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### Optimization of functions

Course: EE 840, Fall 2009
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Word Count: 6460

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ON TOPICS OPTIMIZATION A Class Note For EE 840 Mathematical Methods in Engineering by Nurul Chowdhury Department of Electrical Engineering University of Saskatchewan EE 840 Mathematical Methods in Engineering 1. Convex Sets Convex sets are widely used in the formulation and solution of optimization problems. A convex set is a set of elements from a vector space such that all the points on the straight line...

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Air Force Academy - EE - 840
Suggested Optimization Problems1.3 2 Minimize F ( x1 , x 2 , x 3 ) = x1 x1 x 2 + x 2 9 x1 + 8 x 2 utilizing (a) Classical approach (Hessian Matrix) (b) Multivariate Grid Search (c) Univariate Search method (d) Steepest Descent Method: one variabl
Air Force Academy - EE - 840
Numerical Solutions of Differential EquationsVariables in many engineering disciplines are related by differential equations. Properties of materials, dynamic behaviour of devices and current and fluid flow can be described by differential equations
Air Force Academy - EE - 840
EE 840 Mathematical Methods in EngineeringPartial Differential EquationsFollowing are some classical partial differential equations, where u is assumed to be a function of two or more variables t (time), x and y (spatial coordinates). 2u 2u = c
Air Force Academy - EE - 201
BH Curves Jackson, &quot;Introduction to Electric Circuits, 8th Ed.&quot;, p358
Air Force Academy - EE - 458
Air Force Academy - EE - 458
Drop-InMonolithic AmplifierProduct Features Wideband, DC to 1 GHz High gain, 17.8 dB typ. at 0.1 GHz Low noise figure, 3.5 dB typ. Exact foot print substitute for MSA-0185 Low current, 17mA Cascadable, unconditionally stable Aqueous washabl
Air Force Academy - EE - 402
The Complete Smith ChartBlack Magic Design0.110.12 0.380.13 0.370.14 0.360.1450.91.21.40.08 0.4 20 12550.80.41.01110500.090.40.39 100900.15 0.3580400.1 0.3 47060.7351.60.160 3070.6
Air Force Academy - CE - 311
Name _ Student No. _ Please return this question paper with your answer bookTime for both Parts I and II 3 hoursCE 311 Continuum Mechanics Department of Civil and Geological Engineering University of Saskatchewan Sample Final ExaminationPart II
Air Force Academy - CE - 311
Utah - MATH - 1220
Calculus II Exam 2, Summer 2003, AnswersFind all the integrals. Remember that definite integrals should have numerical answers. You MUST show your work.The last integral is x2 4 C, so the answer is1b.ln x2 dx xwhich is the same answer. Chec
Utah - PROBS - 1220
Calculus II Practice Problems 8: AnswersFor each problem, determine whether or not the series converges or diverges. Give your reasoning. 1.n 1 nn3 Answer. This series converges, by comparison with 1 n2 : n 1 n32n n32.n
Air Force Academy - EE - 441
Air Force Academy - EE - 441
Utah - PROBS - 1220
Calculus II Practice Problems 4: AnswersAs we saw in example 9 (another integration by parts):2. Integratex2 lnxdx.3. Integratearccos xdx. arccosx duThis last we integrate by the substitution w x 1 x2Putting this back in (2) we obtain
Neumont - EN - 1963
Cour suprme du Canada Gardiner v. Minister of National Revenue, [1964] S.C.R. 66 Date: 1963-06-13 Lloyd W. Gardiner in his capacity as Public Trustee for the Province of Alberta and as such the Duly Appointed Administrator of the Estate of Gordon Pap
Air Force Academy - ENGR - 327
ABE 327.3 Transport Processes in Biosystems Assignment #2 Solution No.11 No. 22 No. 33 No. 4ASSUMPTIONS: (1) The skin is modeled as semi-infinite medium, initially at uniform temperature of 37oC, (2) constant skin properties.4 No. 5
Air Force Academy - ENGR - 327
ABE 327.3 Transport Processes in Biosystems Assignment #3 Solution No.1 KNOWN: Hf = 335000 J/kg kice = 2.3 W/m K Tm = 0oC = 1000 kg/m3 T = -10oC h = 20 W/m2K kw = 0.61 W/moC t = 60 daysoASSUMPTIONS: (1) neglect sensible heat, (2) Freezing takes p
Air Force Academy - EE - 800
EE800 Part 1: Fault-Tolerant Digital Systems Instructor Information: Instructor: Li Chen, Office: 2B22, Phone: 966-2507, Email: li.chen@usask.ca Tentative Course Outline: SRAM &amp; DRAM design a. Memory cell and array b. Row and column decoder c. Sense
Neumont - EN - 1958
Supreme Court of Canada McIntosh v. Minister of National Revenue, [1958] S.C.R. 119 Date: 1958-01-28 Ronald Gordon McIntosh Appellant; and The Minister of National Revenue Respondent.1957: December 2; 1958: January 28. Present: Kerwin C.J. and Locke
Neumont - EN - 1963
Supreme Court of Canada Lieberman v. The Queen, [1963] S.C.R. 643 Date: 1963-10-18 Stanley H. Lieberman Appellant; and Her Majesty The Queen, on the information of Foster Thurston, Chamberlain of the City of Saint John Respondent.1963: February 26;
Air Force Academy - EE - 332
EE 332 (Term 2, 2008-2009) Project Presentation and DemonstrationTime 3:30 3:50April 6 (Monday) Duch, Steven; Funk, Benjamin; Gress, Drew Feed Mill Control System Munchinsky, Ryan; Beaulieu, Heather Snake GameApril 8 (Wednesday) Chowdhury, Ari
Air Force Academy - EE - 332
EE 332 (Term 2, 2008-2009) Project Presentation and DemonstrationTime 3:30 3:50April 6 (Monday) Duch, Steven; Funk, Benjamin Feed Mill Control System Munchinsky, Ryan; Beaulieu, Heather Snake GameApril 8 (Wednesday) Chowdhury, Ariq; Edoho, Vic
Utah - MATH - 1210
Calculus I, Math 1210-90, Fall 2004, Palais Practice Exam 3 Solutions, Chapter 5 Integrals and their applications Show all your work on the exam for full credit. You may use graphing (or regular) calculators, but show enough work to demonstrate that
Neumont - EN - 1949
Supreme Court of Canada Grant v. The King, [1949] S.C.R. 647 Date: 1949-04-12 Walter Grant Appellant; and His Majesty The King Respondent.1949: March 23; 1949: April 12. Present: Rinfret C.J. and Kerwin, Taschereau, Rand and Kellock JJ. ON APPEAL FR
Air Force Academy - EE - 395
EE 395- Electrical Engineering Design T2: Jan. Apr., 2009 Instructors: D. Teng, Office: 2B28, Phone: 966-2889, email: daniel.teng@usask.ca A. Dinh, Office: 3B14, Phone: 966-5344, email: anh.dinh@engr.usask.ca Class website: http:/www.engr.usas
Air Force Academy - EE - 395
Design MethodologiesEE395UofSLecture 03 - 1Needs assessmentEE395UofSLecture 03 - 21Requirements AnalysisEE395UofSLecture 03 - 3PREPARING RS Translating Needs to Specifications Specifying the Interfaces Handling Excessive
Air Force Academy - EE - 395
Lecture 5 Managing the Design ProcessReasons to Learn Project Management Professional Engineer Successful career Good mark for this classEE395UofSLecture 05 - 2Is Engineering Design a Project? Design: How will it work? What func
Air Force Academy - EE - 395
EE395 Electrical Engineering Design Lecture 7Detailed DesignEE395Electrical Engineering DesignOutline Detailed design and design process Verification, validation and test Creative design Industrial property Cost-efficient design2Lectu
Neumont - EN - 1951
Supreme Court of Canada Watterworth v. The King, [1952] 1 S.C.R. 122 Date: 1951-10-23 Wilfred Watterworth Appellant; and His Majesty the King Respondent.1895: October 23. PRESENT:-Kerwin, Rand, Kellock, Estey, Locke, Cartwright and Fauteux JJ. ON AP
Neumont - EN - 1950
Supreme Court of Canada Barrick v. Clark, [1951] S.C.R. 177 Date: 1950-10-03 Ralph Newcombe Barrick and Theresa May Florella Barrick, Executors of the Estate of Eli James Barrick, Deceased, and William Hohmann (Defendants) Appellants; and Frank J. Cl
Air Force Academy - ENGR - 822
Following is using information given in Rawls et al., Loam property 5.11 water-retention curve 5.16 K unsat curve, Fig 5.3.2 Calculation of infiltration flux At t = 10 seconds, infiltration of ponded water into a dry soil n 0.4 m3/m3, average porosit
Air Force Academy - EE - 845
Air Force Academy - EE - 845
Air Force Academy - EE - 845
Air Force Academy - EE - 845
Air Force Academy - EE - 845
Air Force Academy - EE - 845
Air Force Academy - CHE - 461
Welcome!Introduction to Biochemical Engineering(CHE 461.3/861.3) Instructor Dr. C. Niu Chemical EngineeringResearch Area Biosorption: Use biomaterials to adsorb inorganic (metals) or organic compounds from liquid phase Biomaterials: microorgani
Air Force Academy - CHE - 461
Classification of Cellular Organism (according to cell structure)Cellular OrganismHave nuclear membrane and membrane bound organells? Yes Nonot free-living organismsProtists: Fungi, Algae, protozoa Plant: seed plants, mosses Animal: vertabrates
Air Force Academy - CHE - 461
Classification of Cellular Organism (according to cell structure)Cellular OrganismHave nuclear membrane and membrane bound organells? Yes Nonot free-living organismsEucaryotesProcaryotes: bacteriaVirusProtists: Fungi, Algae, protozoa Plan
Air Force Academy - CHE - 461
EucaryotesEucaryotes true nucleus, and organelles. andEucaryotes include fungi (yeast and molds), algae, protozoa, and animal and plant cells. Eucaryotic cells are than procaryotic cells in diameter. Yeast is about 5 -10 m, animal 10 m and plant 2
Air Force Academy - CHE - 461
EucaryotesEucaryotes have nuclear membrane and true nucleus, and membrane-bound organelles.Eucaryotes include fungi (yeast and molds), algae, protozoa, and animal and plant cells. Eucaryotic cells are five to ten times larger than procaryotic cells
Air Force Academy - CHE - 461
Eucaryotes- Fungi: yeast and mold - AlgaeEucaryotesFungi Fungi are which need to take nutrients from the environment for living. They are larger than bacteria.FungiTwo major groups are yeast and mold.YeastYeasts are very important economi
Air Force Academy - CHE - 461
Eucaryotes-FungiMoldsMolds are structure. and have a mycelialMycelium is highly branched system of tubes that contains mobile cytoplasm with many nuclei. Hypha is long, thin filaments on the mycelium.Mold Molds are very important economically:
Air Force Academy - CHE - 461
Analysis of Biological SystemDespite of all their complexity, an understanding of biological system can be simplified by analyzing the system at several different levels: the cell level: microbiology, cell biology; the molecular level: biochemistr
Air Force Academy - CHE - 461
Analysis of Biological SystemDespite of all their complexity, an understanding of biological system can be simplified by analyzing the system at several different levels: Cell level: microbiology, cell biology; Molecular level: biochemistry, molec
Air Force Academy - CHE - 461
CarbohydratesCarbohydrates are synthesized from carbon dioxide and water through photosynthesis, (CH2O)n, or Cn(H2O)n-1. Carbohydrates play critical roles as compounds in cells. Carbohydrates are classified by the number of sugar units andCarboh
Air Force Academy - CHE - 461
CarbohydratesCarbohydrates are synthesized from carbon dioxide and water through photosynthesis, (CH2O)n, or Cn(H2O)n-1. Carbohydrates play critical roles as storage and structural compounds in cells. Carbohydrates are classified by the number of
Air Force Academy - CHE - 461
LipidsLipids are energy storage in cell membrane and regulators of cell metabolism. Lipids are biological compounds that are insoluble in water, but soluble in nonpolar solvent such as benze, chloroform and ether. They are present in the nonaqueou
Air Force Academy - CHE - 461
LipidsLipids are energy storage in cell membrane and regulators of cell metabolism. Lipids are hydrophobic biological compounds that are insoluble in water, but soluble in nonpolar solvent such as benze, chloroform and ether. They are present in t
Air Force Academy - CHE - 461
Nucleic Acids - RNA and DNANucleic acid is a complex, high-molecular-weight biochemical macromolecule composed of nucleotide chains that convey genetic information. The most common nucleic acids are deoxyribonucleic acid (DNA) and ribonucleic acid (
Air Force Academy - CHE - 461
Cell NutrientsNutrients required by cells can be classified in two categories: 10-4 M. C, N, O, H, S, P, Mg 2+, and K+. are needed in concentrations larger than-10-4 M. Mo, Zn, Cu, Mn, Ca, Na, vitamins, growth hormones and metabolic precursors.
Air Force Academy - CHE - 461
Cell NutrientsNutrients required by cells can be classified in two categories: - Macronutrients are needed in concentrations larger than 10-4 M. C, N, O, H, S, P, Mg 2+, and K+. - Micronutrients are needed in concentrations less than 10-4 M. Mo, Zn,
Air Force Academy - CHE - 461
Outline of EnzymesIntroduction - Features of enzyme catalysis Enzyme kinetics - Models for enzyme kinetics - Effect of pH and Temperature Immobilized Enzyme System - Method of immobilization - Diffusional limitations Medical and Industrial Utilizati
Air Force Academy - CHE - 461
Outline of EnzymesIntroduction - Features of enzyme catalysis Enzyme kinetics - Models for enzyme kinetics - Effect of pH and Temperature Immobilized Enzyme System - Method of immobilization - Diffusional limitations Medical and Industrial Utilizati
Air Force Academy - CHE - 461
Enzyme KineticsEnzyme Kinetics: Study the rate of enzyme catalyzed reactions. - Models for enzyme kinetics - Michaelis-Menten kinetics - Inhibition kinetics - Effect of pH and TemperatureEnzyme KineticsMichaelis-Menten kinetics or saturation kine
Air Force Academy - CHE - 461
Substrate Concernation versus Time25 Substrate Concentration (M) 20 15 10 5 005101520253035Time (min)Substrate Concernation versus Time25 Substrate Concentration (M) 20 15 10 5 005101520253035Time (min)Use in
Air Force Academy - CHE - 461
Glucoamylase Activity DeterminationEx. One unit of activity of glucoamylase is defined as the amount of enzyme which produces 1 mol of glucose per min in a 4 % solution of Lintner starch at pH4.5 and at 60oC. To measure the amount of glucoamylase in
Air Force Academy - CHE - 461
Example: During a test kinetics of enzyme-catalyzed reaction, the following data E0 (g/l)T(oC) I (mmol/ml) V (mmol/mi-min) S(mmol/ml) 0.92 30 0 0.1 1.64 0.92 30 0 0.02 0.9 0.92 30 0 0.01 0.58 0.92 30 0.6 0.1 1.33 0.92 30 0.6 0.03 0.8 0.92 30 0.6 0.02
Air Force Academy - CHE - 461
Factors Affecting Enzyme Kinetics pH effects - on enzymes - enzymes have ionic groups on their active sites. - Variation of pH changes the ionic form of the active sites. - pH changes the three-Dimensional structure of enzymes. - on substrate - some
Air Force Academy - CHE - 461
Immobilized Enzyme SystemsEnzyme Immobilization: To restrict enzyme mobility in a fixed space.Immobilized Enzyme SystemsEnzyme Immobilization:- Easy separation from reaction mixture, providing the ability to control reaction times and minimize t