2.1: Introduction

2.1: Introduction

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Science fiction writers often imagine spaceships that can travel to far-off planets in distant galaxies. The problem is that the faster an object moves, the more mass it attains (in the form of energy), according to the equation


where (m_0) is the object’s mass at rest, (v) is its speed, and (c) is the speed of light. What is this speed limit? (We explore this problem further in the chapter)

Figure (PageIndex{1}):The vision of human exploration by the National Aeronautics and Space Administration (NASA) to distant parts of the universe illustrates the idea of space travel at high speeds. But, is there a limit to how fast a spacecraft can go? (credit: NASA)

The idea of a limit is central to all of calculus. We begin this chapter by examining why limits are so important. Then, we go on to describe how to find the limit of a function at a given point. Not all functions have limits at all points, and we discuss what this means and how we can tell if a function does or does not have a limit at a particular value. This chapter has been created in an informal, intuitive fashion, but this is not always enough if we need to prove a mathematical statement involving limits. The last section of this chapter presents the more precise definition of a limit and shows how to prove whether a function has a limit.


  • Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at

2.1: Introduction

James stumbled into his position as the human resource manager. He had been working for Techno, Inc. for three years, and when the company grew, James moved from a management position into a human resource management position. Techno, Inc. is a technology and software consulting company for the music industry.

James didn&rsquot have a good handle on how to effectively run a human resources (HR) department, so for much of the time he tried to figure it out as he went. When Techno started seeing rapid growth, he hired thirty people within a one-month period to meet the demand. Proud of his ability to accomplish his task of meeting the business&rsquos current needs, James was rather pleased with himself. He had spent numerous hours mulling over recruitment strategies, putting together excellent compensation plans, and then eventually sifting through résumés as a small part of the hiring process. Now the organization had the right number of people needed to carry out its projects.

Fast forward five months, however, and it turned out the rapid growth was only temporary. James met with the executives of the business who told him the contracts they had acquired were finished, and there wasn&rsquot enough new work coming in to make payroll next month if they didn&rsquot let some people go. James felt frustrated because he had gone through so much effort to hire people, and now they would be laid off. Never mind the costs of hiring and training his department had taken on to make this happen. As James sat with the executives to determine who should be laid off, he felt sad for the people who had given up other jobs just five months before, only to be laid off.

After the meeting, James reflected on this situation and realized that if he had spoken with the executives of the company sooner, they would have shared information on the duration of the contracts, and he likely would have hired people differently, perhaps on a contract basis rather than on a full-time basis. He also considered the fact that the organization could have hired an outsourcing company to recruit workers for him. As Jason mulled this over, he realized that he needed a strategic plan to make sure his department was meeting the needs of the organization. He vowed to work with the company executives to find out more about the company&rsquos strategic plan and then develop a human resource management (HRM) strategic plan to make sure Techno, Inc. has the right number of workers with the right skills, at the right time in the future.

2.1 Introduction

Systematic health assessments are performed regularly in nearly every health care setting. For example:

  • A health history is taken when a patient is admitted and whenever additional subjective information is required to inform care.
  • Comprehensive head-to-toe assessments are done when a patient is admitted, at the beginning of each shift, and when it is determined to be necessary by the patient’s hemodynamic status and context.
  • Brief physical assessments are done as necessary and to identify changes in a patient’s status and for comparison with the previous assessment.
  • Focused assessments are done in response to a specific problem recognized by the assessor as needing further assessment of a body system.
  • Emergency assessments are done in emergency situations.

A routine physical assessment reveals information to supplement a patient’s database. The assessment is documented according to agency policy, and unusual findings are reported to appropriate members of the health care team. Ongoing, objective, and comprehensive assessments promote continuity in health care.

The ability to think critically and interpret patient behaviours and physiologic changes is essential. The skills of physical assessment are powerful tools for detecting both subtle and obvious changes in a patient’s health. The assessment skills outlined in this chapter are meant to provide a framework to develop assessment competencies applicable and salient to everyday practice as recommended by Anderson, Nix, Norman, and McPike (2014).

  • Describe the purposes of physical assessment
  • Describe the different types of assessment and when they should be used to inform care
  • Discuss techniques to promote a patient’s physical and psychological comfort during an examination
  • Make environmental preparations before an assessment
  • Identify data to collect from the nursing history before an examination
  • Incorporate health promotion and health teaching into an assessment
  • Use physical assessment techniques and skills during routine nursing care
  • Document assessment findings according to agency policy
  • Communicate abnormal findings to appropriate members of the health care team

2.1: Introduction

UV/VIS radiation has the proper energy to excite valence electrons of chemical species and cause electronic transitions.

For atoms, the only process we need to think about is the excitation of electrons, (i.e., electronic transitions), from one atomic orbital to another. Since the atomic orbitals have discrete or specific energies, transitions among them have discrete or specific energies. Therefore, atomic absorption spectra consist of a series of &ldquolines&rdquo at the wavelengths of radiation (or frequency of radiation) that correspond in energy to each allowable electronic transition. The diagram in Figure (PageIndex<1>) represents the energy level diagram of any multielectron atom.

Figure (PageIndex<1>). Energy level diagram of a multielectron atom.

The different lines in the spectrum will have different intensities. As we have already discussed, different transitions have different probabilities or different molar absorptivities, which accounts for the different intensities. The process of absorption for helium is shown in Figure (PageIndex<2>) in which one electron is excited to a higher energy orbital. Several possible absorption transitions are illustrated in the diagram.

Figure (PageIndex<2>). Absorption transitions of helium.

The illustration in Figure (PageIndex<3>) represents the atomic emission spectrum of helium and clearly shows the &ldquoline&rdquo nature of an atomic spectrum.

Figure (PageIndex<3>). Atomic emission spectrum of helium.

For molecules, there are two other important processes to consider besides the excitation of electrons from one molecular orbital to another. The first is that molecules vibrate. Molecular vibrations or vibrational transitions occur in the infrared portion of the spectrum and are therefore lower in energy than electronic transitions. The second is that molecules can rotate. Molecular rotations or rotational transitions occur in the microwave portion of the spectrum and are therefore lower in energy than electronic and vibrational transitions. The diagram in Figure (PageIndex<4>) represents the energy level diagram for a molecule. The arrows in the diagram represent possible transitions from the ground to excited states.

Figure (PageIndex<4>). Energy level diagram for a molecule showing electronic, vibrational and rotational states. Arrows represent possible absorption transitions.

Note that the vibrational and rotational energy levels in a molecule are superimposed over the electronic transitions. An important question to consider is whether an electron in the ground state (lowest energy electronic, vibrational and rotational state) can only be excited to the first excited electronic state (no extra vibrational or rotational energy), or whether it can also be excited to vibrationally and/or rotationally excited states in the first excited electronic state. It turns out that molecules can be excited to vibrationally and/or rotationally excited levels of the first excited electronic state, as shown by arrows in Figure (PageIndex<4>). Molecules can also be excited to the second and higher excited electronic states. Therefore, we can speak of a molecule as existing in the second excited rotational state of the third excited vibrational state of the first excited electronic state.

One consequence in the comparison of atomic and molecule absorption spectra is that molecular absorption spectra ought to have many more transitions or lines in them than atomic spectra because of all the vibrational and rotational excited states that exist.

Compare a molecular absorption spectrum of a dilute species dissolved in a solvent at room temperature versus the same sample at 10K.

The difference to consider here is that the sample at 10K will be frozen into a solid whereas the sample at room temperature will be a liquid. In the liquid state, the solute and solvent molecules move about via diffusion and undergo frequent collisions with each other. In the solid state, collisions are reduced considerably.

What is the effect of collisions of solvent and solute molecules? Collisions between molecules cause distortions of the electrons. Since molecules in a mixture move with a distribution of different speeds, the collisions occur with different degrees of distortion of the electrons. Since the energy of electrons depends on their locations in space, distortion of the electrons causes slight changes in the energy of the electrons. Slight changes in the energy of an electron means there will be a slight change in the energy of its transition to a higher energy state. The net effect of collisions is to cause a broadening of the lines in the spectrum. The spectrum at room temperature will show significant collisional broadening whereas the spectrum at 10K will have minimal collisional broadening. The collisional broadening at room temperature in a solvent such as water is significant enough to cause a blurring together of the energy differences between the different rotational and vibrational states, such that the spectrum consists of broad absorption bands instead of discrete lines. By contrast, the spectrum at 10K will consist of numerous discrete lines that distinguish between the different rotationally and vibrationally excited levels of the excited electronic states. The diagrams in Figure (PageIndex<5>) show the difference between the spectrum at room temperature and 10K, although the one at 10K does not contain nearly the number of lines that would be observed in the actual spectrum.

Figure (PageIndex<5>). Comparison of the absorption spectrum of a molecule in a solvent at room temperature and at 10 K.

Are there any other general processes that contribute to broadening in an absorption spectrum?

The other general contribution to broadening comes from something known as the Doppler Effect. The Doppler Effect occurs because the species absorbing or emitting radiation is moving relative to the detector. Perhaps the easiest way to think about this is to consider a species moving away from the detector that emits a specific frequency of radiation heading toward the detector. The frequency of radiation corresponds to that of the energy of the transition, so the emitted radiation has a specific, fixed frequency. The picture in Figure (PageIndex<6>) shows two species emitting waves of radiation toward a detector. It is worth focusing on the highest amplitude portion of each wave. Also, in Figure (PageIndex<6>), assume that the detector is on the right side of the diagram and the right side of the two emitting spheres. The emission process to produce the wave of radiation requires some finite amount of time. If the species is moving away from the detector, even though the frequency is fixed, to the detector it will appear as if each of the highest amplitude regions of the wave is lagging behind where they would be if the species is stationary (see the upper sphere in Figure (PageIndex<6>)). The result is that the wavelength of the radiation appears longer, meaning that the frequency appears lower. For visible radiation, we say that the radiation from the emitting species is red-shifted. The lower sphere in Figure (PageIndex<6>) is moving towards the detector. Now the highest amplitude regions of the wave are appearing at the detector faster than expected. This radiation is blue-shifted. In a solution, different species are moving in different directions relative to the detector. Some exhibit no Doppler shift. Others would be blue-shifted whereas others would be red-shifted and the degree of red- and blue-shift varies among different species. The net effect would be that the emission peak is broadened. The same process occurs with the absorption of radiation as well.

Figure (PageIndex<6>). Representation of the Doppler effect on the wavelength of radiation measured by a detector.

The emission spectrum in Figure (PageIndex<7>) represents the Doppler broadening that would occur for a gas phase atomic species where the atoms are not moving (top) and then moving with random motion (bottom).

Figure (PageIndex<7>). Effect of Doppler broadening on the emission from a gas phase atomic substance.

A practical application of the Doppler Effect is the measurement of the distance of galaxies from the earth. The universe is expanding away from a central point. Hubble&rsquos Law and the Hubble effect is an observation that the further a galaxy is from the center of the universe, the faster it moves. There is also a precise formula that predicts the speed of movement relative to the distance from the center of the universe. Galaxies further from the center of the universe therefore show a larger red shift in their radiation due to the Doppler Effect than galaxies closer to the center of the universe. Measurements of the red-shift are used to determine the placement of galaxies in the universe.

What is NOT Covered in This Module

This module is intended as an introduction to applied optical microscopy for a petrology course, so it does not include ALL possible ways of using a petrographic microscope to analyze minerals and rocks.

If you are interested in learning more in-depth techniques, that is great! The references below provide more detailed discussions of optical techniques and cover additional techniques and microscope accessories, such as the universal stage.

2.1 Introduction to Acceleration

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2.1 Chapter Introduction

Business people-showing teamwork

Successful organizations depend on getting the right mix of individuals in the right positions at the right times.

What’s in It for Me?

Reading this chapter will help you do the following:

  1. Understand the roles of personality and values in determining work behaviors.
  2. Explain the process of perception and how it affects work behaviors.
  3. Identify the major work attitudes that affect work behaviors.
  4. Define the concept of person-organization fit and how it affects work behaviors.
  5. List the key set of behaviors that matter for organizational performance.
  6. Be able to develop your positive attitude skills.

Figure 2.2 The P-O-L-C Framework

Individuals bring a number of differences to work. They have a variety of personalities, values, and attitudes. When they enter into organizations, their stable or transient characteristics affect how they behave and perform. Moreover, companies hire people with the expectation that they have certain knowledge, skills, abilities, personalities, and values.

Recall that you are learning about the principles of management through the planning-organizing-leading-controlling (P-O-L-C) framework. Employees’ personalities, attitudes, and work behaviors affect how managers approach each P-O-L-C dimension. Here are just a few examples:

  • When conducting environmental scanning during the planning process, a manager’s perceptions color the information that is absorbed and processed.
  • Employee preferences for job design and enrichment (aspects of organizing) may be a function of individuals’ personalities and values.
  • Leading effectively requires an understanding of employees’ personalities, values, and attitudes.
  • Absenteeism can challenge a manager’s ability to control costs and performance (both at the group and individual levels).

Therefore, it is important for managers to understand the individual characteristics that matter for employee and manager behaviors.

2.1: Introduction

The main screen provides the main visualization elements for StocksToTrade. It essentially provides all of the information relevant to any given stock.

The main screen is composed of various elements:

The role of the header is to provide an easily accessible view of all open content views.

It is used to place and organize Stock Views and Scanner Views.

The header is composed of the following elements:

  • Search box - allows to open a stock by its symbol
  • Tab selector - allows to place and organize open tabs
  • New tab button - allows to create an empty tab
  • Current user information
  • Settings button
  • Notifications button

Content View

The content view is in charge of displaying the necessary information about the current tab.

The Content View is composed of a Header which provides basic information about a stock as well as the various element buttons and the actual Content View Body to display these widgets on screen.

Content View Header

This header provides the most basic information about a given stock:

Additionally, the header provides a set of widget buttons to populate the view area and display the necessary data on screen for a given tab:

  • Total View - displays all widgets
  • Charting - displays a chart for a given stock
  • Basics - displays basic quantitative information about the stock
  • Level 2 - the Level 2 monitor
  • Time & Sales - opens the time and sales monitor
  • Info - displays News, SEC Filings, Events, Chat, Profile, Key Statistics, Order, Related, Twitter Feed, Rating
  • Tip Ranks - TipRanks lets you see the track record and measured performance of any analyst

Alternatively, a tab header may display empty data without the necessity of displaying a particular stock. This is useful to open only Scanners and keep them in separate tabs.

Empty tabs may be renamed for easy reference.

The Content View Header also allows to undock the current tab as a floating window. This is achieved by clicking on the Undock icon ( )

Content View Body

The Content View Body offers a restricted space in which to place each open widget associated with the current tab.

Each widget in the body may be moved and resized within the boundaries of the container any overflowing items can be accessed with the scrollbars for the container.

Usage and purpose of each of the widgets will be covered in later chapters.

2.1 Introduction

Assessment is an essential part of the nurse’s role and is the first step in the nursing process (Potter et al., 2019). Care provided is based on the assessment findings that the nurse has collected and thought critically about. Nurses work collaboratively with clients and the healthcare team to create care plans that help optimize client health and help the client achieve their health goals.

Depending on the context, nursing assessment can take many forms. Nurses working in communities may perform community assessments nurses working with particular populations may perform population related assessment and nurses working in acute care may perform specific patient assessment. When an assessment is performed, the nurse should do so in a methodical fashion ensuring thoroughness.

This chapter will cover different approaches for nurses to physical health assessment, including health history, vitals, physical assessment with details about focused assessments pertinent to each system, as well as pain assessment and how to do a quick priority assessment. Sample nursing diagnoses are provided to help the learner begin to make connections between assessment and nursing diagnoses.

The skills of physical assessment are powerful tools for detecting both subtle and obvious changes in a patient’s health. Along with this, the ability to think critically and interpret patient behaviours and physiologic changes are essential. The assessment skills outlined in this chapter are meant to provide a framework to develop assessment competencies applicable and salient to everyday practice as recommended by Anderson, Nix, Norman, and McPike (2014).

The content in this chapter is considered basic level for adult assessment. Learners are encouraged to seek other, in-depth resources about assessment to further develop their knowledge and skill.

Watch the video: Lesson Introduction to Matrices and Operators (August 2022).