What This Document Is
This document is an exam from an introductory Differential Equations course (MATH 285) at the University of Illinois at Urbana-Champaign. Specifically, it’s Exam 2, Version A, administered in October 2014. It’s designed to assess a student’s understanding of core concepts covered in the course up to that point in the semester. The exam focuses on applying theoretical knowledge to problem-solving, requiring students to demonstrate their ability to set up and analyze differential equations.
Why This Document Matters
This exam is an invaluable resource for students currently enrolled in a similar Differential Equations course, or those preparing to take one. It’s particularly helpful for understanding the *types* of questions and the level of difficulty expected on assessments. Working through practice problems – and reviewing a completed exam like this one – is a proven method for solidifying understanding and identifying areas where further study is needed. It’s best used as a study aid *after* initial learning has taken place, to test and refine your skills.
Topics Covered
* Population Modeling & Equilibrium
* Linear Independence of Functions
* Homogeneous Differential Equations & Polynomial Differential Operators
* Second-Order Linear Differential Equations with Constant Coefficients
* Damped Harmonic Motion & Spring-Mass Systems
* Non-Homogeneous Linear Differential Equations
What This Document Provides
* A full exam paper with multiple problems, mirroring the format of a typical university-level assessment.
* A range of problem types, covering both theoretical understanding and practical application of differential equation techniques.
* Problems relating to real-world applications, such as population dynamics and mechanical systems.
* An opportunity to gauge your preparedness for an exam on these topics.
* Point values assigned to each problem, indicating the relative weight given to different concepts.
