1. Improper Integrals
2. Change of variable Theorem
3. Green's, Gauss's, Stokes Theorem

• (1) Mathematics is hierarchical. A student who is given a grade of C or higher in a course must have mastery of that material that allows the possibility of succeeding in courses for which that course is a prerequisite.
• (2) Some mathematics courses are primarily concerned with techniques and applications. In such courses student success is measured by the student's ability to model , successfully apply the relevant technique, and bring the calculation to a correct conclusion. The department's 100-level courses and most calculus courses are examples in this category although these are not the only examples. Other courses such as this one are primarily concerned with theoretical structures and proof. In such courses student success is measured by the student's ability to apply the theorems and definitions in the subject, and to create proofs on his or her own using the models and ideas taught during the course. Many courses are partly hybrids incorporating both techniques and applications, and some element of theory. Some lean more toward applications, others more toward theory.

• A: Consistently chooses appropriate models, uses correct techniques, and carries calculations through to a correct answer. Able to estimate error when appropriate, and able to recognize conditions needed to apply models as appropriate.
• B: Usually chooses appropriate models and uses correct techniques, and makes few calculational errors. Able to estimate error when prompted, and able to recognize conditions needed to apply models when prompted.
• C: Makes calculations correctly or substantially correctly, but requires guidance on choosing models and technique. Able to estimate error when prompted and able to recognize conditions needed to apply models when prompted.
• D: Makes calculations correctly or substantially correctly, but unable to do modeling.
• F: Can neither choose appropriate models, or techniques, nor carry through calculations.

Rubric for pure courses:

• A: Applies the important theorems from the course. Constructs counterexamples when hypotheses are weakened. Constructs complete and coherent proofs using the definitions, ideas and theorems from the course. Applies ideas from the course to construct proofs that the student has not seen before.
• B: Applies the important theorems from the course. Constructs counterexamples when hypotheses are weakened. Constructs complete and coherent proofs using the definitions, ideas and theorems from the course.
• C: Applies the important theorems from the course when the application is direct. Constructs simple proofs using the de nitions when there are very few steps between the de nitions and the conclusions. Explains most important counterexamples.
• D: Can do some single step proofs and explain some counterexamples.
• F: Unable to do even single step proofs or correctly use de nitions.

Many courses combine pure and applied elements and the rubrics for those courses will have some combination of elements from the two rubrics above. Detailed interpretation of the rubrics depends on the content and level of the course and will be at the discretion of instructors. Whether to award grades of A+ is at the discretion of instructors.

To rest on the blue of the day, like an eagle rests on the wind, over the cold range, confident on its wings and its breadth.