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.

Content

### Introduction To Course

### Basic Knowledge

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

### Line Integrals of vector Fields -2nd Type

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

### Applications of Line Integrals (work done)