You do not need to use your personal computer to do CS coursework. The department provides machines running Unix (Linux/Solaris) and Windows as well as appropriate software for all CS courses. Machines are located in the department computer labs in the Computer Science Building. Additional information on these facilities is available.
However, students routinely find it convenient to use their own computers to write code for course assignments. What they must keep in mind is that unless an instructor explicitly indicates otherwise, it is always the students' responsibility to ensure their code runs correctly on department machines: instructors and graduate teaching assistants almost always grade assignments on department machines.
Lower division courses using Java typically use tools to write code. Code written using these tools usually transfers easily from a student's machine to a department machine. The current tool is Eclipse and runs under most common operating systems: Linux, Windows, and MacOS.
In upper division courses and courses not using Java, the particulars vary on how to use one's personal computer. Instructors will usually discuss the hardware and software requirements for a course at the beginning of the semester. Again, the student is responsible for submitting completed assignments that work properly on the machines indicated by the instructor.