## Phys 1111K Spring 2005 Introduction Main Sections Ch 1 Pre Requisites St in addition to ards in addition to Units

True, Margot, Food Editor has reference to this Academic Journal, PHwiki organized this Journal Phys 1111K Spring 2005 Course Overview Dr. Perera Room: 507 Science Annex Phone: 651-2709, 3221/3222 Introduction What is Physics Underst in addition to ing nature Laws of Physics Wide spread impact on modern technology Every minute of your life is involved in Physics Needs in addition to Uses Even without knowing it A Fundamental Science Welcome to Introduction to Physics Main Sections Kinematics Classical Mechanics (Chs 1-10) both Transnational in addition to Rotational Dynamics Fluid Mechanics (Ch 11) Thermodynamics (Chs 12-13) Heat Temperature

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Ch 1 Pre Requisites Co-ordinate System (Cartesian) Trigonometry Pythagorean Theorem Sin Cos Pythagorean Theorem Tan Algebra Quadratic Equations Powers of 10 Symbols x, , n, p St in addition to ards in addition to Units Why do we need st in addition to ard units King Louis Yard Royal foot SI Units Le System International Units meter : Light travels in a vacuum in time of 1/ 299792458 seconds kilogram : St in addition to ard cylinder of Pl-Iridium alloy at room temperature second : Cs-133 atomic clock  time as long as 9192631770 wave cycles to occur

Conversion of Units 1 meter = 100 centimeter = 1000 millimeter (mm) 103 meter = 1000 meters = 1 kilometer 0.001 meter = 10-3 meter = 1 millimeter 3.281 feet = 1 meter 5280 feet = 1 mile 3600 seconds = 1 hour 0.65 miles / hour = 95 feet / second = 29 meters / second Significant Figures Keep the same number of significant figures in the answer as in the least accurate number 3.5 × 10.6 = 37 (not 37.1) 0 ± 0.1 0 ± 0.1 35 39 Uncertainty : Quality of the apparatus Skill of the experimenter Number of measurements Dimensional Analysis Distance – [L] Mass – [M] Time – [T] Check whether an equation is mathematically correct Find an unknown exponent

Vectors in addition to Scalars Addition in addition to subtraction Multiplying by a number Components Vector addition by Components Vector addition by Graphing Vector Addition (Due East) Resultant Displacement R = A+ B Due East in addition to then Due north R = A +B 5 = 4 +3 Find Theta What if Vectors are not Perpendicular Can we say R = A +B But Pythagorean Theorem valid Graphical Technique A = 275 m, B =125 m Scale 1 cm = 10 m R = 228 m

Vector Components r = X + Y r A, X Ax Y AY Different Axes Vector Components depend on the orientation of the axes Scalar components (With positive or negative sign) Adding Vectors Using Components C = A +B, C = Cx + CY A = Ax +Ay CX = B = Bx + By CY =

Example 8 A+B=R A=Ax+Ay B=Bx+By Note By is in negative direction. Example 8 (continued) Example 8 (continued)

## True, Margot Food Editor

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## Preparatory Physics (PYPY001 ) Coordinator:

Dreyer, Steve, Executive Editor has reference to this Academic Journal, PHwiki organized this Journal Preparatory Physics (PYPY001)Coordinator: Prof.Dr.Hassan A.MohammedPreparatory Physics PYPY001

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Physical science is concerned with making sense out of the physical environment.Objects in the environment could be quite large, such as the Sun, the Moon, or even the solar system, or invisible to the unaided human eye. Objects can be any size, but people are usually concerned with objects that are larger than a pinhead in addition to smaller than a house. Outside these limits, the actual size of an object is difficult as long as most people to comprehend. CHAPTER 1 What Is Science A generalized mental image of objects called a concept. Your generalized mental image as long as the concept that goes with the word chair probably includes a four-legged object with a backrest. Not all of your concepts are about material objects. You also have concepts about intangibles such as time, motion, in addition to relationships between events. For example, the words second, hour, day, in addition to month represent concepts of time. Properties are the qualities or attributes that, taken together, are usually peculiar to an object. The properties of an object are the effect the object has on your senses. The description of any property implies some kind of referent. The word referent means that you refer to, or think of, a given property in terms of another,more familiar object.

MODELS AND THEORIESOften the part of nature being considered is too small or too large to be visible to the human eye, in addition to the use of a model is needed. A model is a description of a theory or idea that accounts as long as all known properties.At the other end of the size scale, models of atoms in addition to molecules are often used to help us underst in addition to what is happening in this otherwise invisible world.A theory is defined as a broad working hypothesisthat is based on extensive experimental evidence. A scientific theory tells you why something happens.

EXAMPLE:A bicycle has an average speed of 8.00 km/h. How far will it travel in10.0 seconds (Answer: 22.2 m)VELOCITYThe word velocity is sometimes used interchangeably with the word speed, but there is a difference. Velocity describes the speed in addition to direction of a moving object. For example, a speed might be described as 60 km/h. A velocity might be described as 60 km/h to the west. To produce a change in velocity, either the speed or the direction is changed (or both are changed).Acceleration is defined as a change of velocity per unit time, orAcceleration

## Dreyer, Steve Executive Editor

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## Historical Introduction Agenda Fast Fourier Transform

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## Historical Introduction Agenda Fast Fourier Transform

Strayer University-North Raleigh Campus, NC has reference to this Academic Journal, Fast Fourier TransformAgendaHistorical IntroductionCFT in addition to DFTDerivation of FFTImplementationHistorical Introduction

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Continuous Fourier Transform (CFT)Given: Complex Fourier Coefficient:Fourier Series: (change of basis)Given:Discrete Fourier TransformDiscrete Fourier TransformFourier-MatrixDFT of x:Matrix-Vector-Product:N^2 MultiplicationsN(N-1) AdditionsArithmetic Complexity: O(N^2)

Trigonometric InterpolationGiven: equidistant samples of i.e.Goal: find such that alongside Trigonometric InterpolationTheorem:=> Inverse DFT! Derivation of FFT

Historical Introduction Agenda Fast Fourier Transform

FFT ? Lower Bound:(S. Winograd ? Arithmetic Complexity of Computations 1980 CBMS-NSF, Regional Conference Series in Applied Mathematics)FFT if N is primeTwo approaches:Implementation (N = power of 2)

Recursive ImplementationRecursive ImplementationStack-Problem:Space Complexity: O(NlogN)Better Approach:Iterative Implementation => in place! (O(N))Iterative Implementation (N=8)

Iterative Implementation (N=8)Iterative Implementation (N=8)Bit-Inversion:Iterative ImplementationTheorem:The bit inversion yields the result of the permutation graph.

Iterative Implementation

## Chang, Nicole Executive Editor

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