Scientific Computing

Scientific Computing is an interdisciplinary field that employs computational power and numerical algorithms to model, simulate, and analyze complex scientific problems. Often considered the third pillar of science alongside theory and experimentation, it enables the investigation of phenomena that are too intricate for analytical solutions or too expensive, dangerous, or inaccessible for physical experiments. In the context of physics, this involves creating computer models to simulate everything from the quantum behavior of atoms and the evolution of galaxies to fluid dynamics and climate systems, thereby providing critical insights and predictive capabilities that bridge theoretical concepts with real-world applications.

1. Introduction to Scientific Computing
   1. The Third Pillar of Science
      1. Theory, Experiment, and Computation
      2. Historical Development of Scientific Methods
      3. Complementarity of Approaches
      4. Role in Modern Scientific Discovery
      5. Impact on Research and Industry
      6. Examples of Computational Breakthroughs
   2. Defining Scientific Computing
      1. Distinctions from Computer Science
      2. Distinctions from Data Science
      3. Interdisciplinary Nature
      4. Integration with Physical Sciences
      5. Integration with Engineering
      6. Integration with Life Sciences
   3. The Modeling and Simulation Pipeline
      1. From Physical Problem to Mathematical Model
      2. Abstraction and Idealization
      3. Formulation of Governing Equations
      4. From Mathematical Model to Computational Algorithm
      5. Discretization Techniques
      6. Algorithm Selection and Design
      7. Simulation, Analysis, and Visualization
      8. Running Simulations
      9. Post-processing and Data Analysis
      10. Visualization of Results