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Title: **Title:** Differential Equations: Definition, Types, and Applications
Description: **Title:** Differential Equations: Concepts, Types, and Applications **Description:** Explore the fundamentals of differential equations, including their types, methods of solving them, and real-world applications in physics, engineering, and economics. Learn about ordinary and partial differential equations, initial and boundary value problems, and various solution techniques.
Description: **Title:** Differential Equations: Concepts, Types, and Applications **Description:** Explore the fundamentals of differential equations, including their types, methods of solving them, and real-world applications in physics, engineering, and economics. Learn about ordinary and partial differential equations, initial and boundary value problems, and various solution techniques.
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differential equation full notes { mhtcet }
Welcome to the World of Differential Maths
Imagine you're on a road trip, and you're trying to figure out how far you've traveled and how fast
you're going
...
But what if
you wanted to know your average speed over the entire trip? Or what if you wanted to know exactly
where you were 30 minutes ago? That's where differential maths comes in
...
It's like having a superpower that allows you to analyze and understand how things change and
move
...
A limit is a value that a function approaches as
the input (or independent variable) gets arbitrarily close to a certain point
...
As you get
closer and closer, your distance from the wall gets smaller and smaller
...
Calculating Limits: Step by Step
Let's calculate the limit of the function f(x) = 1/x as x approaches 2
...
1
f(2
...
1
Step 3: Evaluate the function at x = 2
...
01) = 1/2
...
Derivatives: The Rate of Change
Now that we have limits, we can talk about derivatives
...
Think of it like this:
Imagine you're driving a car, and you're going uphill
...
The steeper the hill, the faster you're going
...
Using the power rule, which states that if f(x) = x^n, then f'(x) = nx^(n-1), we get:
f'(x) = 2x
So, the derivative of x^2 is 2x
...
(Just Kidding!)
We've just scratched the surface of differential maths
...
Stay tuned
Explicit and Implicit Functions: Unveiling the Mysteries
Imagine you're on a hike, and you stumble upon a hidden trail
...
The map represents an explicit function, where the relationship
between the variables is clearly defined
...
Explicit Functions
An explicit function is a mathematical relationship where the output variable is directly expressed in
terms of the input variable(s)
...
Example 1:
Let's say we have an explicit function: y = 2x + 3
...
For every value of x, we can calculate the corresponding value of y using the function
...
It's like trying to find the hidden trail without
a map; you need to use subtle hints and clues to navigate
...
Here, we can't direct
Title: **Title:** Differential Equations: Definition, Types, and Applications
Description: **Title:** Differential Equations: Concepts, Types, and Applications **Description:** Explore the fundamentals of differential equations, including their types, methods of solving them, and real-world applications in physics, engineering, and economics. Learn about ordinary and partial differential equations, initial and boundary value problems, and various solution techniques.
Description: **Title:** Differential Equations: Concepts, Types, and Applications **Description:** Explore the fundamentals of differential equations, including their types, methods of solving them, and real-world applications in physics, engineering, and economics. Learn about ordinary and partial differential equations, initial and boundary value problems, and various solution techniques.