Mathematical Physics

Physics

1. 1. Dimensional Analysis

   Dimensional Analysis

   dimensional analysis

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2. 2. Vector algebra and Vector calculus

   Vector algebra and Vector calculus

   vector algebravector calculus

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3. 3. Linear vector space

   Linear vector space: basis, orthogonality and completeness

   basisorthogonalitycompleteness

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4. 4. Matrices

   Matrices; similarity transformations, diagonalization, eigenvalues and eigenvectors

   similarity transformationsdiagonalizationeigenvalueseigenvectors

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5. 5. Linear differential equations

   Linear differential equations: second order linear differential equations and solutions involving special functions

   second order linear ODEsspecial functions

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6. 6. Complex analysis

   Complex analysis: Cauchy-Riemann conditions, Cauchy's theorem, singularities, residue theorem and applications

   Cauchy-Riemann conditionsCauchy's theoremsingularitiesresidue theorem

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7. 7. Fourier Series

   Fourier Series

   Fourier series

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8. 8. Fourier and Laplace transforms

   Fourier and Laplace transforms

   Fourier transformLaplace transform

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9. 9. Tensors

   Elementary ideas about tensors: covariant and contravariant tensors

   covariant tensorscontravariant tensors

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10. 10. Probability theory

    Elementary probability theory, random variables, binomial, Poisson and normal distributions. Central limit theorem.

    random variablesbinomial distributionPoisson distributionnormal distributioncentral limit theorem

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