Infrared Spectroscopy Aim: To obtain IR spectra of know solid sample and liquid sample using the following sample preparing technique: Prepare solid IR sample using Solid Pellet Samplin Technique Use IR is used to identify functional groups. 5 major functional groups easily identified by IR spectroscopy: 1. C=O 2. C–O 3. OH 4. Phenols 5. C–H Instrument details Type of spectrophotometer: Nicolet 380 FT-IR spectroscopy‚ Nicolet Avatar 360 & Thermo Scientific iS10 FT-IR Spectrometer
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[pic] Fourier Series: Basic Results [pic] Recall that the mathematical expression [pic] is called a Fourier series. Since this expression deals with convergence‚ we start by defining a similar expression when the sum is finite. Definition. A Fourier polynomial is an expression of the form [pic] which may rewritten as [pic] The constants a0‚ ai and bi‚ [pic]‚ are called the coefficients of Fn(x). The Fourier polynomials are [pic]-periodic functions. Using the trigonometric
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| |Programme |Bachelor of Computer Science (BCS) | |Name of Course / Mode |Discrete Mathematics | |Course Code |CSC 1700 | |Name (s)
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Series FOURIER SERIES Graham S McDonald A self-contained Tutorial Module for learning the technique of Fourier series analysis q Table of contents q Begin Tutorial c 2004 g.s.mcdonald@salford.ac.uk Table of contents 1. 2. 3. 4. 5. 6. 7. Theory Exercises Answers Integrals Useful trig results Alternative notation Tips on using solutions Full worked solutions Section 1: Theory 3 1. Theory q A graph of periodic function f (x) that has period L exhibits the same pattern every L units along the
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Mathematical Database MATHEMATICAL INDUCTION 1. Introduction Mathematics distinguishes itself from the other sciences in that it is built upon a set of axioms and definitions‚ on which all subsequent theorems rely. All theorems can be derived‚ or proved‚ using the axioms and definitions‚ or using previously established theorems. By contrast‚ the theories in most other sciences‚ such as the Newtonian laws of motion in physics‚ are often built upon experimental evidence and can never be
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COMP3054 LAB 6 Name: ID# Section: LAB 6: Frequency Domain Measurements Using the Vector Signal Analyzer Objective: Measure: frequency and amplitude‚ channel power/ band power‚ relative frequency and amplitude‚ improving resolution‚ and spectrogram displays using the VSA Section A: Measuring Frequency and Amplitude
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Propositions The fundamental objects we work with in arithmetic are numbers. In a similar way‚ the fundamental objects in logic are propositions. Definition: A proposition is a statement that is either true or false. Whichever of these (true or false) is the case is called the truth value of the proposition. Here are some examples of English sentences that are propositions: ‘Canberra is the capital of Australia.’ ‘There are 8 days in a week.’ ‘Isaac Newton was born in 1642.’ ‘5 is greater
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DISCRETE MATHEMATICS Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly"‚ the objects studied in discrete mathematics – such as integers‚ graphs‚ and statements in logic – do not vary smoothly in this way‚ but have distinct‚ separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects
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Title #1: Primadona 50% and 30% sale Description: 5 items (Shoes‚ Dress‚ T-shirt‚ Bags‚ Accessories) has 50% sales off. Input the Product Code‚ the Original Price‚ the Quantity of the Product that you will buy then the program will show the Product Description and the Discounted Price. Product Description Product Code Original Price Shoes S or s 1‚500 Dress D or d 550 T-shirt T or t 230 Bags B or b 1‚200 Accessories
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Laplace Transforms Gilles Cazelais May 2006 Contents 1 Problems 1.1 Laplace Transforms . . . . . . 1.2 Inverse Laplace Transforms . 1.3 Initial Value Problems . . . . 1.4 Step Functions and Impulses 1.5 Convolution . . . . . . . . . . 2 Solutions 2.1 Laplace Transforms . . . . . . 2.2 Inverse Laplace Transforms . 2.3 Initial Value Problems . . . . 2.4 Step Functions and Impulses 2.5 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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