Practice Examples for Practice - 2.5 | 2. Classification of PDEs (Elliptic, Parabolic, Hyperbolic) | Mathematics - iii (Differential Calculus) - Vol 2
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Examples for Practice

2.5 - Examples for Practice

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Classify the PDE ∂²u/∂x² + ∂²u/∂y² = 0.

💡 Hint: Check the coefficients and calculate the discriminant.

Question 2 Easy

What type of PDE is ∂u/∂t - ∂²u/∂x² = 0?

💡 Hint: Identify the coefficients and find the discriminant.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the classification type for a PDE with discriminant Δ < 0?

Elliptic
Parabolic
Hyperbolic

💡 Hint: Think about the conditions of steady-state systems.

Question 2

True or False: A parabolic PDE has two distinct characteristic lines.

True
False

💡 Hint: Consider what a parabolic shape looks like.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

For the PDE ∂²u/∂t² - 9∂²u/∂x² = 0, classify, interpret its physical significance, and solve for the general solution.

💡 Hint: Focus on separating variables and considering initial conditions.

Challenge 2 Hard

Classify and analyze the PDE ∂²u/∂x² + 4∂²u/∂y² = 0, ensuring you work out boundary conditions.

💡 Hint: Think about constant solutions in a bounded domain.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.