Solving Linear system of equations Mathematics.pdf.pptx
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This document summarizes a presentation on solving linear systems of equations using Gaussian elimination. It includes the following: - An example linear system involving voltages (V1, V2, V3) and currents (I1-I6) in an electrical circuit with resistors and capacitors. - The steps to set up the linear system as a matrix equation involving the unknown voltages, including applying Kirchhoff's and Ohm's laws. - A flowchart showing the Gaussian elimination process: forming the augmented matrix, checking for zero diagonal/determinant, performing row operations if possible, and back substitution to solve for the unknowns. - The determinant calculation for the 3x3 matrix in this
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Industrial Valves, Instruments Products Profilezebcoeng
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Were excited to share our product profile, showcasing our expertise in Industrial Valves, Instrumentation, and Hydraulic & Pneumatic Solutions.
We also supply API-approved valves from globally trusted brands, ensuring top-notch quality and internationally certified solutions. Lets explore valuable business opportunities together!
We specialize in:
Industrial Valves (Gate, Globe, Ball, Butterfly, Check)
Instrumentation (Pressure Gauges, Transmitters, Flow Meters)
Pneumatic Products (Cylinders, Solenoid Valves, Fittings)
As authorized partners of trusted global brands, we deliver high-quality solutions tailored to meet your industrial needs with seamless support.Syntax Directed Definitions Synthesized Attributes and Inherited Attributes
Syntax Directed Definitions Synthesized Attributes and Inherited AttributesGunjalSanjay
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Syntax Directed Definitions
Best KNow Hydrogen Fuel Production in the World The cost in USD kwh for H2
Best KNow Hydrogen Fuel Production in the World The cost in USD kwh for H2Daniel Donatelli
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The cost in USD/kwh for H2
Daniel Donatelli
Secure Supplies Group
Index
Introduction - Page 3
The Need for Hydrogen Fueling - Page 5
Pure H2 Fueling Technology - Page 7
Blend Gas Fueling: A Transition Strategy - Page 10
Performance Metrics: H2 vs. Fossil Fuels - Page 12
Cost Analysis and Economic Viability - Page 15
Innovations Driving Leadership - Page 18
Laminar Flame Speed Adjustment
Heat Management Systems
The Donatelli Cycle
Non-Carnot Cycle Applications
Case Studies and Real-World Applications - Page 22
Conclusion: Secure Supplies Leadership in Hydrogen Fueling - Page 27
Wireless-Charger presentation for seminar .pdf
Wireless-Charger presentation for seminar .pdfAbhinandanMishra30
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Wireless technology used in charger
Integration of Additive Manufacturing (AM) with IoT : A Smart Manufacturing A...
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Combining 3D printing with Internet of Things (IoT) enables the creation of smart, connected, and customizable objects that can monitor, control, and optimize their performance, potentially revolutionizing various industries. oT-enabled 3D printers can use sensors to monitor the quality of prints during the printing process. If any defects or deviations from the desired specifications are detected, the printer can adjust its parameters in real time to ensure that the final product meets the required standards.Unit II: Design of Static Equipment Foundations
Unit II: Design of Static Equipment FoundationsSanjivani College of Engineering, Kopargaon
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Design of Static Equipment, that is vertical vessels foundation.Water Industry Process Automation & Control Monthly - March 2025.pdf
Water Industry Process Automation & Control Monthly - March 2025.pdfWater Industry Process Automation & Control
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US Patented ReGenX Generator, ReGen-X Quatum Motor EV Regenerative Accelerati...
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US Patented ReGenX Generator, ReGen-X Quatum Motor EV Regenerative Accelerati...
US Patented ReGenX Generator, ReGen-X Quatum Motor EV Regenerative Accelerati...Thane Heins NOBEL PRIZE WINNING ENERGY RESEARCHER
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Solving Linear system of equations Mathematics.pdf.pptx
- 1. Masters in Electrical & Microsystems Engineering Advanced Engineering Mathematics Linear Systems Electric AC Circuit Presented by: Nima Aminfar (3362365) Omer Rahama (3359754)
- 3. By applying Kirchhoff `s current law for points 1,2,3 腫4 腫1 腫2 腫3 腫5 腫6 腫1 腫2 腫1 腫1腫4= 0 腫2 + 腫1 腫5 腫2 = 0 腫3 + 腫2腫6= 0
- 4. 腫1 = + 1 1 腫2 = + 2 2 腫3 = + 3 3 腫4 = 1 0 4 腫5 = 2 0 5 腫6 = 3 0 6 By applying Ohm's law: V=X*I , Y= 1 I=V*Y 腫1 = (12) 1 腫2 = (23) 2
- 5. + 1 1 - (12) 1- 1 0 4 = 0 + 2 2 + (12) 1- 2 0 5 (23) 2 = 0 + 3 3 + (23) 2 3 0 6 = 0 1 = 1 ゐ 2 = 2 ゐ 3 = 3 ゐ + = + ゐ And we know that :
- 6. 1 = 1 1 = 1 1 = 1 103 2 = 1 2 = 1 2 = 1 2103 3 = 1 3 = 1 3 = 1 103 4= 1 4 = 1 4 = 1 2103 5 = 1 5 = 1 5 = 1 103 6 = 1 6 = 1 6 = 1 2103 1 = 1 1 = ゐ1 = 1000 106 = 103 2 = 1 2 = ゐ2 = 1000 0.5 106= 0.5 103 Admittance Calculation:
- 7. Three linear equation would be: 瑞 瑞 瑞 are unknown (1.5 + )*1 + (-i)*2 + (0)*3= 3 ()*1 + (1.5 + 1.5 )*2 + (- 0.5 )*3= 1.5 0 1 + ( 0.5)2 + (1.5 + 0.5)3= 3
- 8. So the matrix will be: = * (. + ) X1 = 1.69369 0.162162 i - 瑞 0 瑞 (. + . ) . 0 -0. (. + . ) 3 1.5 3 瑞 X2= 1.45045 + (0.297297) i X3= 1.85586 (0.135135) i
- 9. Gaussian elimination Method: Gauss Elimination Method is a procedure for solving systems of linear equation. It is also known as Row Reduction Technique. In this method, the problem of systems of linear equation having n unknown variables, matrix having rows n and columns n+1 is formed. This matrix is also known as Augmented Matrix. After forming n x n+1 matrix, matrix is transformed to upper triangular matrix by row operations. Finally result is obtained by Back Substitution. In this project, we are dealing with 3 unknown variables . So the Augmented Matrix would be 3*4.
- 10. Definition Of Complex Numbers Enter The Value Of The Matrix Check 1st diagonal is zero Gauss Elimination Can Not Performed Check The Determina nt is Zero Gauss Elimination Can Not Performed Start End End Proceed To Enter Vector b Print The Values Of V1, V2, V3 and Phases in degree Print The Values Of 1, 2, 3 End Flowchart Of The Program: Yes Yes No No Start The Gauss Elimination Process
- 11. Determinant calculation for 3*3 Matrix: