Vector Calculus: Become An Expert of a Line Integrals



Learn everything from Line Integrals, then test your knowledge with 30+ practice questions

What you will learn

What Is Vector Calculus and its importance

Introduction To Line Integrals

Addition and Subtraction of Vectors

Scalar and Vector Products

Limits of Vector Functions

Differentiation and Integration of Vectors

How To Parameterize the Equations of Curves?

3 Types of line integrals with suitable 15+ examples

How to calculate Work done with suitable examples

Important theorems of line integrals

Fundamental theorem of calculus for line integrals of Vector Fields

Green’s Theorem as well as suitable applications of Green’s Theorem

Description

HOW BECOME A CALCULUS 3 ( LINE INTEGRALS ) EXPERT IS SET UP TO MAKE COMPLICATED MATH EASY:

Do you want to become a calculus Expert?

Do you want to become a vector calculus Expert?

Do you want to learn very important topic line integrals.

If you want to become a line integrals master then you have come on the right place.

This 25-lesson course includes video and text explanations of everything from Line Integrals, and it includes 30+ quizzes (with solutions!) and an additional 28  practice problems, to help you test your understanding along the way. Here is a listing (and brief description) of the material that is in this course:

SECTION I: Intro To Course

In 1st section, we will discuss about Vector Calculus and its importance and we will also start off with a quick review of Line Integrals.

SECTION II: Basic Fundamentals

Before starting  to Line Integrals we will try to explain some of its key concepts. For example,

✅ Addition and Subtraction of         Vectors

✅ Scalar and Vector Products    ✅ Limits of Vector Functions

✅ Differentiation and         Integration of Vectors

✅ How To Parameterize the  Equations of Curves?

And all of these are very important skills that will be required in a great many of the line integrals we evaluate and so needs to be understood.

SECTION III: Line Integrals – 1st Type

In 3rd section, We will  formally define the first kind of line integral and that is line integrals with respect to arc length. We will also try to explain this kind of line integral with three examples.

SECTION IV: Line Integrals – 2nd Type

In 4th section, we will define the 2nd type of line integrals and that is  line integrals of vector fields and We will also see that this particular kind of line integral is related to special cases of the line integrals with respect to x, y and z.

We will also try to explain this kind of line integral with six examples.

This section also contains quizzes that allow you to test your knowledge.


SECTION V: Line Integrals – 3rd Type:

In this section, we will continue looking at line integrals and define the 3rd kind of line integral that is  line integrals with respect to x, y, and/or z. We will also try to explain this kind of line integral with 3 examples.

We also introduce an alternate form of notation for this kind of line integral that will be useful on occasion.

SECTION VI: Applications of Line Integrals

In 6th section,  we will discuss the  applications of line Integral. The line integral has many uses in Physics and Engineering. But in this section, We will cover only one  application that is Work done. We’ll also try to explain three problems about work done.

This section also contains quizzes that allow you to check your knowledge.

SECTION VII: Fundamental Theorem for Line Integrals:

In 7th section we will talk about some important theorems of line integrals and also talk about  fundamental theorem of calculus for line integrals of vector fields. This will illustrate that certain kinds of line integrals can be very quickly computed. We will also give quite a few definitions and facts that will be useful.

SECTION VIII: Green’s Theorem

In 8th section we will discuss Green’s Theorem as well as an interesting application of Green’s Theorem that we can use to find the area of a two dimensional region.we will also explain it through some examples.

Who is course for?

✅ M.Sc. Mathematics students

✅ M.Sc. Physics students

✅ BS 4-Year students

✅ Candidates of CSS

Examination

✅ Candidates of  Other

Competitive Examination

✅ Homeschool parents looking for extra support with Vector


Calculus

✅ Anyone who wants to study Vector Analysis for fun after being away from school for a while. Professionals who need a refresher on this topic for a new career challenge.

English
language

Content

Introduction To Course

Intro And Overview Of The Course
What Is Vector Analysis (Vector Calculus)

Basic Knowledge

Important Definitions
Dot Product of two Vectors
Cross Product of two vectors
Limits of a Vector function

Line Integrals w.r.t. Arc Length – 1st Type

1st Example – Evaluate Line Integrals w.r.t. Arc Length
2nd Example – Evaluate Line Integrals w.r.t. Arc Length
3rd Example – Evaluate Line Integrals w.r.t. Arc Length

Line Integrals of vector Fields -2nd Type

1st Example – Evaluate Line Integrals w.r.t. of Vector Fields
2nd Example – Evaluate Line Integrals w.r.t. of Vector Fields
3rd Example – Evaluate Line Integrals w.r.t. of Vector Fields
4th Example – Evaluate Line Integrals w.r.t. of Vector Fields
5th Example – Evaluate Line Integrals w.r.t. of Vector Fields

Line Integrals w.r.t. x, y, and/or z -3rd Type

1st Example – Calculate Line Integrals w.r.t. x, y, and/or z
2nd Example – Calculate Line Integrals w.r.t. x, y, and/or z
3rd Example – Calculate Line Integrals w.r.t. x, y, and/or z

Applications of Line Integrals (work done)

Over view of the Section
1st Example – Calculate work done
2nd Example – Calculate work done
3rd Example – Calculate work done

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