MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 4 pptx
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 4 pptx
... equations in physics and engineering can be solved by the method of separation of variables. This method helps us to reduce a second-order partial differential equation into a set of ordinary ... following integral definitions: (6 .48 ) and 1 2 (1 - t2)n-6 cosztdt, (n > ). (6 .49 ) Jn(IL.1 = 6 .4 RECURSION RELATIONS OF THE BESSEL FUNCTIONS Using the series definitions ... second kind. Note that N,(z) and Jm(z) are linearly independent even for the integer values of m. Hence it is common practice to take N,(z) and Jm(z) as the two linearly independent...
- 40
- 248
- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 16 pptx
... by determining the u and the solutions in Equation (19.15) as sin bx and sin ko(x - L), respectively. We can now obtain a closed expression for G(z, d) as sin kox sin ICg(x’ ... dk'g(k')eikfZ VG -" and Their inverse Fourier transforms are and Using these in Equation (19.116) we get which gives us Substituting this in Equation (19.118) we obtain Writing g(k') ... Xiyi(z), and integrating over x in the interval [a, b] we obtain two equations and If the kernel satisfies the relation K*(z,t) = K(t,z), Equation (18.99) becomes Subtracting Equations...
- 40
- 205
- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 1 potx
... 14. 7 Applications of Diflerintegrals in Science and Engineering 42 4 14. 7.2 Fractional Fokker-Planck Equations 42 7 Problems 42 9 14. 7.1 Continuous Time Random Walk (CTRW) 42 4 15 INFINITE ... 44 0 15.5 Useful Inequalities About Series 44 2 15.6 Series of Functions 44 2 15.6.1 Uniform Convergence 44 3 15.6.2 Weierstrass M-Test 44 3 15.6.3 Abel Test 44 4 15.7 Taylor Series 44 5 ... I Maclaurin Theorem 44 6 15.7.2 Binomial Theorem 44 7 Variables 44 s 15.8 Power Series 44 9 15.8.1 Convergence of Power Series 45 0 15.8.2 Continuity 45 0 Series 45 0 15.8 .4 Uniqueness...
- 40
- 337
- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 2 pdf
... part of the learning process. In a vast area like mathematical methods in science and engineering, there is always room for new approaches, new applications, and new topics. In fact, the number ... write x = fl in the generating function Equation (2.65) we find (2.85) Expanding the left-hand side by using the binomial formula and comparing equal powers oft, we obtain 9 (1) = 1 ... and for meticulously reading Chapters 1 and 9 with 14 and 20. I also thank Prof. N. K. Pak for many interesting and stimulating discussions, encouragement, and critical reading...
- 40
- 310
- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 3 docx
... as (4. 53) and defining a new parameter (4. 54) 50 - = t, 2 and using the generating function [Eq. (4. 25)], we obtain (4. 55) We now use the orthogonality relation [Eq. (4. 46)] ... (z) , (n 2 m). (4. 41) J-00 Using the Rodriguez formula, we write Equation (4. 41) as After n-fold integration by parts and since n > m, we obtain (4. 43) Since the z dependence ... of the integral in Equation (3.38) can be obtained by expanding in powers of t and s and then by comparing the equal powers of tnsm with the left-hand side of Equation (3 .42 ). If...
- 40
- 479
- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 5 ppsx
... exists a minimum value, mmin, thus determining X as X = mmin (9. 143 ) To find mmin we equate the two expressions [Eqs. (9. 141 ) and (9. 143 )] for X to obtain (9. 144 ) mmin = -1. ... Substituting this into Equation (9.83) and integrating gives us ko(z) = cacota(z +p) + . d sin+ + p) ’ (9.89) where p and d are integration constants. With these Ico and Icl ... -1. (9. 146 ) Since m changes by integer amounts, we could write hin = mmax - integer -1 = 1 - integer 21 = integer. (9. 147 ) This equation says that 1 could only take integer...
- 40
- 237
- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 6 pps
... 1 0 - sin $ cosCp sin4cos$ cosdsin+ -sin4 cos~cos$ (10.93) Reversing the order we get cos $ (10. 94) sin $ sin Cp - sin $ cos Cp R2R1 = 0 cos Cp sin 4 [ sin $ - cos ... choosing three mutually orthogonal straight lines. A point is defined by giving its coordinates, (q,z2,q), or by using the position vector 163 188 COORDINATES AND TENSORS Hence aa and ... axn and Adding the first two equations and subtracting the last one from the result and after some rearrangement of indices we obtain (10.197) I0 COORDINATES and TENSORS Starting with...
- 40
- 229
- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 7 pdf
... be expressed in terms of the poten- tials -A' and 4 as In the Lorentz gauge 2 and 4 satisfy and (10.373) (10.3 74) (10.375) (10.376) (10.377) respectively. Defining a four-potential ... transformation. It gives i3, as a linear Ah' combination of Gar. Using we obtain (10. 340 ) (10. 341 ) (10. 342 ) 222 COORDINATES AND TENSORS and 10.29 Show that the field-strength ... +ae d (TaB) r2sinOaW +a (WE)] After simplifying, the Laplacian is obtained as r2sin6 dr 34 r2sin28 a4 ' (10.239) Here we have obtained a well-known formula in a rather straightfor-...
- 40
- 270
- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 8 pps
... (Q 74) Km(Q, 4) = 4P fimmf and the completeness relation (1 1. 240 ) ( 1 1. 24 1) c c Y,L(Q’ ,4 )Km(B ,4) = G(cosQ-cosQ’)6 (4- 4’), I=O m=-I (11. 242 ) where dQ = sin Qdsdq5. In the ... 256 CONTINUOUS GROUPS AND REPRESENTATIONS and (11. 244 ) aa Glrn(e ,4) = o(- -,Q ,4) Krn(Q ,4) , a6 ' a4 where O($, &, 8 ,4) is some differential operator. For &,(6 ,4) we ... find the inverse matrices we invert Inverse of the d;,,(p) Matrices Km(Q’, 4 ) = R(a, P, Y)Km(Q, 4) (1 1.282) to write Km(Q 94) = R-l(a,p,~)Krn(Q’, 4 ) (11.283) ( 1 1.2 84) ...
- 40
- 258
- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 9 pps
... (11 .44 1) (11 .44 2) (11 .44 3) (11 .44 4) 12 COMPLEX VARIABLES and FUNCTIONS Even though the complex numbers do not exist directly in nature, they are very useful in physics and engineering applications: ... dimensions. 2. The method of analytic continuation is very useful in finding solutions of differential equations and evaluating some definite integrals. 3. Infinite series, infinite products, ... of the points A, B, C, D, F, G, and H in the z-plane as they approach the real axis and the corresponding points in the w-plane (Fig. 12.10): 2 84 CONTINUOUS GROUPS AND REPRESENTATIONS...
- 40
- 333
- 0
Từ khóa: Báo cáo quy trình mua hàng CT CP Công Nghệ NPVchuyên đề điện xoay chiều theo dạngNghiên cứu sự hình thành lớp bảo vệ và khả năng chống ăn mòn của thép bền thời tiết trong điều kiện khí hậu nhiệt đới việt namNghiên cứu tổ hợp chất chỉ điểm sinh học vWF, VCAM 1, MCP 1, d dimer trong chẩn đoán và tiên lượng nhồi máu não cấpđề thi thử THPTQG 2019 toán THPT chuyên thái bình lần 2 có lời giảiĐỒ ÁN NGHIÊN CỨU CÔNG NGHỆ KẾT NỐI VÔ TUYẾN CỰ LY XA, CÔNG SUẤT THẤP LPWANTrả hồ sơ điều tra bổ sung đối với các tội xâm phạm sở hữu có tính chất chiếm đoạt theo pháp luật Tố tụng hình sự Việt Nam từ thực tiễn thành phố Hồ Chí Minh (Luận văn thạc sĩ)Phát hiện xâm nhập dựa trên thuật toán k meansNghiên cứu, xây dựng phần mềm smartscan và ứng dụng trong bảo vệ mạng máy tính chuyên dùngNghiên cứu về mô hình thống kê học sâu và ứng dụng trong nhận dạng chữ viết tay hạn chếĐịnh tội danh từ thực tiễn huyện Cần Giuộc, tỉnh Long An (Luận văn thạc sĩ)Thiết kế và chế tạo mô hình biến tần (inverter) cho máy điều hòa không khíChuong 2 nhận dạng rui roQuản lý nợ xấu tại Agribank chi nhánh huyện Phù Yên, tỉnh Sơn La (Luận văn thạc sĩ)chuong 1 tong quan quan tri rui roGiáo án Sinh học 11 bài 14: Thực hành phát hiện hô hấp ở thực vậtGiáo án Sinh học 11 bài 14: Thực hành phát hiện hô hấp ở thực vậtBÀI HOÀN CHỈNH TỔNG QUAN VỀ MẠNG XÃ HỘIMÔN TRUYỀN THÔNG MARKETING TÍCH HỢPTÁI CHẾ NHỰA VÀ QUẢN LÝ CHẤT THẢI Ở HOA KỲ