Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a Partial Differential Equation (PDE).
💡 Hint: Think about what variables and derivatives are involved.
Question 2
Easy
What distinguishes a linear PDE?
💡 Hint: Recall the characteristics of linear equations.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the general form of a homogeneous linear PDE?
- a) ax + by + c = 0
- b) ∂²z/∂x² + ∂²z/∂y² = 0
- c) ∂²z + 5x = 0
💡 Hint: Recall the properties of homogeneous equations.
Question 2
True or False: In a homogeneous linear PDE, a free term may be present.
- True
- False
💡 Hint: Think about the definition of homogeneity.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Solve the PDE ∂²z/∂x² + 3∂²z/∂y² = 0 and interpret the nature of the roots. What kind of solutions would you expect?
💡 Hint: Focus on how each term in the operator form translates to the auxiliary equation.
Question 2
For the equation ∂²z/∂x² - 6∂²z/∂x∂y + 9∂²z/∂y² = 0, find the general solution and describe the form it takes.
💡 Hint: Recognize how repeated roots influence your complementary function.
Challenge and get performance evaluation