Teaching Resources

This page contains selected course notes and graduate qualifying exam materials made available for educational purposes.

Course Notes

MA 125: Business Calculus (Butler University)

• Chapter 5.3. Consumer Loans and Amortization PDF
• Chapter 5.4. Bonds and Treasury Bills PDF
• Chapter 12.1. Local Extrema PDF

MATH 261 – Multivariable Calculus (Ivy Tech)

• Final Exam Review PDF
Last updated: Fall 2025.

Graduate Qualifying Exam Materials

• MATH 54400: Real Analysis Qualifying Exam: Selected Solutions (PDF)

Disclaimer: These materials reflect one possible approach and may differ from official solutions or grading schemes. They are provided for educational use only.