This rubric is designed to assess the performance of third-year undergraduate students in a Differential Equations course. The evaluation criteria focus on key learning outcomes; ensuring students develop a strong foundation in solving and analyzing differential equations. Mastery of these skills is essential for success in advanced mathematics; engineering; and scientific disciplines. The rubric evaluates students’ ability to classify and solve first-order differential equations; including separable; linear; and exact equations. Students must demonstrate proficiency in applying appropriate techniques and verifying solutions. This ensures they can tackle real-world problems modeled by differential equations. For higher-order linear differential equations; students are assessed on their understanding of homogeneous and nonhomogeneous cases. They must correctly use methods such as undetermined coefficients and variation of parameters. Mastery of these techniques prepares students for more complex applications in physics and engineering. The rubric also measures competency in solving systems of differential equations using eigenvalue methods. Students must show the ability to analyze equilibrium solutions and stability; which is critical for modeling dynamic systems. Additionally; Laplace transform techniques are evaluated for solving initial value problems; reinforcing students’ problem-solving toolkit. Conceptual understanding is assessed through interpretation of solutions in applied contexts. Students must explain the significance of their results; connecting theory to practical scenarios. Clear communication of mathematical reasoning is emphasized; ensuring students can articulate their thought processes effectively. By meeting these criteria; students will gain a rigorous understanding of differential equations; equipping them for advanced coursework and technical careers. The rubric ensures a comprehensive evaluation of analytical skills; problem-solving ability; and conceptual clarity.
