INSTRUCTORS: IF YOU HAVE ADOPTED THIS TEXTBOOK, YOU CAN REQUEST A COPY OF THE INSTRUCTOR'S CD WHICH COMES WITH ALL IMAGES IN THE BOOK PLACED AS SEPARATE SLIDES IN POWERPOINT. See above RESOURCES tab for more information.
Preclinical Speech Science. Second Edition IS suitable for courses that cover the anatomy and physiology of speech production and swallowing, and the acoustics and perception of speech. The book is an ideal offering for communication sciences and disorders programs offering speech science and anatomy courses separately so students only have to purchase one book for two classes. The book can also be used perfectly for a combined course covering all topics in one semester.
Preclinical Speech Science: Anatomy, Physiology, Acoustics, Perception, Second Edition is the text of choice for undergraduate and graduate courses in speech science. Written in a user-friendly style by three distinguished scientists/editors/clinicians who have taught the course to thousands of students at premier educational programs, the text comprehensively covers anatomy, physiology, acoustics, perception, and swallowing. This book helps speech-language pathologists in training understand the science that underpins their work and provides a framework for the evaluation and management of their future clients. It provides all that instructors need to ensure that their students are fully ready for their clinical practicum training.
- Describes scientific principles explicitly and in translational terms that emphasize their relevance to clinical practice.
- Features original, full-color illustrations and artwork designed to be instructive learning tools.
- Includes clinical scenarios woven into the text to emphasize the relevance of the concepts presented and focus the discussion on humanistic values.
- Incorporates analogies that aid thinking about processes from different perspectives.
- Features "sidetracks" that relate interesting historical and contemporary facts to the discipline of speech science.
- Provides a framework for conceptualizing the uses, subsystems, and levels of observation of speech production, speech, and swallowing.
- Includes material that is ideal for preparing both undergraduate and graduate for clinical study.
The second edition of Preclinical Speech Science includes updates of existing chapters, plus a comprehensive, detailed new chapter titled "Brain Structures and Mechanisms for Speech, Language, and Hearing." As in the first edition chapters, this new chapter contains beautifully drawn, full-color, detailed artwork to facilitate the task of learning nervous system structures and physiology. The chapter concludes with a unique section on a brain-based model of communication skills in humans.
The related Preclinical Speech Science Workbook is also available to help reinforce the textbook content and increase student comprehension. Learn more about the Preclinical Speech Science Workbook, Second Edition.
Save 15% on the textbook and workbook together.
Amy T. Neel, PhD, ASHA SID 5, Perspectives (2008):
"... A text that can be used for both anatomy and speech science courses, provides thorough and clear explanations of speech production and speech perception, and addresses clinical topics through case studies at the beginning and end of each chapter. ... Graduate students and professionals will use it as a resource long after their undergraduate course work is complete. [Refers to the first edition.]"
I.G. Ashbaugh, Choice (April 2009):
"This textbook is an easy-to-read, well-organized resource that would be appropriate for courses in both speech science and the anatomy/physiology of the speech mechanism. Summing up: Highly recommended. [Refers to the first edition.]"
Julie Liss, PhD (Arizona State University), Doody's Review Service (2008):
"***** Five Stars! The chapters are uniform in their coverage of a historical perspective as well as state-of-the-art knowledge and research.... Provides a resource that is at once detailed, comprehensive, exceptionally written, and engaging. [Refers to the first edition.]"
Doody's (May 2018):
"Named to Doody's Core Titles in the Health Sciences - Speech, Language & Hearing 2018 list."
Calum Delaney, Cardiff Metropolitan University (2013):
"The figures, diagrams and explanations, particularly on the vocal tract, are superb...[A] resource for those students that sometimes struggle with visualising vocal tract anatomy and physiology and understanding some of the concepts."
William Sennett, Saint Xavier University (2013):
"The new chapter on brain structures and mechanisms is a good addition."
Denise Stats-Caldwell, Arizona State University (2013):
"Its content can be applied to a variety of disorder types instead of being disorder specific. It looks like a great functional resource for students to have during undergraduate, graduate school and beyond."
Marjorie Taylor, Richard Stockton College of New Jersey (2013):
"The illustrations and the layout look great."
Richard Zraick, University of Arizona Little Rock (2013):
"Both [the textbook and workbook] are a wonderful resource."
Richard Andreatta, University of Kentucky (2013):
"...Over all the additions and changes are good. I especially like the new chapter on brain function. The authors have done a terrific job further enhancing the usability of the book. I really think this book has become the new "Zemlin" in CSD (alluding to the Zemlin's Speech & Hearing Sciences book by Prentice Hall)...I'm very pleased by the new edition and new additions."
June Levitt, Texas Womans University (2013):
"Both [the textbook and workbook] are fantastic books."
Julie Miller, University of Arizona (2013):
"It is well written with great visuals."
Patricia Peifer-Arens, Pace University (2013):
"[I] find it a very thorough and useful text. I particularly like chapter 4, Ethics of Professional Writing, and Chapter 9, Clinical Goals, Reports, and Referrals."
Jon Brumberg, University of Kansas (2013):
"I found the newly added chapters a great addition to the book content and will be a great resource for my students."
Focus of the Book
Domain of Preclinical Speech Science
Levels of Observation
Subsystems of Speech Production and Swallowing
Applications of Data
2 BREATHING AND SPEECH PRODUCTION
Fundamentals of Breathing
Anatomical Bases of Breathing
Breathing Apparatus and Its Subdivisions
Forces and Movements of Breathing
Forces of Breathing
Realization of Active and Passive Forces
Movements of Breathing
Adjustments of the Breathing Apparatus
Pulmonary Apparatus-Chest Wall Unit
Output Variables of Breathing
Neural Control of Breathing
Control of Tidal Breathing
Control of Special Acts of Breathing
Ventilation and Gas Exchange During Tidal Breathing
Breathing and Speech Production
Breathing in Extended Steady Utterances
Breathing in Running Speech Activities
Adaptive Control of Speech Breathing
Body Position and Speech Breathing
Extended Steady Utterances in the Supine Body Position
Running Speech Activities in the Supine Body Position
Speech Breathing in Other Body Positions
Ventilation, Gas Exchange, and Speech Breathing
Drive to Breathe and Speech Breathing
Cognitive-Linguistic Factors and Speech Breathing
Conversational Interchange and Speech Breathing
Body Type and Speech Breathing
Development and Speech Breathing
Age and Speech Breathing
Sex and Speech Breathing
Measurement of Breathing
Speech Breathing Disorders
Clinical Professionals and Speech Breathing Disorders
3 LARYNGEAL FUNCTION AND SPEECH PRODUCTION
Fundamentals of Laryngeal Function
Anatomy of the Laryngeal Apparatus
Forces and Movements of the Laryngeal Apparatus
Forces of the Laryngeal Apparatus
Movements of the Laryngeal Apparatus
Adjustments of the Laryngeal Apparatus
Abduction of the Vocal Folds
Adduction of the Vocal Folds
Changing the Length of the Vocal Folds
Changing the Position and/or Configuration of the Ventricular Folds
Changing the Position and/or Configuration of the Epiglottis
Changing the Position of the Laryngeal Housing
Control Variables of Laryngeal Function
Laryngeal Opposing Pressure
Laryngeal Airway Resistance
Glottal Size and Configuration
Stiffness of the Vocal Folds
Effective Mass of the Vocal Folds
Neural Substrates of Laryngeal Control
Degree of Coupling Between the Trachea and Pharynx
Protection of the Pulmonary Airways
Containment of the Pulmonary Air Supply
Laryngeal Function in Speech Production
Turbulence Noise Production
Running Speech Activities
Sound Pressure Level
Development and Laryngeal Function in Speech Production
Age and Laryngeal Function in Speech Production
Sex and Laryngeal Function in Speech Production
Measurement of Laryngeal Function
Laryngeal Disorders and Speech Production
Clinical Professionals and Laryngeal Disorders in Speech Production
4 VELOPHARYNGEAL-NASAL FUNCTION AND SPEECH PRODUCTION
Fundamentals of Velopharyngeal-Nasal Function
Anatomy of the Velopharyngeal-Nasal Apparatus
Forces and Movements of the Velopharyngeal-Nasal Apparatus
Forces of the Velopharyngeal-Nasal Apparatus
Movements of the Velopharyngeal-Nasal Apparatus
Adjustments of the Velopharyngeal-Nasal Apparatus
Coupling Between the Oral and Nasal Cavities
Coupling Between the Nasal Cavities and Atmosphere
Control Variables of Velopharyngeal-Nasal Function
Velopharyngeal-Nasal Airway Resistance
Velopharyngeal Sphincter Compression
Velopharyngeal-Nasal Acoustic Impedance
Neural Substrates of Velopharyngeal-Nasal Control
Ventilation and Velopharyngeal-Nasal Function
Nasal Valve Modulation
Nasal Cycling (Side-to-Side)
Velopharyngeal-Nasal Function and Speech Production
Velopharyngeal-Nasal Function and Sustained Utterances
Velopharyngeal-Nasal Function and Running Speech Activities
Gravity and Velopharyngeal-Nasal Function in Speech Production
Development of Velopharyngeal-Nasal Function in Speech Production
Age and Velopharyngeal-Nasal Function in Speech Production
Sex and Velopharyngeal-Nasal Function in Speech Production
Measurement of Velopharyngeal-Nasal Function
Velopharyngeal-Nasal Disorders and Speech Production
Clinical Professionals and Velopharyngeal-Nasal Disorders in Speech Production
5 PHARYNGEAL-ORAL FUNCTION AND SPEECH PRODUCTION
Fundamentals of Pharyngeal-Oral Function
Anatomy of the Pharyngeal-Oral Apparatus
Temporomandibular Joint Movements
Forces and Movements of the Pharyngeal-Oral Apparatus
Forces of the Pharyngeal-Oral Apparatus
Movements of the Pharyngeal-Oral Apparatus
Adjustments of the Pharyngeal-Oral Apparatus
Adjustments of the Pharynx
Adjustments of the Mandible
Adjustments of the Tongue
Adjustments of the Lips
Control Variables of Pharyngeal-Oral Function
Pharyngeal-Oral Lumen Size and Configuration
Pharyngeal-Oral Structural Contact Pressure
Pharyngeal-Oral Airway Resistance
Pharyngeal-Oral Acoustic Impedance
Neural Substrates of Pharyngeal-Oral Control
Degree of Coupling Between the Oral Cavity and Atmosphere
Sound Generation and Filtering
Pharyngeal-Oral Function in Speech Production
The Speech Production Code
The Speech Production Stream
A Primer on Theories of Speech Production
Traditional Theory of Feature Spreading
Articulatory Phonology or Gesture Theory
Development and Pharyngeal-Oral Function in Speech Production
Age and Pharyngeal-Oral Function in Speech Production
Sex and Pharyngeal-Oral Function in Speech Production
Measurement of Pharyngeal-Oral Function
X-Ray Microbeam Imaging
Magnetic Resonance Imaging
Pharyngeal-Oral Disorders and Speech Production
Clinical Professionals and Pharyngeal-Oral Disorders in Speech Production
6 BRAIN STRUCTURES AND MECHANISMS FOR SPEECH, LANGUAGE, AND HEARING
The Nervous System: An Overview and Concepts
Central Versus Peripheral Nervous System
Anatomical Planes and Directions
White Versus Gray Matter, Tracts Versus Nuclei, Nerves Versus Ganglia
Gray Matter and Nuclei
White Matter and Fiber Tracts
Efferent and Afferent
Lateralization and Specialization of Function
Cerebral Hemispheres and White Matter
Limbic System (Limbic Lobe)
Cerebral White Matter
Descending Projection Tracts
Ascending Projection Tracts
Subcortical Nuclei and Cerebellum
Cerebellum and Basal Ganglia: New Concepts
Brainstem and Cranial Nerves
Surface Features of the Brainstem: Ventral View
Ventral Surface of Midbrain
Ventral Surface of Pons
Ventral Surface of Medulla
Surface Features of the Brainstem: D orsal View
Dorsal Surface of Midbrain
Dorsal Surface of Pons
Dorsal Surface of Medulla
Cranial Nerves and Associated Brainstem Nuclei
Cranial Nerve I (Olfactory)
Cranial Nerve II (Optic)
Cranial Nerve III (Oculomotor)
Cranial Nerve IV (Trochlear)
Cranial Nerve V (Trigeminal)
Cranial Nerve VI (Abducens)
Cranial Nerve VII (Facial)
Cranial Nerve VIII (Auditory-Vestibular Nerve)
Cranial Nerve IX (Glossopharyngeal)
Cranial Nerve X (Vagus)
Cranial Nerve XI (Spinal Accessory Nerve)
Cranial Nerve XII (Hypoglossal)
Cortical Innervation Patterns
Why These Innervation Patterns Matter
The Cranial Nerve Exam and Speech Production
Spinal Cord and Spinal Nerves
Nervous System Cells
Cell Body (Soma)
Axon and Terminal Button
Resting Potential, Action Potential, and Neurotransmitters
Synaptic Transmission and Neurotransmitters
Meninges, Ventricles, Blood Supply
Meninges and Clinically-Relevant Spaces
Cerebral Aqueduct, Fourth Ventricle, and Other Passageways for CSF
Production, Composition, and Circulation of CSF
Blood Supply of Brain
Circle of Willis
MCA and Blood Supply to the Dominant Hemisphere
Speech and Language Functions of the Brain: Possible Sites and Mechanisms
DIVA: Speech Sound Map (IvPMC)
DIVA: Articulatory Velocity/Position Maps (PMC)
DIVA: Auditory and Somatosensory Processing: Parietal Cortex and Frontal-Parietal Association Tracts
DIVA: Where is Aphasia, Where are Dysarthria Types?
The Motions of Vibrating Air Molecules Are Governed by Simple Forces
The Motions of Vibrating Air Molecules Change the Local Densities of Air
Pressure Waves, Not Individual Molecules, Propagate Through Space and Vary as a Function of Both Space and Time
The Variation of a Pressure Wave in Time and Space Can be Measured
Pressure Waves: A Summary and Introduction of Sinusoids
Sinusoidal Motion (Simple Harmonic Motion) Is Derived from the Linear Projection of Uniform Circular Speed
When the Linear Projection of Uniform Circular Speed Is Stretched Out in Time, the Result is a Sine Wave
Sinusoidal Motion Can Be Described by a Simple Formula, and Has Three Important Characteristics: Frequency, Amplitude, and Phase
Sinusoidal Motion: A Summary
Complex Acoustic Events
Complex Periodic Events Have Waveforms That Repeat Their Patterns Over Time, and Frequency Components That Are Harmonically Related
A Complex Periodic Waveform Can Be Considered as the Sum of the Individual Sinusoids at the Harmonic Frequencies
Complex Aperiodic Events Have Waveforms in Which No Repetitive Pattern Can Be Discerned, and Frequency Components That Are Not Harmonically Related
Complex Acoustic Events: Summary
A Simple Spring-Mass Model Can Be Used to Explain the Concept of Resonance
The Relative Values of Mass (M) and Elasticity (K) Determine the Frequency of
Vibration of the Simple Spring-Mass Model
The Effects of Mass and Stiffness (Elasticity) on a Resonant System: A Summary
Acoustic Resonance: Helmholtz Resonators
The Neck of the Helmholtz Resonator Contains a Column, or Plug of Air, That Behaves Like a Mass When a Force Is Applied to It
The Bowl of a Resonator Contains a Volume of Air That Behaves Like a Spring When a Force is Applied to It
Acoustic Resonance: Tube Resonators
Resonance in Tubes: A Summary
Resonance Curves, Damping, and Bandwidth
Energy Loss (Damping) in Vibratory Systems Can Be Attributed to Four Factors
Time- and Frequency-Domain Representations of Damping in Acoustic Vibratory Systems
An Extension of the Resonance Curve Concept: The Shaping of a Source by the Acoustic Characteristics of a Resonator
Resonance, Damping, and Bandwidth: A Summary
8 ACOUSTIC THEORY OF VOWEL PRODUCTION
What Is the Precise Nature of the Input Signal Generated by the Vibrating Vocal Folds?
The Time Domain
The Frequency Domain
The Periodic Nature of the Waveform
The Shape of the Waveform
The Ratio of Open Time to Closed Time
Nature of the Input Signal: A Summary
Why Should the Vocal Tract Be Conceptualized as a Tube Closed at One End?
The Response of the Vocal Tract to Excitation
How Are the Acoustic Properties of the Vocal Tract Determined?
Area Function of the Vocal Tract
How Does the Vocal Tract Shape the Input Signal? (How Is the Source Spectrum Combined with the Theoretical Vocal Tract Spectrum to Produce a Vocal Tract Output?)
Acoustic Theory of Vowel Production: A Summary
What Happens to the Resonant Frequencies of the Vocal Tract When the Tube Is Constricted at a Given Location?
The Three-Parameter Model of Stevens and House
Configuration of the Lips
Importance of the Stevens and House Rules: A Summary
The Connection Between the Stevens and House Rules and Perturbation Theory
Why Are the Stevens and House Rules Important?
Another Take on the Relationship Between Vocal Tract Configuration and Vocal Tract Resonances
Confirmation of the Acoustic Theory of Vowel Production
9 THEORY OF CONSONANT ACOUSTICS
Why Is the Acoustic Theory of Speech Production Most Accurate and Straightforward for Vowels?
What Are the Acoustics of Coupled (Shunt) Resonators, and How Do They Apply to
Energy Loss in the Nasal Cavities, Antiresonances, and the Relative Amplitude of Nasal Murmurs
Nasal Murmurs: A Summary
Nasalization: A Summary
The Importance of Understanding Nasalization
Coupled (Shunt) Resonators in the Production of Lateral Sounds
Coupled (Shunt) Resonators in the Production of Obstruent Sounds
What is the Theory of Fricative Acoustics?
Fluid Flow in Pipes and Source Types
Aeromechanic/Acoustic Effects in Fricatives: A Summary
A Typical Fricative Waveform and Its Aeromechanical Correlates
Mixed Sources in Fricative Production
Shaping of Fricative Sources by Vocal Tract Resonators
Measurement of Fricative Acoustics
The Acoustic Theory of Fricatives: A Summary
What is the Theory of Stop Acoustics?
Intervals of Stop Consonant Articulation: Aeromechanics and Acoustics
Closure (Silent) Interval
Release (Burst) Interval
Frication and Aspiration Intervals
Shaping of Stop Sources by Vocal Tract Resonators
The Nature of Stop Sources
The Shaping of Stop Sources
Measurement of Stop Acoustics
Stop Consonants: A Summary
What Is the Theory of Affricate Acoustics?
What Kinds of Acoustic Contrasts Are Associated with the Voicing Distinction in Obstruents?
10 SPEECH ACOUSTIC ANALYSIS
A Brief Historical Prelude
The Original Sound Spectrograph: History and Technique
The Original Sound Spectrograph: Summary
Interpretation of Spectrograms: Specific Features
Silent Intervals and Stop Bursts
Segmentation of Spectrograms
Speech Acoustics is Not All About Segments: Suprasegmentals
Digital Techniques for Speech Analysis
Speech Analysis by Computer: From Recording to Analysis to Output
Sampling Rate Sidebar: Anti-Aliasing Filters
Analysis and Display
11 ACOUSTIC PHONETICS DATA
Vowel Acoustics, Dialect, and a Multicultural View of Acoustic Phonetics
Within-Speaker Variability in Formant Frequencies
Summary of Vowel Formant Frequencies
A Brief Note on Vowel Formant Frequencies Versus Formant Trajectories
Intrinsic Vowel Durations
Extrinsic Factors Affecting Vowel Durations
Utterance Position Effects
Formant Transitions and Fricative Distinctions
Closure Interval and Burst
Closure Duration and Place of Articulation
Stop Voicing: Some Further Considerations
Acoustic Invariance and Theories of Speech Perception
Acoustic Invariance at the Interface of Speech Production and Perception
Acoustic Characteristics of Prosody
Phrase-level F0 Contours
Phrase-level Intensity Contours
12 SPEECH PERCEPTION
Early Speech Perception Research and Categorical Perception
The /ba/-/da/-/ga/ Experiment
Categorical Perception: Some General Considerations
Labeling Versus Discrimination
Categorical Perception: So What?
Speech Perception Is Species Specific
Categorical Perception of Stop Place of Articulation Shows the Match to Speech Production
The Competition: General Auditory Explanations of Speech Perception
Sufficient Acoustic Invariance
Replication of Speech Perception Effects Using Nonspeech Signals
Animal and Infant Perception of Speech Signals
The Competition: D irect Realism
A Tentative Summary
Speech Perception and Word Recognition
Why Should Speech-Language Pathologists Care About Speech Perception?
Explanatory Speech Intelligibility Tests
Scaled Speech Intelligibility
Breathing, Laryngeal, Velopharyngeal-Nasal, and Pharyngeal-Oral Structures
Forces and Movements of Swallowing
Oral Preparatory Phase
Oral Transport Phase
Pharyngeal Transport Phase
Esophageal Transport Phase
Overlap of Phases
Breathing and Swallowing
Neural Control of Swallowing
Role of the Peripheral Nervous System in Swallowing
Role of the Central Nervous System in Swallowing
Variables that Influence Swallowing
Bolus Characteristics and Swallowing
Taste and Temperature
Single Versus Sequential Swallows
Cued Versus Uncued Swallows
Body Position and Swallowing
Development and Swallowing
Age and Swallowing
Sex and Swallowing
Measurement of Swallowing
Clinical Professionals and Swallowing Disorders
About The Authors
Thomas J. Hixon, PhD, CCC-SLP (1940-2009) received his PhD from the University of Iowa and did postdoctoral work in physiology at Harvard University. He was Professor Emeritus of Speech, Language, and Hearing Sciences and Dean Emeritus of the Graduate College at the University of Arizona and had been Head of the Department of Speech, Language, and Hearing Sciences, Director of the National Center for Neurogenic Communication Disorders, Director of Graduate Interdisciplinary Programs, Director of the Movement Neuroscience Program, Research Integrity Officer, and Associate Vice President for Research at the same institution. Dr. Hixon was a Fellow of the American Speech-Language-Hearing Association and was awarded Honors of the Association, the Council of Editors Award, two Journal Editors Awards from the Association for the outstanding article of the year, and a Career Teaching Award from the University of Arizona. Dr. Hixon served as Editor of the Journal of Speech and Hearing Research, Speech Section Editor of the Journal of Speech, Language, and Hearing Research, and an editorial reviewer and/or Associate Editor to over a dozen other speech and voice journals. His research interests centered on normal and abnormal speech production and the biomechanics of singing.
Gary Weismer, PhD, is Oros-Bascom Professor Emeritus in the Department of Communication Sciences & Disorders, University of Wisconsin-Madison. He received his bachelors and masters degrees from the Pennsylvania State University, and his doctorate from UW-Madison in 1975. Dr. Weismers research publications concern speech production in healthy talkers, and speech production and intelligibility phenomena in persons with motor speech disorders. Dr. Weismer served twice as Associate Editor for the Journal of Speech, Language, and Hearing Research (formerly the Journal of Speech and Hearing Research), as Associate Editor at Folia Phoniatrica et Logopaedica (FPL) from 1994-2011, and as Editor-in-Chief at FPL from 2011-2016. During his 35 years at UW-Madison Dr. Weismer won several teaching awards, including for mentoring efforts in the UW-Madison Honors program. Dr. Weismer mentored 16 doctoral students during his career, many of whom are currently scientific leaders and university administrators. He is a past member of the Executive Board of the International Association of Logopedics and Phoniatrics, a Fellow of the Acoustical Society of America, and past Chair of his department. His research was supported by NIH for more than 25 years.
Jeannette D. Hoit, PhD, is Professor in the Department of Speech, Language, and Hearing Sciences at the University of Arizona and a speech-language pathologist. Dr. Hoit received her BA in Anthropology from University of California at Los Angeles, her MA in Communicative Disorders from San Diego State University, her PhD in Speech and Hearing Sciences from the University of Arizona, and she pursued postdoctoral study in the Harvard School of Public Health Respiratory Biology Program and the Massachusetts Institute of Technology Speech Research Laboratory. Dr. Hoits research focuses on speech physiology, with an emphasis on normal aging and development, neuromotor speech disorders, and respiratory function and dysfunction. Dr. Hoit is a past and current editor of the American Journal of Speech-Language Pathology, a Fellow of the American Speech-Language-Hearing Association, and past president of the American Association of Phonetic Sciences. She has received a Distinguished Alumnus Award from San Diego State University and several teaching and mentoring awards from the University of Arizona.
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INSTRUCTORS: IF YOU HAVE ADOPTED THIS TEXTBOOK, YOU CAN REQUEST A COPY OF THE INSTRUCTOR'S CD WHICH COMES WITH ALL IMAGES IN THE BOOK PLACED AS SEPARATE SLIDES IN POWERPOINT. Send an email to firstname.lastname@example.org. Please give your course adoption information (course number, course name, semester, and number of students).