Physical oceanography is the branch of oceanography that deals with the physical properties and processes of the ocean. It focuses on the dynamics of ocean waters and their interactions with the atmosphere, the seafloor, and marine ecosystems. Key areas of study within physical oceanography include: 1. **Ocean Currents**: Understanding the movement of water masses, including surface currents, deep ocean currents, and tidal forces.

Soil physics is a branch of soil science that focuses on the physical properties and processes of soil and how these affect its ability to support plant growth and environmental quality. It involves the study of various physical aspects of soil, including: 1. **Soil Texture**: The size distribution of soil particles (sand, silt, clay) which influences water retention, nutrient availability, and air movement.

Medical physics is a multidisciplinary field that applies principles and techniques from physics to medicine, particularly in the diagnosis and treatment of diseases. It primarily focuses on the use of radiation and other physical principles in healthcare. Medical physicists work in various areas, including: 1. **Radiology**: They help in the safe and effective use of imaging technologies such as X-rays, MRI, CT scans, and ultrasound. They ensure that imaging studies are performed safely and produce high-quality images for diagnosis.

Mathematical economics is a field that applies mathematical methods and techniques to represent economic theories, analyze economic problems, and derive economic relationships. It utilizes mathematical concepts such as calculus, linear algebra, and optimization to model economic behaviors and interactions quantitatively. The primary objectives of mathematical economics include: 1. **Modeling Economic Behavior**: Creating models that describe how individuals, firms, and markets behave under various conditions. This includes utility functions, production functions, and demand and supply models.

Applied probability is a branch of probability theory that focuses on the application of probabilistic models and statistical techniques to solve real-world problems across various fields. It involves using mathematical tools and concepts to analyze and interpret random phenomena, make predictions, and inform decision-making under uncertainty. Key aspects of applied probability include: 1. **Modeling Real-World Situations**: Applied probability is used to create models that represent random processes or systems.

Inverse problems refer to a class of problems where one seeks to deduce unknown causes or parameters from observed effects or data. This is contrasted with direct problems, where the process is straightforward: given a set of inputs, one can directly compute the outputs. Inverse problems typically arise in fields such as physics, engineering, medical imaging, geophysics, and many other areas where one must infer the properties of a system from measured data.