{"product_id":"2940012229397","title":"Advanced Mathematics Personal Study Notes- Part II","description":"This is Part II of my personal study notes in advanced mathematics. It entails theoretical analysis, solved examples, and exercises on the following topics:\u003cbr\u003e----\u003cbr\u003e9. Functions of Complex Variable\u003cbr\u003e\u003cbr\u003eIntroduction to complex numbers\u003cbr\u003eThe real and imaginary parts of a complex number\u003cbr\u003eModulus and Argument of a complex number\u003cbr\u003eComplex number as vectors\u003cbr\u003eCartesian and Polar representation of complex numbers\u003cbr\u003ePure Real and Imaginary numbers\u003cbr\u003eRepresentation of complex numbers on a Riemann Sphere\u003cbr\u003eAlgebraic operations on complex numbers.\u003cbr\u003eConformal Mapping\u003cbr\u003eInverse Transformation\u003cbr\u003eSeries of complex numbers\u003cbr\u003eCauchy's Theorem\u003cbr\u003eCauchy’s Theorem of Residue\u003cbr\u003eCauchy's Integral formula\u003cbr\u003e -----\u003cbr\u003e10. Theory of Probability\u003cbr\u003e\u003cbr\u003eMathematical definition of probability\u003cbr\u003eExclusive events\u003cbr\u003eIndependent events\u003cbr\u003eRules governing probability of independent events\u003cbr\u003eDependent events\u003cbr\u003eBinomial law of probability\u003cbr\u003eRandom variables\u003cbr\u003eDiscrete distribution\u003cbr\u003eContinuous distribution\u003cbr\u003eJoint distribution of several variables\u003cbr\u003eExpectation\u003cbr\u003eParameters of a frequency distribution\u003cbr\u003eSheppard’s correction\u003cbr\u003eBinomial frequency distribution\u003cbr\u003eStirling’s formula for the approximation of factorials of large numbers\u003cbr\u003eChekychef’s Theorem\u003cbr\u003eNormal frequency distribution or Gaussian distribution\u003cbr\u003ePoission’s distribution\u003cbr\u003eLaw of large numbers\u003cbr\u003eCorrelation\u003cbr\u003eScatter diagram\u003cbr\u003eStandard error of the mean SEM\u003cbr\u003e\u003cbr\u003e11. Laplace Transforms\u003cbr\u003e\u003cbr\u003eThe Laplace transformation.\u003cbr\u003eThe Laplace transformation of the sum of two functions\u003cbr\u003eSectionally or piecewise continuous functions\u003cbr\u003eFunctions of exponential order\u003cbr\u003eInverse Laplace transforms\u003cbr\u003eTransforms of derivatives\u003cbr\u003eTransforms of integrals\u003cbr\u003eThe first shift theorem of multiplying the object function by eat\u003cbr\u003eLaplace’s solution of linear differential equations with constant coefficients\u003cbr\u003eThe second translation or shifting property\u003cbr\u003eThe unit impulse function\u003cbr\u003eThe unit doublet\u003cbr\u003eDifferentiation of transform\u003cbr\u003eThe Heaviside's expansion formulae\u003cbr\u003eUsing Laplace Transformation in solving Linear Partial Differential Equations\u003cbr\u003e\u003cbr\u003e12. Ordinary and Partial Differential Equations\u003cbr\u003e\u003cbr\u003eTotal Differential Equations\u003cbr\u003eOrdinary differential equations\u003cbr\u003eLinear simultaneous equations with constant coefficients\u003cbr\u003eSimultaneous Total Differential Equations\u003cbr\u003eFirst Order differential equations \u003cbr\u003eSeparable Equations \u003cbr\u003eHomogeneous Equations \u003cbr\u003eDifferential equations of the second order\u003cbr\u003eLinear differential equations of the second order\u003cbr\u003ePartial Differential Equations of the First Order\u003cbr\u003eNon linear partial differential equations of the first order\u003cbr\u003eDamped mechanical  oscillations\u003cbr\u003eElectrical oscillations- RCL circuit\u003cbr\u003e \u003cbr\u003e13. Applications in Engineering and Physics\u003cbr\u003e14. Solved Problems and Exercises","brand":"Shaymaa Publishing Corporation","offers":[{"title":"Default Title","offer_id":47069148348656,"sku":"2940012229397","price":9.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940012229397_p0.jpg?v=1763553934","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940012229397","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}