### Introduction

### Integration - Introduction to integration

1

List of some formulas for integration

2

Definition of integration and understand it graphically

3

Calculate the area under the curve using Riemann sum method and integration

4

Integration is the opposite of differentiation, how?

### Integration - Definite integral equations

1

What is definite integral and how it looks like graphically?

2

Rules of definite integral equations

3

Types of definite integral equations

4

Find the integration of single definite integral equation

5

Integration of double definite integral equations

6

Integration of triple definite integral equations

### Integration - Indefinite integral equation

1

What is Indefinite integral equation?

2

Learn how to solve an indefinite integral equation

3

Find the integration of some basic integral functions

4

Integration of some indefinite integral functions separating their terms

5

Integration of some indefinite integral exponential functions

6

Indefinite integral of fractional, rational and trigonometric functions

### Integration - Indefinite integral - U-substitution method

1

Solve some algebraic, fractional and root functions by U-substitution method

2

Indefinite integral of some exponential functions

3

Indefinite integral of some some trigonometric functions

### Integration - Integration by parts

1

What is mean by integration by parts?

2

Techniques to solve the indefinite integration by parts

3

Learn how to use the two techniques of integration by parts

4

Indefinite Integration of the product of algebraic & exponential by parts

5

Indefinite Integration of the product of a constant & logarithmic by parts

6

Indefinite Integration of the product of algebraic & trig functions by parts

7

Solve the product of three functions using substitution method

8

Solve the addition of two indefinite integrals using integration by parts

9

Solve the addition of two indefinite integrals using integration by parts

10

Solve the product of multi functions by parts with inverse trig function as well

11

Solve the integrals of the product of multi functions with a cubic function

### Differentiation - Introduction to differentiation

1

Definition, mathematical representation and notations of differential equation

2

Orders of the differential equations

3

Order and Power of a differential equation

4

Two main types of differential equations

### Differentiation - Partial differential equations

1

Introduction to partial differential equation, mathematically and graphically

2

Partial differential equation vs Ordinary differential equations

3

Procedure to solve the partial differential equation

4

Solve some equations using partial differentiation

### Differentiation - Separable differential equations

1

Learn how to separate the variables of the given function?

2

Solution of some tutorials to understand the separation of the variables

### Differentiation - Linear differential equations

1

Introduction to the linear differential equation and how it looks like?

2

The graph of a linear equation is always a straight line, how? let's do it

3

Some important conditions of the linear differential equation

4

Orders of the differential equations

5

Learn the procedure to solve a linear differential equation in just two steps

6

Solution of the numerical of some linear differential equations

### Differentiation - Bernoulli's differential equation

1

What is bernoulli's differential equation and how it looks like mathematically?

2

Procedure to solve a bernoull's differential equation

3

Learn two different procedures to the bernoulli's differential equation

4

Solution of one more numerical of bernoulli's differential equation

### Differentiation - Maxima & Minima equations of a single and two variables

1

What is mean by mixima and minima equation of a single variable?

2

Steps to solve the Maxima and Minima differential equation with graphs

3

Solve a numerical of the Mixima and Minima differential equation of one variable

4

What is mean by mixima and minima equation of two variables?

5

Steps to solve the Maxima and Minima differential equation with variables

6

Solution of a maxima & minima differential equation carrying two variables

### Differentiation - Ist order homogeneous equations

1

Introduction to ist order homogeneous differential equation, how it looks like?

2

Try a test to check that whether it's ist a order homogeneous equation or not

3

Learn the procedure to solve a first order homogeneous differential equation

4

Solutions of some problems of ist order homogeneous differential equations

### Differentiation - 2nd order Homogeneous & Non homogeneous

1

Introduction to 2nd order homogeneous equation and check how it looks like

2

Procedure to solve the 2nd order homogeneous differential equation

3

Solve 2nd order homogeneous equation applying real/complex root expressions

4

Introduction to 2nd order Non homogeneous and check how its equation looks like

5

Learn how to solve 2nd order non homogeneous equation in five steps

6

Solve one more example of 2nd order non homogeneous differential equation

### Newton's Raphson Method

1

Introduction to Newton's Raphson Method

2

Procedure of three steps only to solve a function using Newton's Raphson method

3

Determine the root up to three decimal places using Newton's Raphson method

### Runge-Kutta Method

1

Introduction to Runge-Kutta Method and how it looks like mathematically?

2

Solve a problem in one step size using 4th ordered Runge-Kutta Method

3

Solve another problem in two step size using 4th ordered Runge-Kutta Method

### Newton's Interpolation Method - Forward, backward and Central interpolations

1

Introduction to difference interpolation method

2

Introduction to Newton's Forward difference interpolation method

3

Data points table of the Newton's Forward difference interpolation method

4

Solve a problem using Newton's Forward difference interpolation method

5

Introduction to Newton's Backward difference interpolation method

6

Data points table of the Newton's Backward difference interpolation method

7

Solve a problem using Newton's Backward difference interpolation method

8

Introduction to Newton's Central difference interpolation method

9

Data points table of the Newton's Central difference interpolation method

10

Solve a problem using Newton's Central difference interpolation method