I am a scientist in the research and analysis division of the Submarine Launched Ballistic Missile (SLBM) program here at the Naval Surface Warfare Center Dahlgren Division. To do my job well I must be able to write software tools for data analysis, model both simple and complex problems using mathematics, verify and validate data analysis tools, and understand the complex error models that we use to validate our system. To say that mathematics has provided me the tools to do my job well would be an understatement. Mathematics truly is the queen of the sciences. One would be hard pressed to find any area within the SLBM program whose foundation is not grounded in math. At the Naval Surface Warfare Center we take pride in our technical expertise, especially in the area of mathematics and other areas where math is the core of the discipline, i.e., physics, electrical and mechanical engineering, operations research, etc. …

Just a few of the areas in mathematics that we use on a daily basis are:

1. Control Theory–Optimal and Suboptimal Kalman Filtering

2. Geometry–Euclidean and Spherical Geometry (As it is used in Astronomy)

3. Differential Equations–Systems of Differential Equations (Missile Trajectory Models)

4. Numerical Analysis–Runge and Kutta schemes, Newton iterative schemes, Matrix decomposition algorithms, and Legendre functions for Gravity error modeling

5. Linear Algebra–Least-Squares, Rotation Matrices, eigenvalues/eigenvectors

6. Calculus–Multivariate Calculus

7. Probability–Probability Density Functions (Normal, exponential, uniform, etc.), Expected values, Conditional Expectation

One of my jobs is to update and analyze one of our legacy functions used to preset the missile.