Laplace Transforms in Python with SymPy | Basic Tutorial

Learn how to compute Laplace transforms in Python using `sympy` in this beginner-friendly tutorial! We’ll calculate the Laplace transform of `f(t) = t` and `f(t) = exp(2t)*sin(3t)`, showing how `sympy` simplifies symbolic math for engineering and math problems. Perfect for students studying signals, control systems, or differential equations, as well as Python learners exploring symbolic computation!

🔍 **What You'll Learn:**
- Setting up `sympy` for Laplace transforms
- Transforming `f(t) = t` and `f(t) = exp(2t)*sin(3t)`
- Understanding the `laplace_transform` function
- Applying results to engineering problems

💻 **Code Used in This Video:**
from sympy import symbols, laplace_transform, exp, sin

# Define symbols
t, s = symbols('t s')

# Laplace transform of f(t) = t
f1 = t
F1 = laplace_transform(f1, t, s, noconds=True)
print(F1) # Output: 1/s**2

# Laplace transform of f(t) = exp(2t)*sin(3t)
f2 = exp(2*t)*sin(3*t)
F2 = laplace_transform(f2, t, s, noconds=True)
print(F2) # Output: 3/((s - 2)**2 + 9)

🌟 **Why Learn Laplace Transforms with SymPy?**
Laplace transforms are essential for solving differential equations in engineering, physics, and signal processing. With `sympy`, Python automates the process, transforming `f(t) = t` to `1/s^2` and `exp(2t)*sin(3t)` to `3/((s-2)^2 + 9)`. We’ll explain each step, show how `noconds=True` simplifies output, and discuss applications like circuit analysis. Master this, and you’ll simplify complex math problems with ease!

📚 **Who’s This For?**
- Students in engineering or math courses
- Python learners exploring symbolic math
- Professionals working on signal processing

👍 Like, subscribe, and comment: What math topic should we code next? Next up: Fourier Transforms—stay tuned!

#PythonTutorial #LaplaceTransform #SymPyMath #EngineeringMath #LearnPython

from sympy import symbols, laplace_transform, exp, sin

# Define the symbols for time (t) and frequency domain (s)
t, s = symbols('t s')

# Laplace transform of f(t) = t
f1 = t
F1 = laplace_transform(f1, t, s, noconds=True)
print(F1) # Output: 1/s**2
# This is the standard Laplace transform of t: L{t} = 1/s^2 (for s {greater than symbol} 0)

# Laplace transform of f(t) = exp(2t)*sin(3t)
f2 = exp(2*t)*sin(3*t)
F2 = laplace_transform(f2, t, s, noconds=True)
print(F2) # Output: 3/((s - 2)**2 + 9)
# This matches the formula for L{exp(at)*sin(bt)} = b/((s-a)^2 + b^2), where a=2, b=3