## Calculus& Analytical Geometry

Q1: Find the derivative of the following functions using the rules:
a) ????(????) = √2???? + 1
b) ???? =
????
2????+1
Q2: Find the critical point.
• ????(????) = ????
2 + 2???? + 1
10 M
2
Q3: Use the mean value theorem to find c:
a) ????(????) = 3 + √ ???? ???????? [0 , 4]
Q4: find the antiderivative of the following functions:
a) ????(????) = 4???? − 3
b) ????(????) = 8 ????
3 + 12
Q5: Evaluate the following integrals by using the given
substitutions:
a) ∫ ????
3
(????
4 − 1)
2 ????????, ???? = ????
4 − 1
3

## thermodynamic 2 in chemical engineering ## biology

1. Schmitz (1998) studied indirect interactions in a 3-level system: predator (Spider), herbivore (Grasshopper), and resources (Grass and Herbs). This plot shows Herb abundance with resources alone (1-level), resources and herbivores (2- level), and all three levels (Risk = spiders can’t eat, Predation =spiders eat). Based on these data, what how would you describe the impact of Spiders on Herbs here?
2. TMII and DMII
3. TMII but almost no DMII
4. DMII but almost no TMII
5. Neither TMII nor DMII

1. Sale (1979) did a removal experiment with territorial damselfish on coral reefs. They removed individuals of three species and asked whether the individual taking over that spot would be the same species. The circular arrows represent the same species returning, while the others represent a different species colonizing a spot. What result would be most consistent with the predictions from niche theory?
2. P. wardi replaces itself and takes over others’ sites.
3. Each species replaces itself the great majority of the time.
4. Each species takes over for others often, colonists are a more-or-less random “lottery”.

1. MacNeil et al. (2005) sampled stable isotopes in sharks to ask whether they preyed on bluefish (a large-bodied, high-trophic level species) that migrate through the area in spring. Liver tissue “turns over” quickly, so its isotopic signature reflects the animal’s recent diet more strongly than other tissues like cartilage. Which interpretation of these data is most consistent with your understanding of stable isotopes?

A..Makos feed on higher trophic level food all year long.

1. Makos prey on the spring bluefish much more than blue sharks and threshers do.
2. All three species eat lots of bluefish in the spring.

1. Which of the following would be an example of a trophic cascade?
2. Praying mantises consume ladybugs, thereby increasing the population density of aphids.
3. Mantises consume invasive Japanese ladybugs, thereby increasing the diversity of native ladybugs.
4. Beetles drill into trees, creating habitat under the bark for leafhoppers, aphids, and other invertebrates.

1. You collect two samples of invertebrates from two pots. Which diversity measure would indicate that Pot A had greater diversity than Pot B? Note that both A and B have the same proportions of the same taxa.

 Taxon Pot A Pot B Worm 20 200 Fly 10 100 Roach 5 50 Toad 2 20 Ant 1 10 Mpede 1 10 Cpede 1 10
1. Shannon Index (H’) B. Probability of an Interspecific Encounter (PIE) C. Chao’s Estimator

1. Based on this plot from Chase (2003), what would be the β richness for a really isolated pond (neighbor distance = 1000m)? Remember that β richness = γ/α.

1. β = 1 B. β = 2.5                    C. β = 12                     D. β = 27

1. Which of these ponds would Chase (2003) say you’d be most likely to find a

1. Separation distance <100m
2. Separation distance 300- 600m
3. Separation distance >800m

1. The Theory of Island Biogeography holds that large islands should have more species. Which of these plausible explanations is the one MacArthur and Wilson proposed?
2. Large islands can host larger populations, which reduces extinction rates.
3. Large islands are big targets, so they have greater immigration rates.
4. Large islands have greater species turnover, so more species are there.

1. Based on the IUCN Red List, the primary force that has caused animals to become threatened or endangered is

1. Habitat loss
2. Invasive species
3. Climate change

1. Most of the time, a non-native species introduced to a new place never becomes common in the new place. How would Elton explain that failure?
2. Native species lack predators to limit their populations.
3. Native species have better adaptations for that local environment.
4. Native species represent more of the species pool, so they’ll “get lucky” in establishing themselves.

1. Atlantic cod were top predators in North Atlantic Ocean food webs. Their populations crashed in the 1990’s, and the abundance of phytoplankton (their food’s food’s food) has increased dramatically. This is an example of
2. Keystone predation
3. Ecosystem engineering

1. Herring worms are long-lived parasites of orcas. Based on what you know about trophic relations and stable isotopes, what would you expect to be true of herring worm tissue?
2. Ratio of δ15N to be about equal to that of orcas.
3. Higher ratio of δ15N than orcas.
4. Higher ratio of δ15N than free-living worms, but lower than orcas.

1. The simple web below goes from a top predator (A) to intermediate consumers (B, C, D) to phytoplankton (E and F). Suppose a disease wiped out species B. Which result would support top-down control of populations in this food web?
2. Populations of Species A decrease.
3. Populations of Species C increase.
4. Populations of Species D increase.

1. Suppose you had data for 20 open and 50 covered samples of soil invertebrates. Based on the richness observed in the samples collected, which type of habitat do you think has greater diversity?
2. open samples
3. covered samples
4. they have equal diversity
5. One important difference between the conservation of terrestrial and marine animals is that
6. Marine animals tend to disperse over far greater distances.
7. Marine animals have less complex life cycles.
8. Marine animals experience greater temperature stress due to climate change.

Short answers (6 pts unless noted otherwise)

1. The Oostvaardersplassen is a natural park in the Netherlands that aims to “re-wild” the wetland and grassland ecosystem near Amsterdam. What is the biggest difference between the current ecosystem and the one the planners were trying to re-create (eg, the area about 5,000 years ago)? What would you recommend they do to make the current system more closely match the “natural” state?

1. A new species of crayfish, which has European origin, appears in a pond in a nature preserve in VA. The plot shows the rank-abundance for taxa before the crayfish colonized the pond (open red) and after (filled blue).

(a) How has the crayfish altered the richness and evenness of the pond community?

1. Rangers in the Everglades cruise roads at night to survey mammal abundance. Their observations found that most mammals were far more common before pythons were present (green filled) than after they had established (red open).

Give two effects pythons could have on mammals to account for the decline in observations. Note that direct predation by pythons will not fit for either effect.

 Effect type Description Trait-mediated direct Density-mediated indirect

1. Potluck. Write a good question from this part of the course that could be worth six points. Note that good questions involve some analysis, not just ask respondents to report facts. “What is β diversity?” wouldn’t qualify, but “How would Chase (2003) expect β diversity to change in a network of ponds if you started fertilizing them regularly?” would.

1. How to manage wild horses in western North America is a controversial topic. Given what we’ve read about them, make an argument for why we should or shouldn’t consider them to be a harmful invasive species here.

1. (3 pts) What advice would you give to students who were about to take this course? What should they do to be successful in this class? With your permission, I’ll attach some of your advice to next fall’s syllabus.

Equations galore!

)

Good luck!

Is this and multiple stable equilibria the same thing?

## Engineering: solar energy

This online test contains 4 questions, each worth 25 marks.

Attempt ALL FOUR questions.

 Q1. a.      Calculate the sun altitude and azimuth angles at 2 pm on 20th May in Aberdeen         (latitude 57.1o north). Then determine the solar collector angles (both tilt and azimuth), assuming the collector uses an ideal tracking system. b.      Calculate the daytime hours for that day. Hint: the altitude angle is zero at sunrise and sunset times, and the daytime is the difference between these two times. c.       Calculate the global solar radiation (sum of direct and diffuse solar radiations) at that time (2 pm). d.      Now assume that the solar irradiance variation is approximately given by I = 900 × cos(15o×(local solar hour-12)) W/m2 for a specific day, and the sunrise and sunset times are respectively 6 am and 6 pm. Calculate the absorbed solar irradiation (energy) for that day and the peak sun hour. [8 marks]     [6 marks]   [6 marks]   [5 marks] Total Question 1 [25 marks] Q2. a.       In an ideal buck DC/DC converter, the input and output voltages are respectively 30 V and 15 V, the output current is 5 A, the switching frequency is 50 kHz, the output inductance is 0.5 mH and the capacitance is 100 μF. Determine the converter operating mode and calculate the peak-to-peak output voltage ripple.   b.      Assume that a PV module with below IV characteristics is directly connected to a load with resistance R=3 ohm. Determine the approximated power delivered to the load, and its voltage and current. [6 marks]       [6 marks]

[6 marks]

1. Now assume a buck DC/DC converter (operating in CCM) is placed between the PV module and load R, and P&O MPPT algorithm is  implemented to keep the output of the PV module at MPP.

Calculate the power delivered to the load, and its voltage and current.

1. The PV module is composed of 72 cells in series, and each cell has a [3 marks] parallel resistance of 4.8 ohm. Ignore the series resistance. If only            [4 marks] the top PV cell is shaded and the module current is the same Impp, calculate the module MPP voltage and power for two cases;
1. Without bypass diode,
2. With a bypass diode across each cell with on-state voltage of

0.6 V.

Total Question 2                                                                                                                                         [25 marks]

Q3.      It is required to design a stand-alone PV system for a house in a remote    location, where the annual insolation is 1800 kWh/m2 and the energy

consumption is given in Table Q3a. The PV module data (under STC) and

battery specifications are given in Table Q3b. The PV system nominal DC voltage is 48 V. Assume the irradiance at earth in a sunny day is 1000

W/m2.

Table Q3a.

 DC devices Power (W) Hours AC devices Power (W) Hours Air conditioner 1500 8 Fridge/  Freezer 100 24 Lamps 200 5 TV 100 3 Washing machine 1000 1 Microwave 800 0.5

Table Q3b.

 PV module Battery module Voc 59 V Nominal voltage 48 V Isc 5.8 A Capacity 8.8 kWh Vmp 51.5 V Type Li-ion Imp 4.86 A efficiency 92% Temperature coefficient of Pmax -0.4 %/oK depth of discharge (DoD) 88% Temperature coefficient of Voc -0.3 %/oK Temperature coefficient of Isc 0.04 %/oK

1. Calculate the total electricity required (in Wh per day) and the [8 marks] module arrangement for the solar array. Assume the inverter efficiency is 97% and other losses (excluding inverter loss) is 9%.
2. According to the battery specification given in Table Q3b, [5 marks] calculate the required battery capacity and number of battery modules if reserve time of 3 days is required.
3. Assume that the PV system overall cost is £10,000, the retail energy [6 marks] price is £0.18/kWh and it is constant over time (no inflation). Also, assume the Feed in Tariff (FiT) payment is £0.03/kwh with an extra export tariff of £0.04/kwh for 50% of the generation. Calculate the  pay-back time for this PV system with and without FiT.
4. The PV cells temperature may increase to much higher degrees in [6 marks] summer. Calculate the power generated by the PV array assuming the PV cell average temperature is 45 o Comment if the number of PV modules should be changed at this temperature.

Total Question 3                                                                                                                                         [25 marks]

Q4.      You need to design a 250 kW PV plant with the inverter and PV modules  data given below (under STC) for a location with average sunny hours of

4.5 hours/day. Assume the irradiance at earth in a sunny day is 1000

W/m2, and the system other losses (excluding inverter) is 8%.

Table Q4.a – Inverter data                               Table Q4.b – PV module data

 Inverter AC power output 300 kVA Maximum DC voltage 1000 V MPP tracking 250 V – 750 V Maximum DC current 600 A Efficiency 98 %

 PV module Output Power 415 W VOC 54.1 V ISC 9.9 A Vmpp 45 V Impp 9.22 A Efficiency 20%

1. Calculate the area of each module (in m2).
2. Determine the PV array arrangement and calculate the annual

energy generation.    [2 marks] c. The PV modules degrade 2% for year 1 and then 0.6% for years        [8 marks] 2-25. Calculate the Annual generated energy for year 20. Assume          the degradation happens at the end of each year.   [4 marks]

1. i) Repeat the design and determine the PV array arrangement if  the inverter maximum DC current is 500 A.
2. ii) Determine the lowest limit of the “maximum DC current” of [6 marks] the inverter that makes it inappropriate for this design. Consider  a safety margin of 10% for maximum DC voltage/current.         [5 marks]

Total Question 4                                                                                                                                         [25 marks]

Total

## ECE 2020 Fall 2022 HW10

1.) Find the Laplace transform of the following functions:
a. ��(�) = sin (4�)�(�)
b. ��(�) = ��−2�
�(�)
c. ��(�) = (� − 1)�(� − 1)
d. ��(�) = (� − 1)�(�)
2.) Use partial fraction expansion and the Laplace Transform tables to find the inverse Laplace
Transform for the following functions.
a. ��(�) = �
�2+4�+3
b. ��(�) = 2�
�2+2�+2
3.) In the circuit below, vi(t) = 5e-4000t
cos(3000t) V R = 12Ω, C = 83.3µF, L = 1mH.
a.) Find s.
b.) Find the s-domain equation for voltage across the resistor, VO(s)
c.) Find vO(t)
4.) For the circuit below, the input Vi is a 10V pulse that lasts for 1 second. R = 106Ω, C = 44.4nF, L =
1mH. Assume all initial conditions are zero.
a.) Find the equation for Vi(t)
b.) Find Vi(s)
c.) Find the s-domain equation for voltage across
the capacitor, Vo(s).Find the voltage across the
capacitor, vo(t)
[ a ) h { sin ω t ) :twr
c ( 3 ( Ʃ tu ( t ) } =
h ⼀
TS
4 cttt sC-
) eFcssTuce .
Ts =
a{ ) FS =
s ~+ 16 < { ( t –
7 ) u ( t –
1 | =②

⾼ i
< b ) L [ e

ats = sta |= c
[ } ) =
e .
s

LEtf ( t 1 } = –
ds E [ 3 ) cd ) L ( 5 dit ) } = L ( tuct ) ) – LLu (t ) ]
( ct a
2t
u < t ) } = 皆
< ( sti 1
FB ( S ) =
stzn Fd ( s >=

b …

}
LS [
+
C 品 tan | = simat
CG> FaEb ) = {
+1 ” ) < st 3 )
[ b ) Fn [ { ) =
( s + 1 ^+ 1
= –
z { st) + 点 ( st33
L ”
( ! +
. 1 = cost ”
c +
nau)
= ertost ‘
” c
itowr ) =
coswtuC ☆ ninlkeetcswe
L ”
( Fa ( s > ] =
L

(
– {
ast.) + 童 ( st 3 )
} ( ” ( ☆ea ) ^
tw. ) = e
-at sinwt
L +
[ 焱n
+ t
( }
= [
^ { ☆
t” ^+ 1 –

t 1 ” ) z
+ 、 )
⼆⼀定 e ⽐七 {
e 张
( ) usy = Ze –
t
etsintTu cost –
2 ( t )
5 424 S + 22816 .
6
《 ) Wo < s ) =

0 .
G 243 –
135 1 .
a ☆
5 + 1000 .
4 st 12* ( 0 b
+ g 2 t8000 s tz5 × 10 c

924 c st 500 .
2 ) –
889 .
76 5 GL 4 { ) + 40003 –
87 G .
4
Ca ) { = juw 1 × 10 H =
( st 5 00 .
27 ^
+ s 427 . 79
⼗ 2 [ ☆+ 400033 + 30002
S = j 3000
Vo < t ] = – O
. 代
24 e –
500 .rt
cos ( 3423 . 7 Gt )
– { 859 .
7427.
79
} e
-500 .
rt
cb>÷L
1 s
=

40 oot
co s C 3000 t ) – (
8700 ) e
-40 ot

83 .
3 × 10
~
6 F sincsoω t 3 )
< s =
e

40 t ( 5 . 4 r osot3 1 }-o .2 a sin ( soo .t )
=
LCs ^+ 1
( × 10
~
3 a

s 0 at ( o .
9 os ( s 4 L 7 . 9 I t 3 + 0 . 26 sin ( 342799e) }
=
1 × ( 0
” × 83 . 1003 × > 5 ← 1
=
12004 .
8
z +
12 ×<oc
v 。
cs ) = ( 贤 + 2 ) U . ( ∞ )
5 cst 4000 )
5 { { ^+ ( 2 x (
6
] { st 4000 )
72 [ S ^← 2 × 10 + 1000 . 4 S 7 ( } ~+ 8000 s ,
+ 35 x 0 )
= 12 t02004
. 8 tnx 1 o
6
s
‘ ct 80 osti5 xi0
1× 10

}

[ C ) 2 us ) =÷<
Ca 3 Ui ( t ) = ( 0 { ut ) –
ω< t –
( ) ) Z ( ( 3 ) =

5 uRcLtSht 级
HS 级 E
106 44 .
4 ×<0
61-
Ui ( s ) ,
☆ ( RSE ]
( b 3 vics ) = L τ ( ( o ( U (t ) –
U ( t –
+ ) } U 0 [ s } =
CR / c ] + L
R lo –
coe

s
= 10 C ÷ –

( 0 E 1 –
e ”
) CO 6 lo –
loe

s
= [ –
O < st 106 之 38 . 5
) (
st [ 06218 . 5
) 2 + 16 –
( × 10 ‘ 0
t
( 062 ⻢ 8 .
5
Cs + 100 L38 .
5 ) ^≈ 1 .
1 α 100 + 号 ) C ( –
e

」 =
47 xl 0

astio ”
s s… =
S

1 . 0 % 285× ( 05 dt 11
Uo { t | = [ Lo –
LO ←^ 1 .0621 ∞ 5 × 105 t
Cos C ( × Lo 5 tj } ust ) tl 0 ←
1 . 062 ] 85

## BLDG 3100 Construction Operations

FINAL EXAM

Note: Each Question is worth 5 points = 210 points

True or False

T          F          Prime Contractors and General Contractors perform the same work.

T          F          OSHA only regulates safety rules for construction.

T          F          Heavy Construction involves building construction.

T          F          Larger earthmoving equipment has stabilized the heavy construction market.

T          F          Soil classifications are based on the building code.

T          F          Most materials swell when they are excavated.

T          F          The shrinkage of a material is most important when excavation is being performed.

T          F          A cubic yard of bank material weighs less than a cubic yard of loose soil.

T          F          A backhoe is an excellent general use piece of equipment.

T          F          A dozer excavates by cutting into the soil and pushing to a stockpile

T          F          Daily excavate removal is based on the capacity of the trucks.

T          F          Production during excavation is independent of the bucket size.

T          F          Trenchless technology is losing popularity due to excessive excavation.

T        F           Tower cranes are not used more often based on lack of versatility.

T        F           Owning Equipment is easier than leasing equipment.

T          F          The higher the concrete strength the more economical it is?

T          F          Concrete is sprayed with water during the curing process to keep it clean.

T          F          A low-cost type of compaction method is to allow vehicles to drive on the roadway for an extended period before paving.

1. What are three (4) things a construction manager manages?

1. List three (3) pieces of equipment used in the rock crushing process.

1. What is the difference between aggregate and an admixture?

1. What is the formula for concrete?

1. What group sets the standards for concrete mixes?

1. Why is bituminous concrete a preferred material in the Northeast?

1. Why do we use an efficiency factor in production equations? Why is job efficiency important?

1. Explain soil “Swell”, why do some site contractors cover the excavate piles?

1. How many processes does aggregate typically go through before it is suitable for use?

1. What is the relationship between an excavator’s daily capacity and truck hauling?

1. What is OSHA and what does it do?

1. What is the minimum depth for an excavation support system?

1. What is the depth of frost in Massachusetts?

1. What happens when the material used in cement concrete are mixed together?
1. What are 3 factors that can drive up the cost of concrete?

1. When is it more likely that a track boom crane would be used rather than a tower crane?

1. What factors must be considered when determining how much weight a crane can lift safely?

1. For one working day what costs would you include under the crane crew?

1. What factors contribute to loss of efficiency in a hose?

1. What makes an excavator so desirable, what ability does it have that changed the earthwork industry?

1. What is excavation and why is it needed in building construction? What divisions outline the scope of Earthwork?

1. Explain why when you dig a hole and then back fill and it the hole with the soil you had removed there is never enough soil to fill the hole up.

1. Explain two different ways that construction managers evaluate production.

1. Why is swing depth factor so important when calculating excavator production?

## prove of an almost surely convergence to 0 ## Financial Engineering and Machine Learning FINA1147

You will use one market index and four companies’ daily data and these companies should be
from two different sectors. (The required data can be downloaded from Yahoo finance:
http://uk.finance.yahoo.com/). The sample period should be latest and at least 2 years in
length (for example, from Jan 2018 to Jan 2020). For the volatility forecast, the required FX
data can be downloaded from the course Moodle page. For the empirical analysis, you can
use statistical software such as EViews, STATA, or SPSS etc., which has to specify in the
report.
A. Mean-Variance Optimization
1. Briefly explain mean-variance portfolio optimization.
(5 Marks)
2. Estimate the covariance matrix for the selected four companies’ stocks.
(5 Marks)
3. Plot by creating portfolios using the selected four companies and the obtained covariance
matrix. Discussing the results of the portfolio.
(10 Marks)
B. Panel Data Analysis
1. Construct a panel data set using the latest 100 days of the four stock prices. Transfer the
stock prices, market index, and risk-free rate into log returns.
(8 Marks)
2. Verify the CAPM theory using OLS, FE, and RE estimators. Select the appropriate model
(OLS, FE or RE). Discuss the obtained regression results.
(12 Marks)
C. Time-Series Data Analysis
1. Choose one of your stock price series, compute ACF and PACF for the log returns. Discuss
the results.
(4 Marks)
2. Forecast the log returns with AR(5) model and verify the forecasting accuracy by
considering the last 6 months of the data as out-of-sample.
(8 Marks)
3. Estimate the ARMA(3,2) model and comment on the estimations.
(8 Marks)
D. Volatility Analysis
1. Choose one of your stock price series, verify the ARCH effect and estimate GARCH(1, 1)
model.
(10 Marks)
2. Using the data provided, carry out a GARCH(1, 1) volatility forecasting by considering the
last 6 months of the data as out-of-sample. Discuss the results.
(10 Marks)
E. Discussions on Machine Learning Application
1. Discuss the following concepts.
a) Machine Learning
b) Supervised Learning
c) Differentiate between test set and training set
(12 Marks)
2. Explain your understanding on neural network in machine learning. Provide one possible
application of neural network in the financial practice and explain the processes.
(8 Marks)
You need to do all the above tasks and submit your results with detailed discussion on the
tests in a report form (using academic style and minimum 2000 words).
deduction of marks ranging from 10 to 30 will be applied. You will use one market index and four companies’ daily data and these companies should be
from two different sectors. (The required data can be downloaded from Yahoo finance:
http://uk.finance.yahoo.com/). The sample period should be latest and at least 2 years in
length (for example, from Jan 2018 to Jan 2020). For the volatility forecast, the required FX
data can be downloaded from the course Moodle page. For the empirical analysis, you can
use statistical software such as EViews, STATA, or SPSS etc., which has to specify in the
report.
A. Mean-Variance Optimization
1. Briefly explain mean-variance portfolio optimization.
(5 Marks)
2. Estimate the covariance matrix for the selected four companies’ stocks.
(5 Marks)
3. Plot by creating portfolios using the selected four companies and the obtained covariance
matrix. Discussing the results of the portfolio.
(10 Marks)
B. Panel Data Analysis
1. Construct a panel data set using the latest 100 days of the four stock prices. Transfer the
stock prices, market index, and risk-free rate into log returns.
(8 Marks)
2. Verify the CAPM theory using OLS, FE, and RE estimators. Select the appropriate model
(OLS, FE or RE). Discuss the obtained regression results.
(12 Marks)
C. Time-Series Data Analysis
1. Choose one of your stock price series, compute ACF and PACF for the log returns. Discuss
the results.
(4 Marks)
2. Forecast the log returns with AR(5) model and verify the forecasting accuracy by
considering the last 6 months of the data as out-of-sample.
(8 Marks)
3. Estimate the ARMA(3,2) model and comment on the estimations.
(8 Marks)
D. Volatility Analysis
1. Choose one of your stock price series, verify the ARCH effect and estimate GARCH(1, 1)
model.
(10 Marks)
2. Using the data provided, carry out a GARCH(1, 1) volatility forecasting by considering the
last 6 months of the data as out-of-sample. Discuss the results.
(10 Marks)
E. Discussions on Machine Learning Application
1. Discuss the following concepts.
a) Machine Learning
b) Supervised Learning
c) Differentiate between test set and training set
(12 Marks)
2. Explain your understanding on neural network in machine learning. Provide one possible
application of neural network in the financial practice and explain the processes.
(8 Marks)
You need to do all the above tasks and submit your results with detailed discussion on the
tests in a report form (using academic style and minimum 2000 words). 