Note: Use software such as Lucidchart, Visio, PowerPoint, or Word to create diagrams. Hand$-$drawn diagrams will not receive any credit. You can upload your response as a file to this question

Given the following scenario, design an Entity$-$Relationship Diagram $($ERD$)$ that accurately represents the data model:

A university system needs to store information about students, courses, and enrollments. Each student has a unique ID$,$ name, and date of birth. Each course has a unique course ID$,$ name, and description. A student can enroll in many courses, and each course can have many students enrolled. Additionally, the system needs to track the grades that students receive in each course they take.

Part $1$: Create an ERD that includes the necessary entities, relationships, primary keys, and foreign keys. Label all entities and relationships, and make sure to specify the cardinalities of the relationships. Provide an explanation of your design choices.

Part $2$: Suppose the university system needs to add a new feature where students can take multiple courses in different departments, and each department has a department head. How would you modify your ERD to incorporate this new requirement? What new entities or relationships would you introduce?