Georgetown College. Georgetown University.

Dr. Der-Chen Chang works out a problem on the white board in his office. (Photo: Roland Dimaya)
Dr. Chang's current work is supported by a grant from the Research Grant Council of the Hong Kong Government. (Photo: Roland Dimaya)
Students like Cynthia Anyanwu appreciate the one-on-one guidance Dr. Chang provides. (Photo: Roland Dimaya)

"From the equation itself, you can see the geometry behind the equation. There's unity and simplicity. It enables physicists and engineers to write down the universe."
--Dr. Der-Chen Chang

By LiAnna Davis

Dr. Der-Chen Chang opens his desk drawer and pulls out a stack of envelopes and brightly colored postcards. Affixed with stamps from all around the world, the letters confirm a simple fact: Georgetown students love Dr. Chang, so much so that they continue to update him on their lives long after they’ve graduated. The feeling is mutual.

“Georgetown students are nice, clever, and polite,” says Dr. Chang, a professor of mathematics. “In China, the relationship between student and teacher is like between father and son or father and daughter. Learning and teaching benefit each other. All my students are my children. As a teacher, you should have compassion for your students and try to impact their lives.”

Dr. Chang learned this method of teaching from his own educational experience, first as an undergraduate in Taiwan, then in his graduate work at Princeton and his post-doctorate work at the University of California at Berkeley.

“I’ve had many good teachers, especially at Princeton,” he says. “I’ve learned from them and continue to stay in touch with them.”

In addition to being one of the most popular professors on campus, Dr. Chang is one of the foremost researchers on partial differential equations, which express a relationship between independent variables and a partial derivative. Dr. Chang focuses on geometric properties induced by partial differential equations, especially from quantum mechanics. Of the three classifications of partial differential equations—hyperbolic, parabolic, and elliptic—Dr. Chang’s research falls into the latter category, with a particular focus on subelliptic partial differential equations. He has studied extensively (including a new research grant) in the field of subriemannian geometry, a new field related to quantum mechanics.

“Partial differential equations can be applied to all fields,” Dr. Chang says, citing biomedicine, finance, mathematics, and signal processing as examples. Because they are used to solve for unknown variables, partial differential equations offer scientists the ability to trace movement through time and space.

One of Dr. Chang’s main research areas explores questions related to aeronautics. He is working with two professors, Norman Wereley and Gang Wang, of the Department of Aerospace Engineering at University of Maryland at College Park, to study the vibrations of helicopters. Partial differential equations can describe the vibrations in the helicopter blades, which can in turn be used to determine better design practices that will reduce those vibrations.

Dr. Chang also applies his work in the field of medicine. Working with Dr. Esther Chang and other colleagues at Georgetown Medical Center’s Lombardi Cancer Center, Dr. Chang uses data from functional magnetic resonance imaging, or fMRI, and partial differential equations to track the diffusion of a disease. His work enables doctors to trace how particles are moving through the human system, providing doctors a way to describe the location of tumors and discover more about the science of tumors.

Although he began his career studying mathematics, this broad range of potential applications is what attracted Dr. Chang specifically to the field of partial differential equations.

“This subject combines all kinds of mathematics. Just like a symphony, you need all kinds of instruments to come up with a very beautiful composition,” he says. “Once you see the beauty, you’re really excited. Mathematics is another way, a language, to understand nature or God’s creation. Every day you see something new. From the equation itself, you can see the geometry behind the equation. There’s unity and simplicity. It enables physicists and engineers to write down the universe.”

Dr. Chang's passion for the subject matter, along with his deep commitment to teaching, inspires his students and keeps them engaged and curious about the important role of mathematics in our world.

“Anyone who has had the pleasure of taking any of his courses will tell you that he is an amazing person and an incredibly intelligent professor,” says Cynthia Anyanwu, a junior who has taken several courses from him. “People like Dr. Chang are the reason so many Hoyas love Georgetown. He doesn’t teach courses solely because it’s a job, I feel he does so because he wants to share his love of mathematics. He’s always so energetic about the topics, and he challenges us in a way that encourages us to reach our potential. I’m currently taking a course with Dr. Chang, and the first day of class was like a family reunion because he had gone on sabbatical for a semester and we students were so happy to be back together with him. Simply put, anyone who’s had Dr. Chang comes back for more.”

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