Scientific Calculations with Julia

Julia is an open-source programming language for numerical calculations and scientific applications, published since 2012 and released under the MIT License. It can be an excellent alternative to Matlab, which has a commercial license.

You can install additional packages for Julia to perform specific operations. For example, DifferentialEquation for solving differential equations, Roots for finding the real roots of an equation, Plots for displaying graphs, JuMP for linear programming, and so on.

To install Julia on your computer, visit http://julialang.org/downloads/ and follow the instructions. You can then run the Julia interpreter using a terminal app on your computer. This method is known as using the REPL. Basically, after installing Julia on your PC and configuring the environment variables, simply type "julia" in the terminal or console to activate the REPL app and enter the Julia code to run.

Alternatively, you can use Julia online, in your browser, on sites like NextJournal and Repl.it.

If you prefer to work locally as an alternative to the REPL, you can also use free but more powerful (and complicated) software packages like VisualStudio Code.

Another popular way to run Julia is via Jupyter with the IJulia.jl package. Jupyter is an interactive notebook technology that allows you to run Julia, Python, and R code in a browser window, in appropriate code cells. In a Jupyter notebook, you can also comment on your code in Markdown text cells. Configuring Jupyter to work with Julia is generally straightforward, but you will need to carefully follow a list of instructions. Basically, you first need to install Jupyter on your PC and then the IJulia package via Pkg. However, the easiest way to start running Julia code is using the REPL.

• Operations Research:
  • Personal Budget Optimization
  • Profit Maximization
  • Cost Minimization
  • Shortest Path
  • Traveling Salesman
• Financial Mathematics:
  • Mortgages and Loans
• Finance:
  • Pension Simulator
  • Risk Minimization in Finance
  • Maximizing Returns in Finance
  • Portfolio Optimization in Finance
• Sports Betting:
  • Basic Model of Sports Betting
• Economics:
  • Supply and Demand
• Mathematics:
  • Game Theory
• Demography:
  • Population Growth
• Agriculture:
  • Land Cultivation
• Physics:
  • Big Bang
• Electrical Engineering:
  • Electrical Circuits
• Artificial Intelligence:
  • Diagnosing Heart Disease
• Biology:
  • SIR Model
  • Predator-Prey Model
• Appendix:
  • Exercises in Julia
• New Calculations:
  • Investing in options
  • Analyze your genome