradient of a Scalar Point Function ( Examples )24:38
Tangent Plane and Normal14:11
Conditions of Gradient for Tangent Plane and Normal and solved Exercise.
Divergence and Curl of a Vector22:50

In course , Vector Calculus Part 1 the student will learn about the following topics:

Basic concepts of Vectors and detailed definitions
Scalar and Vector point functions
Constant Vectors and all Based Theorems.
The proof of the Theorem that every Differentiable vector function is Continuous.
The proof of the result that_The Necessary and sufficient condition for a vector point function to be Constant.
The proof of the result that _If vector function has a Constant magnitude then f and df/dt are perpendicular.
The Necessary and sufficient condition for a vector function to have Constant magnitude.
The Necessary and sufficient condition for a vector function to have Constant direction.
Directional Derivatives with examples
Tangent Plane and Normal, Level Surfaces with definitions and detailed explanation
Geometrical interpretation of vectors
Geometrical Interpretation of Gradient of scalar point function
Gradient, Divergence, and Curl of a vector and Many more Based examples and assignments with Theorems and proofs.
Del Operator & Laplacian operator with examples.
Solenoidal vector & Irrotational vector
Important various Results, Expected Theorems, and Based Assignment

If you need any help in understanding the topics or If you have any queries, feel free to revert back. The instructor is always there to help you.

Thanks and Regards!