The study of analysis provides a basic understanding of qualitative and quantitative problem-solving techniques, the ability to analyze new areas of interest, and the ability to interact with colleagues from other disciplines in a problem-solving situation. Modern applications of analysis include biomedical modeling, image analysis, robotic control, ecology, environmental modeling, and financial engineering.

- J. Brannan: Mathematical modeling, stochastic analysis, financial mathematics
- T. Khan: Inverse problems, parameter estimation, optical tomography, biomedical imaging, control problems
- S. Liu: Inverse problems, boundary control theory, partial differential equations
- M. Mitkovski: Complex analysis, harmonic analysis, operator theory
- J. Peterson: West nile virus and tularaemia infection models, soft computing and cognitive modeling
- M. Schmoll: (geometric) control theory, differential topology, symplectic geometry, differential geometry, dynamical systems, in particular, polygonal billiards
- J. R. Yoon: Medical imaging, inverse problems, elasticity theory, seismic inversion