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 C, 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 analyze and interpret mathematical models.
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 completed exams like this one – is a proven strategy for exam success. It’s best used as part of a comprehensive study plan, after initial learning and practice with textbook examples. Accessing the full exam allows for a realistic practice experience.
Topics Covered
* Population Modeling & Equilibrium
* Linear Independence of Functions
* Homogeneous Differential Equations with Polynomial Operators
* Second-Order Linear Differential Equations with Constant Coefficients
* Damped Harmonic Motion & Spring-Mass Systems
* Solutions to Differential Equations (real and complex)
What This Document Provides
* A full exam paper with multiple problems, mirroring a classroom assessment.
* A range of problem types commonly found in introductory differential equations courses.
* Problems requiring both analytical and computational skills.
* An opportunity to gauge understanding of key concepts related to differential equations and their applications.
* A time constraint indication (50 minutes) to simulate exam conditions.
