This channel is made for the illustration of concepts in hydrology, hydraulics, statistics, stochastic modelling, computational methods, simulations, civil and environmental engineering. It also shows some presentations at conferences in the fields mentioned above. Most of the illustrations use animation to illustrate the concepts. It also uses spreadsheets to make it easy for students who do not like programming. Some of the spreadsheets are available for free from the website mentioned on the research gate of the author. Anyone can download it for free. هذه القناه تم إنشاؤها بغرض شرح مفاهيم أساسية في مجال الهيدرولوجيا والهيروليكا والإحصاء والنمذجة الإتفاقية والطرق الحسابية والمحاكاة والهندسة المدنية و البيئية. كما تحتوي على عروض مرئية والتي ألقيت في بعض المؤتمرات العلميه التي حضرها صاحب القناه في المجالات المذكورة أعلاه. تم عمل معظم المفاهيم باستخدام برنامج أكسل وذلك لسهوله استخدامه من قبل الطلاب والذين لا يحبوب عمليه البرمجه. بعض هذه Spreadsheet موجودة على موقع research gate
Complex numbers are fake invented math because (1) the definition of a complex number contradicts to the laws of formal logic, because this definition is the union of two contradictory concepts: the concept of a real number and the concept of a non-real (imaginary) number-an image. The concepts of a real number and a non-real (imaginary) number are in logical relation of contradiction: the essential feature of one concept completely negates the essential feature of another concept. These concepts have no common feature (i.e. these concepts have nothing in common with each other), therefore one cannot compare these concepts with each other. Consequently, the concepts of a real number and a non-real (imaginary) number cannot be united and contained in the definition of a complex number. The concept of a complex number is a gross formal-logical error; (2) the real part of a complex number is the result of a measurement. But the non-real (imaginary) part of a complex number is not the result of a measurement. The non-real (imaginary) part is a meaningless symbol, because the mathematical (quantitative) operation of multiplication of a real number by a meaningless symbol is a meaningless operation. This means that the theory of complex number is not a correct method of calculation. Consequently, mathematical (quantitative) operations on meaningless symbols are a gross formal-logical error; (3) a complex number cannot be represented (interpreted) in the Cartesian geometric coordinate system, because the Cartesian coordinate system is a system of two identical scales (rulers). The standard geometric representation (interpretation) of a complex number leads to the logical contradictions if the scales (rulers) are not identical. This means that the scale of non-real (imaginary) numbers cannot exist in the Cartesian geometric coordinate system.
I'm a (retired) electronic engineer and we use complex numbers all the time to solve real problems. Yes, they are an artificial mathematical construction, but no more so than negative numbers. Think about it: you can't have -3 apples any more than √-1 apples. The thing about complex numbers is that they are stepping stones that allow us to start with a real engineering problem, do some complex arithmetic and then to convert the result back into a real result that can be applied to the problem. There's always a way to solve such problems without using complex numbers, but using them makes the maths much simpler. For example, using complex numbers allows us to handle two coordinates at the same time. If you wanted to avoid complex numbers, then you'd need to do two separate calculations. Using complex numbers to represent two dimensions works really well, even though imaginary numbers don't actually exist. Maths is full of such artificial ideas, for example 0! (0 factorial), ∞, etc. If you want an even weirder idea, look at p-adic numbers.
The formula is decomposed into two components sinw and cosine. Real and imaginary parts. It is related to trigonometric relationships and the relationship between polar and cartesian coordinates.
RU-vid keeps recommending me really obscure videos. They're usually so random/absurd that they're funny, but this one is really jarring because I'm actually familiar with the subject matter. It's the same feeling as running into your teacher at a restaurant. Thanks, RU-vid algorithm.
Thanks for your comment. These vedios are made for my students. I use them during my lecture in groundwater modelling. They are not made for every one. People familiar with the topic can only understand it.
Actually, this used during my lecture in class to illustrate how the solution conveges to analytical solution for those who study groundwater modelling.
Actually this vedio is used during my lecture in class to illustrate to students how the solution conveges to analytical solution in the course in groundwater modelling. It may be not clear to those not familiar with the topic. So it is very specific to groundwater modellers
