كتاب Advanced Mathematical Tools for Automatic Control Engineers
 منتدى هندسة الإنتاج والتصميم الميكانيكى بسم الله الرحمن الرحيم أهلا وسهلاً بك زائرنا الكريم نتمنى أن تقضوا معنا أفضل الأوقات وتسعدونا بالأراء والمساهمات إذا كنت أحد أعضائنا يرجى تسجيل الدخول أو وإذا كانت هذة زيارتك الأولى للمنتدى فنتشرف بإنضمامك لأسرتنا وهذا شرح لطريقة التسجيل فى المنتدى بالفيديو : http://www.eng2010.yoo7.com/t5785-topic وشرح لطريقة التنزيل من المنتدى بالفيديو: http://www.eng2010.yoo7.com/t2065-topic إذا واجهتك مشاكل فى التسجيل أو تفعيل حسابك وإذا نسيت بيانات الدخول للمنتدى يرجى مراسلتنا على البريد الإلكترونى التالى : Deabs2010@yahoo.com             منتدى هندسة الإنتاج والتصميم الميكانيكى :: المنتديات الهندسية :: منتدى الكتب والمحاضرات الهندسية :: منتدى كتب ومحاضرات الأقسام الهندسية المختلفة Tweetشاطر

# كتاب Advanced Mathematical Tools for Automatic Control Engineers كاتب الموضوعرسالة
Admin
مدير المنتدى  عدد المساهمات : 15189
التقييم : 25181
تاريخ التسجيل : 01/07/2009
العمر : 30
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية  موضوع: كتاب Advanced Mathematical Tools for Automatic Control Engineers الجمعة 05 يوليو 2013, 11:03 am أخوانى فى اللهأحضرت لكم كتابAdvanced Mathematical Tools for Automatic Control EngineersVolume 1: Deterministic TechniquesAlexander S. PoznyakSeptember 21, 2007ويتناول الموضوعات الأتية :I MATRICES AND RELATED TOPICS 11 Determinants 31.1 Basic definitions 31.1.1 Rectangularmatrix 31.1.2 Permutations, number of inversions and diagonals 41.1.3 Determinants 51.2 Properties of numerical determinants, minors and cofactors 71.2.1 Basic properties of determinants 71.2.2 Minors and cofactors 121.2.3 Laplace’s theorem. 141.2.4 Binet-Cauchy formula 161.3 Linear algebraic equationsand the existence of solutions 171.3.1 Gauss’smethod 171.3.2 Kronecker-Capelli criterion 191.3.3 Cramer’s rule 202 Matrices and Matrix Operations 212.1 Basic definitions 212.1.1 Basic operations overmatrices 212.1.2 Special forms of squarematrices 222.2 Somematrix properties 242.3 Kronecker product 292.4 Submatrices, partitioning of matrices and Schur’s formulas 322.5 Elementary transformations onmatrices 352.6 Rank of amatrix 402.7 Trace of a quadraticmatrix 423 Eigenvalues and Eigenvectors 453.1 Vectors and linear subspaces 453.2 Eigenvalues and eigenvectors 493.3 The Cayley-Hamilton theorem 593.4 The multiplicities and generalized eigenvectors 603.4.1 Algebraic and geometric multiplicities 603.4.2 Generalized eigenvectors 624 Matrix Transformations 654.1 Spectral theorem for Hermitian matrices 654.1.1 Eigenvectors of a multiple eigenvalue forHermitianmatrices 654.1.2 Gram-Schmidt orthogonalization 664.1.3 Spectral theorem 674.2 Matrix transformation to the Jordan form 684.2.1 The Jordan block 684.2.2 The Jordanmatrix form 694.3 Polar and singular-value decompositions 704.3.1 Polar decomposition 704.3.2 Singular-value decomposition 734.4 Congruent matrices and the inertia of a matrix 774.4.1 Congruentmatrices 774.4.2 Inertia of a squarematrix 784.5 Cholesky factorization 814.5.1 Upper triangular factorization 814.5.2 Numerical realization 835 Matrix Functions 855.1 Projectors 855.2 Functions of amatrix 875.2.1 Main definition 875.2.2 Matrix exponent 895.2.3 Square root of a positive semidefinite matrix 935.3 The resolvent formatrix 945.4 Matrix norms 985.4.1 Norms in linear spaces and in Cn 985.4.2 Matrix norms 1005.4.3 Compatible norms 1035.4.4 Inducematrix norm 1046 Moore-Penrose Pseudoinverse 1076.1 Classical Least Squares Problem 1076.2 Pseudoinverse characterization 1106.3 Criterion for pseudoinverse checking 1136.4 Some identities for pseudoinversematrices 1156.5 Solution of Least Square Problemusing pseudoinverse 1176.6 Cline’s formulas 1206.7 Pseudo-ellipsoids 1206.7.1 Definition and basic properties 1206.7.2 Support function 1226.7.3 Pseudo-ellipsoids containing vector sum of twopseudo-ellipsoids 1236.7.4 Pseudo-ellipsoids containing intersection of twopseudo-ellipsoids 1257 Hermitian and Quadratic Forms 1277.1 Definitions 1277.2 Nonnegative definitematrices 1307.2.1 Nonnegative definiteness 1307.2.2 Nonnegative (positive) definitenessof a partitionedmatrix 1337.3 Sylvester criterion 136vi CONTENTS7.4 The simultaneous transformation of pair of quadraticforms 1387.4.1 The case when one of quadratic form isstrictly positive 1387.4.2 The case when both quadratic forms are nonnegative. 1397.5 Simultaneous reduction of more than two quadratic forms1417.6 A related maximum-minimumproblem 1427.6.1 Rayleigh quotient 1427.6.2 Main properties of the Rayleigh quotient 1437.7 The ratio of two quadratic forms 1458 Linear Matrix Equations 1478.1 General type of linear matrixequation 1478.1.1 General linearmatrix equation 1478.1.2 Spreading operator and Kronecker product 1478.1.3 Relation between the spreading operatorand theKronecker product 1488.1.4 Solution of a general linear matrix equation 1508.2 Sylvestermatrix equation 1518.3 Lyapunovmatrix equation 1529 Stable Matrices and Polynomials 1539.1 Basic definitions 1539.2 Lyapunov stability 1549.2.1 Lyapunov matrix equation for stablematrices 1549.3 Necessary condition of the matrixstability 1599.4 The Routh-Hurwitz criterion 1609.5 The Liénard-Chipart criterion 1699.6 Geometric criteria 1709.6.1 The principle of argument variation 1709.6.2 TheMikhailov’s criterion 1729.7 Polynomial robust stability 175CONTENTS vii9.7.1 Parametric uncertainty and robuststability 1759.7.2 TheKharitonov’s theorem 1779.7.3 The Polyak-Tsypkin geometric criterion 1809.8 Controllable, stabilizable, observable and detectable pairs1829.8.1 Controllability and a controllable pair ofmatrices 1829.8.2 Stabilizability and a stabilizable pair ofmatrices 1889.8.3 Observability and an observable pair ofmatrices 1899.8.4 Detectability and a detectable pair ofmatrices 1939.8.5 Popov-Belevitch-Hautus (PBH) test 19310 Algebraic Riccati Equation 19510.1 Hamiltonianmatrix 19510.2 All solutions of the algebraic Riccati equation 19610.2.1 Invariant subspaces 19610.2.2 Main theorems on the solution presentation 19710.2.3 Numerical example 20010.3 Hermitian and symmetric solutions 20110.3.1 No pure imaginary eigenvalues 20110.3.2 Unobservablemodes 20610.3.3 All real solutions 20710.3.4 Numerical example 20810.4 Nonnegative solutions 21010.4.1 Main theorems on the algebraic Riccatiequation solution 21011 Linear Matrix Inequalities 21511.1 Matrices as variablesand LMI problem 21511.1.1 Matrix inequalities 21511.1.2 LMI as a convex constraint 21711.1.3 Feasible and infeasible LMI 21711.2 Nonlinear matrix inequalitiesequivalent to LMI 218viii CONTENTS11.2.1 Matrix normconstraint 21811.2.2 Nonlinear weighted normconstraint 21911.2.3 Nonlinear trace normconstraint 21911.2.4 Lyapunov inequality 21911.2.5 Algebraic Riccati - Lurie’s matrix inequality 22011.2.6 Quadratic inequalities and S-procedure 22011.3 Some characteristics of linearstationary systems (LSS) 22111.3.1 LSS and their transfer function 22111.3.2 H2 norm 22211.3.3 Passivity and the positive-real lemma 22211.3.4 Nonexpansivity and the bounded-reallemma 22411.3.5 H norm 22611.3.6 γ-Entropy 22711.3.7 Stability of stationary time-delay systems 22711.3.8 Hybrid time-delay linear stability 22811.4 Optimization problems with LMIconstraints 22911.4.1 Eigenvalue problem(EVP) 22911.4.2 Tolerance level optimization 23011.4.3 Maximization of the quadratic stability degree 23011.4.4 Minimization of linear function Tr (CP C|) underthe Lyapunov-type constraint 23111.4.5 The convex function log det A−1 (X)minimization 23211.5 Numerical methods for LMIsresolution 23311.5.1 What does itmean "to solve LMI"? 23311.5.2 Ellipsoid algorithm 23311.5.3 Interior-pointmethod 23712 Miscellaneous 23912.1 Λ-matrix inequalities 23912.2 MatrixAbel identities 24012.2.1 Matrix summation by parts 24012.2.2 Matrix product identity 241CONTENTS ix12.3 S-procedure and Finsler lemma 24212.3.1 Daneš’ theorem 24212.3.2 S-procedure 24412.3.3 Finsler lemma 24712.4 Farkaš lemma 24912.4.1 Formulation of the lemma 24912.4.2 Axillary bounded LS-problem 25012.4.3 Proof of Farkaš lemma 25212.4.4 The steepest descent problem 25312.5 Kantorovichmatrix inequality 253II ANALYSIS 25513 The Real and Complex Number Systems 25713.1 Ordered sets 25713.1.1 Order 25713.1.2 Infimumand supremum 25813.2 Fields 25813.2.1 Basic definition andmain axioms 25813.2.2 Some important properties 25913.3 The real field 26113.3.1 Basic properties 26113.3.2 Intervals 26213.3.3 Maximumandminimumelements 26213.3.4 Some properties of the supremum 26313.3.5 Absolute value and the triangle inequality 26413.3.6 The Cauchy-Schwarz inequality 26613.3.7 The extended real number system 26613.4 Euclidian spaces 26713.5 The complex field 26813.5.1 Basic definition and properties 26813.5.2 The imaginary unite 26913.5.3 The conjugate and absolute value of a complexnumber 27013.5.4 The geometric representation of complex numbers27213.6 Some simplest complex functions 27413.6.1 Power 274x CONTENTS13.6.2 Roots 27513.6.3 Complex exponential 27613.6.4 Complex logarithms 27713.6.5 Complex sines and cosines 27814 Sets, Functions and Metric Spaces 28114.1 Functions and sets 28114.1.1 The function concept 28114.1.2 Finite, countable and uncountable sets 28214.1.3 Algebra of sets 28314.2 Metric spaces 28714.2.1 Metric definition and examples of metrics 28714.2.2 Set structures 28814.2.3 Compact sets 29214.2.4 Convergent sequences in metric spaces 29414.2.5 Continuity and function limits in metric spaces 30114.2.6 The contraction principle and a fixed point theorem. 31014.3 Resume 31015 Integration 31115.1 Naive interpretation 31115.1.1 What is the Riemann integration? 31115.1.2 What is the Lebesgue integration? 31215.2 The Riemann-Stieltjes integral 31315.2.1 Riemann integral definition 31315.2.2 Definition of Riemann-Stieltjes integral 31515.2.3 Main properties of the Riemann-Stieltjes integral 31615.2.4 Different types of integrators 32115.3 The Lebesgue-Stieltjes integral 33215.3.1 Algebras, σ-algebras and additive functions of sets33215.3.2 Measure theory 33515.3.3 Measurable spaces and functions 34415.3.4 The Lebesgue-Stieltjes integration 34815.3.5 The "almost everywhere" concept 35215.3.6 "Atomic" measures and δ - function 354CONTENTS xi16 Selected Topics of Real Analysis 35716.1 Derivatives 35716.1.1 Basic definitions and properties 35716.1.2 Derivative of multivariable functions 36216.1.3 Inverse function theorem 36816.1.4 Implicit function theorem 37116.1.5 Vector and matrix differential calculus 37416.1.6 Nabla-operator in 3-dimensional space 37616.2 OnRiemann-Stieltjes integrals 37816.2.1 The necessary condition for existence of Riemann-Stieltjes integrals 37816.2.2 The sufficient conditions for existence of Riemann-Stieltjes integrals 38016.2.3 Mean-value theorems 38116.2.4 The integral as a function of the interval 38316.2.5 Derivative integration. 38416.2.6 Integrals depending on a parameters and differentiationunder integral sign 38516.3 On Lebesgue integrals 38816.3.1 Lebesgue’s monotone convergence theorem 38816.3.2 Comparison with the Riemann integral 39016.3.3 Fatou’s lemma 39116.3.4 Lebesgue’s dominated convergence 39316.3.5 Fubini’s reduction theorem 39416.3.6 Coordinate transformation in an integral 39916.4 Integral inequalities 40116.4.1 Generalized Chebyshev Inequality 40116.4.2 Markov and Chebyshev Inequalities 40216.4.3 Hölder Inequality 40316.4.4 Cauchy-Bounyakovski-Schwartz inequality 40516.4.5 Jensen inequality 40616.4.6 Lyapunov inequality 41016.4.7 Kulbac inequality 41216.4.8 Minkowski inequality 41316.5 Numerical sequences 41616.5.1 Infinite series 41616.5.2 Infinite products 42816.5.3 Teöplitz lemma 432xii CONTENTS16.5.4 Kronecker lemma 43316.5.5 Abel-Dini lemma 43416.6 Recurrent inequalities 43616.6.1 On the sumof a series estimation 43616.6.2 Linear recurrent inequalities 43716.6.3 Recurrent inequalities with root terms 44217 Complex Analysis 44717.1 Differentiation 44717.1.1 Differentiability 44717.1.2 Cauchy-Riemann conditions 44817.1.3 Theorem on a constant complex function 45117.2 Integration 45217.2.1 Paths and curves 45217.2.2 Contour integrals 45417.2.3 Cauchy’s integral law 45617.2.4 Singular points and Cauchy’s residue theorem 46017.2.5 Cauchy’s integral formula 46317.2.6 Maximummodulus principle and Schwarz’s lemma46817.2.7 Calculation of integrals and Jordan lemma 47017.3 Series expansions 47417.3.1 Taylor (power) series 47417.3.2 Laurent series 47817.3.3 Fourier series 48317.3.4 Principle of argument 48417.3.5 Rouché theorem. 48617.3.6 Fundamental algebra theorem 48817.4 Integral transformations 48917.4.1 Laplace transformation (K (t, p) = e−pt) 49017.4.2 Another transformations 49818 Topics of Functional Analysis 50718.1 Linear and normed spaces of functions 50818.1.1 Space mn of all bounded complex numbers 50818.1.2 Space lnp of all summable complex sequences 50918.1.3 Space C [a, b] of continuous functions 50918.1.4 Space Ck [a, b] of continuously differentiable functions. 509CONTENTS xiii18.1.5 Lebesgue spaces Lp [a, b] (1 ≤ p < ) 50918.1.6 Lebesgue spaces L [a, b] 51018.1.7 Sobolev spaces Slp(G) 51018.1.8 Frequency domain spaces Lm×kp , RLm×kp , Lm×kand RLm×k. 51018.1.9 Hardy spaces Hm×kp , RHm×kp , Hm×kand RHm×k51118.2 Banach spaces 51218.2.1 Basic definition 51218.2.2 Examples of incomplete metric spaces 51218.2.3 Completion ofmetric spaces 51318.3 Hilbert spaces 51518.3.1 Definition and examples 51518.3.2 Orthogonal complement 51618.3.3 Fourier series in Hilbert spaces 51818.3.4 Linear n-manifold approximation 52018.4 Linear operators and functionals in Banach spaces 52118.4.1 Operators and functionals 52118.4.2 Continuity and boundedness 52218.4.3 Compact operators 53018.4.4 Inverse operators 53218.5 Duality 53718.5.1 Dual spaces 53718.5.2 Adjoint (dual) and self-adjoint operators 54018.5.3 Riesz representation theorem for Hilbert spaces 54318.5.4 Orthogonal projection operators in Hilbert spaces54318.6 Monotonic, nonnegative andcoercive operators 54618.6.1 Basic definitions and properties 54718.6.2 Galerkin method for equations withmonotone operators 55018.6.3 Main theorems on the existence of solutions forequations withmonotone operators 55218.7 Differentiation of NonlinearOperators 55518.7.1 Fréchet derivative 55518.7.2 Gáteaux derivative 55718.7.3 Relation with "Variation Principle" 55818.8 Fixed-point Theorems 55918.8.1 Fixed-points of a nonlinear operator 559xiv CONTENTS18.8.2 Brouwer fixed-point theorem 56118.8.3 Schauder fixed-point theorem 56518.8.4 The Leray-Schauder principle and a priory estimates. 567III DIFFERENTIAL EQUATIONS ANDOPTIMIZATION 56919 Ordinary Differential Equations 57119.1 Classes ofODE 57119.2 RegularODE 57219.2.1 Theorems on existence 57219.2.2 Differential inequalities, extension anduniqueness 57919.2.3 LinearODE 59019.2.4 Index of increment for ODE solutions 59919.2.5 Riccati differential equation 60019.2.6 Linear first order partial DE 60319.3 Carathéodory’s TypeODE 60619.3.1 Main definitions 60619.3.2 Existence and uniqueness theorems 60719.3.3 Variable structure and singular perturbed ODE 61019.4 ODE withDRHS 61219.4.1 Why ODE with DRHS are important in ControlTheory 61219.4.2 ODE with DRHS and differential inclusions 61719.4.3 Slidingmode control 62320 Elements of Stability Theory 64320.1 Basic Definitions 64320.1.1 Origin as an equilibrium 64320.1.2 Positive definite functions 64420.2 Lyapunov Stability 64620.2.1 Main definitions and examples 64620.2.2 Criteria of stability: non - constructive theory 64920.2.3 Sufficient conditions of asymptotic stability: constructivetheory 658CONTENTS xv20.3 Asymptotic global stability 66320.3.1 Definition of asymptotic global stability 66320.3.2 Asymptotic global stability for stationary systems66320.3.3 Asymptotic global stability for non - stationarysystem 66620.4 Stability of Linear Systems 66920.4.1 Asymptotic and exponential stability of lineartime-varying systems 66920.4.2 Stability of linear system with periodic coefficients67220.4.3 BIBO stability of linear time-varying systems 67320.5 Absolute Stability 67620.5.1 Linear systems with nonlinear feedbacks 67620.5.2 Aizerman andKalman conjectures 67720.5.3 Analysis of absolute stability 67920.5.4 Popov’s sufficient conditions 68220.5.5 Geometric interpretation of Popov’s conditions 68420.5.6 Yakubovich-Kalman lemma 68621 Finite-Dimensional Optimization 69121.1 Some Properties of SmoothFunctions 69121.1.1 Differentiability remainder 69121.1.2 Convex functions 69621.2 UnconstrainedOptimization 70321.2.1 Extremumconditions 70321.2.2 Existence, uniqueness and stability of a minimum70521.2.3 Some numerical procedure of optimization 70821.3 ConstrainedOptimization 71621.3.1 Elements of ConvexAnalysis 71621.3.2 Optimization on convex sets 72521.3.3 Mathematical programming and Lagrange principle. 72821.3.4 Method of the subgradient projection to simplestconvex sets 73621.3.5 Arrow-Hurwicz-Uzawa method withthe regularization 739xvi CONTENTS22 Variational Calculus and Optimal Control 74922.1 Basic Lemmas of Variation Calculus 74922.1.1 Du Bois-Reymond lemma 74922.1.2 Lagrange lemma 75322.1.3 Lemma on quadratic functional 75422.2 Functionals and Their Variations 75522.3 ExtremumConditions 75622.3.1 Extremal curves 75622.3.2 Necessary conditions 75722.3.3 Sufficient conditions 75822.4 Optimization of integral functionals 76022.4.1 Curves with fixed boundary points 76022.4.2 Curves with non-fixed boundary points 77122.4.3 Curves with a non-smoothness point 77422.5 Optimal Control Problem 77522.5.1 Controlled plant, cost functionals and terminalset 77522.5.2 Feasible and admissible control 77722.5.3 Problem setting in the general Bolza form 77722.5.4 Mayer formrepresentation 77822.6 MaximumPrinciple 77922.6.1 Needle-shape variations 77922.6.2 Adjoint variables and MP formulation 78222.6.3 The regular case 78622.6.4 Hamiltonian form and constancy property 78722.6.5 Non fixed horizon optimal control problem andZero-property 78922.6.6 Joint optimal control and parametric optimizationproblem. 79222.6.7 Sufficient conditions of optimality 79422.7 Dynamic Programming 80022.7.1 Bellman´s Principle of Optimality 80122.7.2 Sufficient conditions for BP fulfilling 80222.7.3 Invariant embedding 80422.7.4 Hamilton-Jacoby-Bellman equation 80722.8 LinearQuadraticOptimal Control 81122.8.1 Non stationary linear systems and quadratic criterion22.8.2 LinearQuadratic Problem 81222.8.3 Maximum Principle for DLQ problem 81322.8.4 Sufficiency condition 81422.8.5 Riccati differential equation and feedback optimalcontrol 81522.8.6 Linear feedback control 81522.8.7 Stationary systems on the infinite horizon 81922.9 Linear-Time optimization 82722.9.1 General result 82722.9.2 Theorem on n-intervals for stationary linear systems23 H2 and H Optimization 83123.1 H2 -Optimization 83123.1.1 Kalman canonical decompositions 83123.1.2 Minimal and balanced realizations 83623.1.3 H2 normand its computing 84023.1.4 H2 optimal control problem and its solution 84423.2 H -Optimization 84823.2.1 L, H norms 84823.2.2 Laurent, Toeplitz and Hankel operator 85223.2.3 Nehari problem in RLm×k23.2.4 Model-matching (MMP) problem 87023.2.5 Some control problem converted to MMP 881أتمنى أن تستفيدوا منه وأن ينال إعجابكمرابط تنزيل كتاب Advanced Mathematical Tools for Automatic Control Engineers شارك معنا فى حملة فيد وإستفيدشارك معنا فى المسابقة الهندسية الشهريةكيفية التسجيل فى منتدى هندسة الإنتاج والتصميم الميكانيكى*****************************************************************************************   محمد محمد أحمد
مهندس فعال جدا جدا  عدد المساهمات : 655
التقييم : 697
تاريخ التسجيل : 14/11/2012
العمر : 27
الدولة : EGYPT
العمل : Student
الجامعة : Menoufia  موضوع: رد: كتاب Advanced Mathematical Tools for Automatic Control Engineers الجمعة 26 يوليو 2013, 5:09 pm جزاك الله عنا كل خير  Admin
مدير المنتدى  عدد المساهمات : 15189
التقييم : 25181
تاريخ التسجيل : 01/07/2009
العمر : 30
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية  موضوع: رد: كتاب Advanced Mathematical Tools for Automatic Control Engineers الجمعة 26 يوليو 2013, 5:12 pm @محمد محمد أحمد كتب:جزاك الله عنا كل خيرجزانا الله وإياك خيراً شارك معنا فى حملة فيد وإستفيدشارك معنا فى المسابقة الهندسية الشهريةكيفية التسجيل فى منتدى هندسة الإنتاج والتصميم الميكانيكى*****************************************************************************************   كتاب Advanced Mathematical Tools for Automatic Control Engineers صفحة 2 من اصل 1

صلاحيات هذا المنتدى:لاتستطيع الرد على المواضيع في هذا المنتدى انتقل الى: اختر منتدى||--المنتديات العامة والإسلامية|   |--منتدى الترحيب والتهانى والمواضيع العامة|   |--المنتدى الإسلامى|       |--منتدى القرآن الكريم والتفسير|       |--منتدى المواقع الإسلامية|       |--منتدى الصوتيات والفيديوهات والمقاطع الإسلامية|       |--منتدى الموضوعات الدينية|       |--منتدى شهر رمضان الكريم|       |--منتدى نصره النبى صلى الله عليه وسلم|       |--منتدى البرامج والاسطوانات الإسلامية|       |--منتدى الكتب الدينية|   |--المنتديات الهندسية|   |--منتدى الطلبات والإستفسارات|   |--منتدى المقالات والمواضيع الهندسية|   |--منتدى المواقع الهندسية والعلمية|   |--منتدى كل مايخص الفرقة الإعدادية بكليات الهندسة|   |--منتدى الكتب والمحاضرات الهندسية|   |   |--منتدى الكتب والمحاضرات الهندسية العربية|   |   |--منتدى الكتب والمحاضرات الهندسية الأجنبية|   |   |--منتدى كتب ومحاضرات الأقسام الهندسية المختلفة|   |   |--منتدى تبادل الخبرات فى الكتب|   |   |   |--منتدى الدورات والكورسات الهندسية|   |--منتدى الفيديوهات و المحاضرات المرئية و الاسطوانات التعليمية|   |--منتدى البرامج الهندسية|   |--منتدى شروحات البرامج الهندسية|   |--منتدى الأبحاث الهندسية والرسائل العلمية|   |--منتدى التجارب ونماذج الأسئلة والإمتحانات والجداول الدراسية|   |--منتدى المشاريع الهندسية|   |--منتدى دليل الدورات والمنح والبعثات الهندسية والعلميه|   |--المنتديات التعليمية المتنوعة والثقافية|   |--منتدى تعليم اللغات|   |--المنتدى التعليمى لطلاب ماقبل المرحلة الجامعية|   |   |--منتدى مرحلة رياض الأطفال|   |   |--منتدى المرحلة الإبتدائية|   |   |--منتدى المرحلة الإعدادية|   |   |--منتدى المرحلة الثانوية|   |   |   |--المنتدى الأدبى والثقافى|   |--منتدى إدارة الموارد البشرية وتطوير الذات|   |--منتدى الأسرة والمجتمع|   |--منتدى الصحة والطب|   |--منتدى التسويق الإلكترونى والربح من الإنترنت|   |--منتدى التاريخ والجغرافيا والعلوم السياسية|   |--منتدى التكنولوجيا والإبتكارت العلمية|   |--منتدى العلوم الطبيعية|   |--منتدى العلوم الإجتماعية والإنسانية|   |--منتدى الكتب العامة والثقافية والمتنوعة|   |--المنتديات الخدمية    |--منتدى الوظائف وفرص العمل    |--منتدى كل ما يخص الكمبيوتر والموبايل والانترنت وشروحاتهم    |--منتدى دليل الخدمات والمواقع الخدمية    |--منتدى الإقتراحات والشكاوى    |--منتدى المواضيع المحذوفة والمكررة