Applied Mathematics

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Applied Mathematics is the branch of mathematics which deals with applications of mathematics to the real world problems, often from problems stemming from the fields of engineering or theoretical physics. It is differentiated from Pure Mathematics, which deals with more abstract problems. There is also something called Applicable Mathematics, which deals with real world problems which need the techniques and mindset usually used in Pure Mathematics. These distinctions do not really become apparent during school level mathematics.

Examples of topics in Applied Mathematics:

  • Fluid Dynamics: the mathematics of fluid flow
  • Quantum Mechanics applied to Engineering and Computer Science problems
    1. Numerical Calculus
      1. Error calculations
      2. Solving Linear Equations numerically
      3. Special methods for solving of Linear Equations
    2. Numerical Methods of solving Differential Equations
    3. Optimization
    4. Fluid Dynamics
  1. Theory of The Fourier Transform and Its Applications
    1. The Basics of Theory of The Fourier Transform
    2. Fourier Series
    3. General Fourier Transform
    4. Fourier Sine Series
    5. Fourier Cosine Series
    6. Fourier Integral Transforms
    7. Parseval's Theorem
    8. Signal Processing and Analysis
    9. Quantum Theory
  2. Bessel Functions
  3. Laplace Transforms
  4. Complex Integration
  5. Linear Algebra
    1. The Basics
    2. Leontif Input-Output Model
    3. Markov Chains
    4. Finding Eigenvalues
    5. Orthogonalization and Normalization
    6. Least Squares Fit
    7. Finding Inverses
    8. Hermitian Matrices
    9. Singular Value Decomposition
  6. Calculus of Variations
    1. Lagrange Equations
  7. Vector Calculus
  8. Mathematics applied to problems in Physics
    1. General and Special Relativity
    2. Quantum Mechanics
    3. The State Equation
  1. Appendices
    1. Appendix A: Historical overview
    2. Appendix B: Applied Mathematics and Computer Science
    3. Appendix C: Applied Mathematics and Physics