Line Integrals, Surface Integrals & Space Integrals Part 1

Line integrals, Surface Integrals, Multivariable Calculus, Vector Calculus, Gauss Divergence Theorem

What you’ll learn
Introduction of Normal surface Integrals, Flux of a Vector Function, Circulation of a Vector point Function
Evaluating the Line Integrals along the Curves, along the path joining the points,along the Unit Circle etc.
How to evaluate Surface integrals and Volume Integrals , Surface Integrals for Sphere, Ellipsoid, Part of the Sphere in first octant, Cylinder etc.
Gauss Divergence Theorem and its proof including Corollary and Results.
How to use Gauss Divergence Theorem for evaluating Surface Integrals

Requirements
Solving Integrals, double Integrals, Triple Integrals

Description
VECTOR CALCULUS in Mathematics is a sub-division of Calculus that deals with the differentiation and integration of Vector Functions. Vector Calculus, also known as Vector Analysis, deals with the differentiation and integration of vector field, especially in the three-dimensional Euclidean space.This Course on Vector Calculus is covering the LINE INTEGRALS & SURFACE INTEGRALS that is beautifully covered with the contents that are listed below_LINE INTEGRALS1) Introduction to Line integrals and Detailed concept of Tangential Line Integrals2) Circulation of a vector along the Curves.3)Evaluating the Line integrals along the parabolic curve, curve joining the two points.4) Evaluating the Line Integrals along the Triangles, Rectangles along the path with parametric equations, along the Straight Line joining the points and along the Closed Path.SURFACE INTEGRALS1) Introduction to Surface Integrals and Normal Surface Integrals2) Detailed concepts about the Direction Cosines and Unit Vector Normal3) Evaluating the Surface Integrals & Volume Integrals with detailed concepts.4) Evaluating the Surface Integrals for a Sphere with origin at center, Sphere in the first Octant, part of the sphere in the first octant.5)Evaluating the Surface Integrals for a Plane in the first Octant, for a Cylinder in the first Octant.6) Finding the Total Work Done in moving a particle in a force Field.7) Investigating a Vector Point Function to be the Gradient Vector.GAUSS DIVERGENCE THEOREM1) Statement and Proof of Gauss Divergence Theorem and its Corollary with Important Results covering Gradient, Divergence and Curl of a Vector Function.2) Evaluating the Surface Integrals using Gauss Divergence Theorem including Solved Assignments.And, all the Expected Theorems, Results and assignments covering all the above Contents.Thanks and Regards!

Overview
Section 1: LINE INTEGRALS (Vector Calculus)

Lecture 1 Introduction of Line Integrals (Vector Calculus)

Lecture 2 Evaluate the Line Integral over the Curve y = x²

Lecture 3 Evaluate the Line Integrals over the Curve in Polar Coordinates

Lecture 4 Evaluate the Line Integral over the Triangle for given Vertices.

Lecture 5 Evaluate the Line Integrals over the Path for a Vector Point Function

Lecture 6 Evaluate the Line Integral along the Straight Line

Lecture 7 Evaluate the Line Integral along the Straight Line joining the two Points

Lecture 8 Evaluate the Line Integral along the Unit Circle

Lecture 9 Evaluate the Line Integral along the Curve using Parametric Equations

Lecture 10 Evaluate the Line Integral along the Curve dependent on variable with limits.

Lecture 11 Evaluate the Line Integral along the Curve dependent on variable with limits

Section 2: CIRCULATION OF A VECTOR

Lecture 12 Find the Circulation of a Vector around the Unit Circle

Lecture 13 Find the Circulation of a Vector along the rectangle with Given Vertices

Lecture 14 Find the Circulation of a Vector along arc y = x²- 4

Lecture 15 Find the Circulation of a Vector along the Given Axis

Lecture 16 Evaluate the Line Integral along the Reactangle in xy Plane bounded by lines.

Lecture 17 Find the Circulation of a Vector around the Curves y = x² & x = y²

Lecture 18 Find the Circulation around the Closed Path with given Diagram

Section 3: FLUX OF A VECTOR POINT FUNCTION

Lecture 19 Introduction of a Flux of a Vector Point Function & Normal Surface Integral

Lecture 20 Evaluating the Surface Integrals & Volume Integrals

Lecture 21 Surface Integrals for a Sphere with Centre at the Origin.

Lecture 22 Surface Integral for a Sphere in the first Octant.

Lecture 23 Surface Integral for a Unit Sphere

Lecture 24 Surface Integral for a part of a Sphere lies in the First Octant

Lecture 25 Surface Integral across the Surface of Cylinder in the first Octant.

Lecture 0 Find the Total Work Done in moving a particle in a given Force Field

Lecture 0 Find the Total Work Done along the Circle in xy plane.

Lecture 0 Investigate is Vector Function a Gradient Vector

Section 4: USE OF GAUSS’S DIVERGENCE THEOREM

Lecture 26 Proof of Gauss’s Divergence Theorem

Lecture 27 Gauss Divergence Theorem (Corollary)

Lecture 28 Show that the given Surface Integral is equal to the volume enclosed by Surface

Lecture 29 Use of gauss Divergence Theorem to evaluate the Surface Integrals (Assignment 1)

Lecture 30 Use of gauss Divergence Theorem to evaluate the Surface Integral (Assignment 2)

Lecture 31 Use of gauss Divergence Theorem to evaluate the Surface Integral (Assignment 3)

Lecture 32 Use of gauss Divergence Theorem to evaluate the Surface Integrals(Assignment 4)

Lecture 33 Use of gauss Divergence Theorem to evaluate the Surface Integrals(Assignment 5))

Students of Engineering Mathematics, Vector Calculus, multivariable calculus, Graduate or post Graduates , Master in Mathematics,