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

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