This book includes four main chapters: 1. Indefinite Integral. 2. Methods of Integration. 3. Definite Integral. 4. Multiple Integral. In addition to many examples and exercises for the purpose of acquiring the student's ability to think correctly in solving mathematical questions.
In this research, we find the Bayesian formulas and the estimation of Bayesian expectation for product system of Atlas Company. The units of the system have been examined by helping the technical staff at the company and by providing a real data the company which manufacturer the system. This real data include the failed units for each drawn sample, which represents the total number of the manufacturer units by the company system. We calculate the range for each estimator by using the Maximum Likelihood estimator. We obtain that the expectation-Bayesian estimation is better than the Bayesian estimator of the different partially samples which were drawn from the product system after it checked by the
... Show MoreNanomaterials enhance the performance of both asphalt binders and asphalt mixtures. They also improve asphalt durability, which reduces resource consumption and environmental impact in the long term associated with the production and transportation of asphalt materials. Thus, this paper studies the effectiveness of Nano Calcium Carbonate (Nano CaCO3) and Nano Hydrated Lime (NHL) as modifiers and examines their impact on ranges from 0% to 10% through comprehensive laboratory tests. Softening point, penetration, storage stability, viscosity, and mass loss due to short-term aging using the Rolling Thin Film Oven Test (RTFO) were performed on asphalt binders. Results indicated a significant improvement in binder stiffness, particularly
... Show MoreThe influence of adding metal foam fins on the heat transfer characteristics of an air to water double pipe heat exchanger is numerically investigated. The hot fluid is water which flows in the inner cylinder whereas the cold fluid is air which circulates in the annular gap in parallel flow with water. Ten fins of metal foam (Porosity = 0.93), are added in the gap between the two cylinder, and distributed periodically with the axial distance. Finite volume method is used to solve the governing equations in porous and non-porous regions. The numerical investigations cover three values for Reynolds number (1000 ,1500, 2000), and Darcy number (1 x10-1, 1 x10-2, 1x10-3). The comparison betwee
... Show MorePublic spending represents the government’s financial leverage and has a significant impact on real and monetary economic variables, and one of these effects is the effect of public spending on the exchange rate as an important monetary variable for monetary policy, As we know that public spending in Iraq is financed from oil revenues sold in US dollars, and the Ministry of Finance converts the US dollar into Iraqi dinars to finance the government's need to spend within the requirements and obligations of the state's general budget, And converting the US dollar into Iraqi dinars has an impact on the parallel exchange market, even if there is a contractual exchange rate between the Ministry of Finance and the Central Bank of Iraq to
... Show MoreThis paper deals the prediction of the process of random spatial data of two properties, the first is called Primary variables and the second is called secondary variables , the method that were used in the prediction process for this type of data is technique Co-kriging , the method is usually used when the number of primary variables meant to predict for one of its elements is measured in a particular location a few (because of the cost or difficulty of obtaining them) compare with secondary variable which is the number of elements are available and highly correlated with primary variables, as was the&nbs
... Show MoreSatire is genre of the literary arts that has always been the source of human interest. Because it is difficult to accept direct criticism, Satire appears as a literary tool in which vices, follies, abuses and shortcomings are held up to ridicule, with the intent of shaming individuals, corporations, government, or society itself into improvement. A satirical critic usually employs irony to attain this goal. Although satire is usually meant to be humorous, its greater purpose is often profitable social criticism, using wit to draw at
... Show MoreThis paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient
Experimental programs based test results has been used as a means to find out the response of individual elements of structure. In the present study involves investigated behavior of five reinforced concrete deep beams of dimension (length 1200 x height 300 x width150mm) under two points concentrated load with shear span to depth ratio of (1.52), four of these beams with hallow core and
retrofit with carbon fiber reinforced polymer CFRP (with single or double or sides Strips). Two shapes of hallow are investigated (circle and square section) to evaluated the response of beams in case experimental behavior. Test on simply supported beam was performed in the laboratory & loaddeflection, strain of concrete data and crack pattern of
In this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using Mathcad 15.and graphic in Matlab R2015a.