Niels Otani
Associate Professor
School of Mathematical Sciences
College of Science
585-475-5140
Office Location
Niels Otani
Associate Professor
School of Mathematical Sciences
College of Science
Education
BA, University of Chicago; Ph.D., University of California at Berkeley
585-475-5140
Areas of Expertise
Applied and Computational Mathematics
Biomechanical Imaging
Cardiac Electrical Dynamics
Cardiac Electrophysiology
Chaos
Computational Biology
Computational Modeling
Differential Equations
Dynamical Systems
Image Processing
Inverse Problems
Linear Algebra
Mathematical Biology
Mathematical Modeling
Modeling and Simulation
Partial and Ordinary Differential Equations
Partial Differential Equations
PDE
Scientific Computing
Visualization and Simulation
Currently Teaching
MATH-219
Multivariable Calculus
3 Credits
This course is principally a study of the calculus of functions of two or more variables, but also includes the study of vectors, vector-valued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, and includes applications in physics. Credit cannot be granted for both this course and MATH-221.
MATH-221
Multivariable and Vector Calculus
4 Credits
This course is principally a study of the calculus of functions of two or more variables, but also includes a study of vectors, vector-valued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, Stokes' Theorem, Green's Theorem, the Divergence Theorem, and applications in physics. Credit cannot be granted for both this course and MATH-219.
MATH-331
Dynamical Systems
3 Credits
The course revisits the equations of spring-mass system, RLC circuits, and pendulum systems in order to view and interpret the phase space representations of these dynamical systems. The course begins with linear systems followed by a study of the stability analysis of nonlinear systems. Matrix techniques are introduced to study higher order systems. The Lorentz equation will be studied to introduce the concept of chaotic solutions.
MATH-431
Real Variables I
3 Credits
This course is an investigation and extension of the theoretical aspects of elementary calculus. Topics include mathematical induction, real numbers, sequences, functions, limits, and continuity. The workshop will focus on helping students develop skill in writing proofs.
MATH-495
Undergraduate Research in Mathematical Sciences
1 - 3 Credits
This course is a faculty-directed project that could be considered original in nature. The level of work is appropriate for students in their final two years of undergraduate study.
MATH-498
Independent Study in Mathematical Sciences
1 - 3 Credits
This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.
MATH-631
Dynamical Systems
3 Credits
This course is a study of dynamical systems theory. Basic definitions of dynamical systems are followed by a study of maps and time series. Stability theory of solutions of differential equations is studied. Asymptotic behavior of solutions is investigated through limit sets, attractors, Poincaré–Bendixson theory, and index theory. The notion of local bifurcation is introduced and investigated. Chaotic systems are studied.
MATH-790
Research & Thesis
0 - 9 Credits
Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.
MATH-791
Continuation of Thesis
0 Credits
Continuation of Thesis
In the News
-
May 29, 2019
![Two head-and-shoulder shots of male researchers.]()
RIT researchers receive NSF award to develop new diagnostic tool for cardiac disease
Researchers at RIT are providing a better map to the human heart. They are developing a critical tool that will help clinicians identify damaged areas in the heart to more accurately diagnose cardiac disease.
