Functions
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I, Hrishikesh Choudhari, gave this presentation, the second one to have my Zen nature, for my MTH-111 course. It is very unique in its content. Even though it is about the basic concept of a 'function' in mathematics, I have made it very visual and it keeps you awake till the end. My professor, Mr. George Thankachan, said that this was the best presentation he had seen in years. That pumped me up, and set the bar for all my future presentations.
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1) The document discusses using the residue theorem to evaluate a complex contour integral to calculate the Laplace transform of the output of an ideal sampler. This provides a closed-form solution that is less painful than the infinite series form.
2) An ideal sampler can be modeled as a carrier signal modulated by the input signal. The output of the sampler is then sent to a zero-order hold.
3) By choosing an appropriate contour, the complex contour integral can be evaluated using the residue theorem. This gives the Laplace transform of the sampler output in terms of the residues of the integrand's poles.
Introduction to Neural Networks and Deep Learning from Scratch
If you're willing to understand how neural networks work behind the scene and debug the back-propagation algorithm step by step by yourself, this presentation should be a good starting point.
We'll cover elements on:
- the popularity of neural networks and their applications
- the artificial neuron and the analogy with the biological one
- the perceptron
- the architecture of multi-layer perceptrons
- loss functions
- activation functions
- the gradient descent algorithm
At the end, there will be an implementation FROM SCRATCH of a fully functioning neural net.
code: https://github.com/ahmedbesbes/Neural-Network-from-scratch
mat lab introduction and basics to learn
This document provides an overview of MATLAB, including its common uses in engineering fields like rocket design, its basic commands and functions for mathematics, matrices, polynomials, and more. Key features of MATLAB covered include its command window, editor, predefined math functions, matrix commands using colons, reading and writing files, and basic programming statements.
1531 fourier series- integrals and trans
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
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17, r) -,r I : -l
19.t:...: 1
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/ 23. ^t: -rr - 1)t I,r r.= ll-vl
11 1
Evaluating a Function In Exercises 29-14, evaluate the
function at each specified value of the independent
variable and simplify.
29.fO-3t+t
(a) f(2) (b) /(-4) (c) f(r + 2)
30. s(y) :1 - 3y
(a) s(o) tul s(l) (c) s(s + 2)
tlzt.t(t):t2-2t
(a) h(.2) ft) /,(1.s) (c) h(x + 2)
32. v(r) - !rr3
(a) v(3) (b) Y(;) k) v(2r)
33./(.-r)::-./y
@) f(a) (u) l(0.2s) (c') [email protected])
3a.f(x)- aE+8+2
(a) f (-+) (b) /(8)
1
' x'-9
(a) q(-3) (b) q(z)
)t2+\
36. ./(r)- t'
(il qQ) 0) q(o)
lrl
37. i(r) : "'x
ar f(e) (b) /(-e)
38. -.,. : -r *4
: , -i (b) /(_5)
-, - l. x<0
'lq -, - l. .r > 0'\-
'\-
6r t(0)
', - -:. -r < 0t.
> |
1..
1OG Chapter I Functjons and Their Graphs
Testing for Functions Represented Algebraically In
Exercises 77-28. determine whether the equation
represents,r' as a function of r.
18.x:]2+1
20. y :-lf+ 5
22.r:-.y+5
24.r'l!2:3
20. lyl :1-x
28.r,:8
(c) /(x - 8)
(c) q(y + 3)
(.c) q(.- x)
(c) /(t)
(c) f(t)
(c) JQ)
,cl .f(l)
Evalr.rating a Fr.lnction In Exercises 45-48, assume that
the domain of/is the setA = {-2, - 1, 0, 1, 2}. Determine
the set of ordered pairs representing the function/.
[.rr-4. x<o42.fG)-1r_r,., r>0L1 - i.\
(il f?2) (b) /(0)
[.r- ]. t<0
I
a3.f(x)-1a. 0<r<2
L*, + t. r > 2
(a) .f(.-2) (b) /(1)
(s - ), r < otJ
44. ffrr --]s. us r < I
l.+*- r, r2 l
(a) J(. 2) (b) /(])
(c) /(1)
@ f(a)
(c) f(t)
a6. .f(.x) : x2 - 3
as. /(x) : lx + 1l
45. f(x) - x2
a7. f(x): lxl + z
Evaluating a Function In Exercises 49 and 50, complete
the tahle.
4s. h(t): llr + :l
l" - ?l50..f(r) -:
Finding the lnputs That Have Outputs of Zers In
Exercises 51-54, find all values of x such that/(r) = g'
st. 16) : 15 - 3x 52. f(x): 5r * I
3r-4
sa. f(x') - 2r-3s3. /(x) :
Finding the Dornain of a Function In Exercises 55-6J.
find the domain of the function.
,l ss. fG): 5x2 + 2x - | s6. s(ir) : 7 - 2x2
4-3v
57. hhl - ' 58. ,s( r') -I y-)
se. /(x) - 1C - 1 60. /(x) : X/" + 3x
. t 3 l0
{ el. gtrt - ' - 62. h(r) - .., 1..I f t- i LA
r'*2 -,8+6
64./(:r) :--' o f .t
t -5 -4 -3 -1
It(r)
,t 0 l2
I
2
4
/(')
63. s(.v) : 5- 10
the Domain and Range of a Function In 1)
mriffs 65-68, use a graphing utility to graph the
hhu Find the domain and range of the function.
. ,.-
-E' - \
+ i 66. f(x): 1F I 1
68. g(x) : I, - sl.j1- -r,-; : i1r + 3l
I. Geometry Write the areaA of a circle as a function of
rs --ircumference C.
il" Cmmetry Write the arca A of an equilaterai tiangle
"ts i tunction of the length s of its sides.
1!- E4loration An open box of maximum volume is to
s made from a square piece of mateial, 24 centimeters
cm a side, by cutting equal squares from the corners and
uuia-e up the sides (see figure).
,"1 , The table shows the volume 7 (in cubic centimeters)
of the box for various heights x (in centimeters).
L-se the table to estimate the maximum volume.
i Plot the points (x, I/) from the table in part (a). Does
rtre relation defined.
3.1 Characteristics of Polynomial Functions.pptx
This document provides information about polynomial functions including:
- Their general form as a sum of terms with variables raised to whole number powers and real number coefficients.
- Characteristics like degree, leading coefficient, constant term, and their relationship to the graph.
- Examples of graphs of polynomial functions of varying degrees and their characteristics like possible intercepts and behavior at endpoints.
- Worked examples identifying characteristics of given polynomial functions.
Open GL T0074 56 sm4
The document discusses drawing 2D primitives such as lines, circles, and polygons in a raster graphics system. It covers:
- Representations of lines, circles, and polygons using implicit, explicit, and parametric formulas
- Scan conversion algorithms to draw these primitives by mapping them to pixels, including basic and midpoint line algorithms, a circle midpoint algorithm, and flood fill and scan conversion approaches for polygon fill
- Components of an interactive graphics system including the application model, program, and graphics system that interfaces with display hardware like CRT and FED displays
Statistical Physics Assignment Help
I am Stacy W. I am a Statistical Physics Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from, University of McGill, Canada
I have been helping students with their homework for the past 7years. I solve assignments related to Statistical.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Statistical Physics Assignments.
DIGITAL IMAGE PROCESSING - Day 4 Image Transform
The document discusses digital image processing and two-dimensional transforms. It provides an agenda that covers two-dimensional mathematical preliminaries and two transforms: the discrete Fourier transform (DFT) and discrete cosine transform (DCT). It then discusses the DFT and DCT in more detail over several pages, covering properties, examples, and applications such as image compression.
Introduccio al calculo vectorial
This document introduces vector fields and defines scalar and vector fields. It defines a vector field F over a planar region D as a function that assigns a vector to each point, given by the components P and Q. Similarly, a vector field over a spatial region E is given by components P, Q, and R. Examples of vector fields include velocity fields and gravitational and electric force fields. It also defines the gradient of a scalar field, divergence and curl of a vector field, and discusses integral calculations for scalar and vector fields along curves.
5-1-reimann-sums.ppt
This document discusses the concept of the definite integral and Riemann sums. It explains that if the velocity over time is not constant, the definite integral is used to find the total distance by approximating the area under the curve representing velocity versus time. This is done by dividing the interval into subintervals and taking the sum of rectangles approximating small sections of the area. As the number of subintervals increases, the Riemann sum converges to the definite integral, which precisely calculates the area and extends the concept of summation to integration.
Unit 1
This document provides an overview of communication engineering concepts including probability, random variables, and noise. It defines key probability terms and axioms. Random variables are introduced as functions that assign outcomes to real numbers, and common distributions like Gaussian, Rayleigh, uniform, and exponential are described. Noise sources are classified as external or internal to a communication system, with thermal noise defined using Boltzmann's constant within a bandwidth.
Engineering formula sheet
1. The document provides engineering formulas and equations for statistics, mechanics, electricity, fluid mechanics, thermodynamics, structural analysis, and simple machines.
2. Key formulas include those for mean, median, mode, standard deviation, and probability. Mechanics formulas include those for force, torque, energy, power, and kinematics.
3. Formulas are also provided for stress, strain, modulus of elasticity, beam deflection, truss analysis, and mechanical advantage of simple machines like levers, inclined planes, and gears.
Difference quotient algebra
The document discusses the difference quotient formula for calculating the slope between two points (x1,y1) and (x2,y2) on a function y=f(x). It shows that the slope m is equal to (f(x+h)-f(x))/h, where h is the difference between x1 and x2. This "difference quotient" formula allows slopes to be calculated from the values of a function at two nearby points. Examples are given of simplifying the difference quotient for quadratic and rational functions.
characteristic of function, average rate chnage, instant rate chnage.pptx
A power function is a polynomial function of the form y=xn, where n is a real number constant called the exponent. Power functions can be odd or even degree. Odd degree power functions have point symmetry about the origin, while even degree functions may have line symmetry. The instantaneous rate of change at a point is the slope of the tangent line to the curve at that point and can be estimated from graphs, tables of values, or equations.
Developing Expert Voices
The student reflects on completing a math project for their calculus course as a way to study for an upcoming exam. They acknowledge that they procrastinated significantly but were able to cover a broad range of calculus concepts through multi-step word problems selected from different units. While the assignment did not dramatically increase their knowledge, it helped reinforce some details and connections between topics. The student resolves to select deadlines more wisely and stop procrastinating for future projects.
Engineering formula sheet
This document contains formulas and definitions for engineering concepts related to probability, statistics, geometry, trigonometry, mechanics, electricity, thermodynamics, materials properties, and structural analysis. Some key formulas included are for binomial probability, mean, standard deviation, circle area and circumference, trigonometric ratios, force, work, power, heat transfer, stress, strain, modulus of elasticity, centroid location, and beam reactions and deflections. SI prefixes and unit conversions are also provided.
Similar to Functions (20)
Introduction to Neural Networks and Deep Learning from Scratch
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17, r) -,r I -l19.t... 121.2t-314 23. ^t -rr - .docx
17, r) -,r I -l19.t... 121.2t-314 23. ^t -rr - .docx
characteristic of function, average rate chnage, instant rate chnage.pptx
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Functions
- 1. Chapter One : Functions, Graphs and Graphers.
- 2. The idea of a function.
- 3. The distance, in miles, is 1/5 of the time, in seconds. 15 seconds --> 3 miles
- 4. x 15 3 (15,3) 3 15 10 2 (10,2) 2 10 5 1 (5.1) 1 5 1 1/5 (1,1/5) 1/5 1 0 0 (0,0) 0 0 Correspondence Ordered pairs (x,y) y
- 6. y = (1/5)x Distance is a function of time.
- 7. A function is a correspondence between a first set, called domain , and a second set, called the co-domain , and only the elements which have a pre-image in the domain, make up the range.
- 8. Notation – inputs (members of the domain) are values of x outputs (members of the range) are values of y
- 9. function f input x corresponding output f (x)
- 10. f (x) does not mean f*x
- 11. ?
- 12. Vertical Line Test If it is possible for a vertical line to cross a graph more than once, then the graph is not a graph of a function.
- 14. Finding the domain – The input should give real output
- 15. f (x)=
- 17. Speed of Sound
- 20. t=temperature in Fahrenheit; S=speed of sound in feet/sec boeing.com/commercial/industry_info.html
- 21. 1544.955 500 1464.967 400 1380.511 300 1290.197 200 1193.292 100 1087.700 0 970.737 -100 837.599 -200 678.823 -300 469.099 -400 Y X
- 22. Temp Speed
- 23. Temp Speed
- 24. Temp Speed
- 25. Temp
- 26. Temp
- 29. Anthropology
- 30. humerus
- 31. 131.98 22 151.23 29 142.98 26 F(x) X
- 32. Humerus Height
- 33. Height
- 34. y = 2.5x + 71.48
- 35. Height Humerus
- 41. For a run of hundred feet, a rise of twenty feet is permitted.
- 42. x = run f(x) = rise
- 45. Meteorology
- 47. Temp in F Month
- 48. polynomial function 0.2607392 x 2 + 3.620379 x + 72.090909
- 52. 400 ft 120 t d Express d as a function of t
- 54. Population
- 55. N 0 is the starting population N is the population after a certain time, t , has elapsed, r is the rate of natural increase ( birth rate - death rate ) and e is the constant 2.71828...
- 58. Microbiologists
- 59. 2048 11 1024 10 512 9 256 8 128 7 64 6 32 5 16 4 8 3 4 2 2 1 1 0 Cells Time
- 60. Time (sec) Cells
- 62. A cardioid is a curve that can be produced as the path (or locus) of a point on the circumference of a circle as that circle rolls around another fixed circle with the same radius. wiki
- 64. Cos = red Exp = black Mathworld.wolfram.com
- 65. Hoffman-Singleton graph Mathworld.wolfram.com
- 66. Variation
- 67. Direct variation
Editor's Notes
- Chapter One : Functions, Graphs and Graphers.