Today physicists and mathematicians throughout the world are feverishly working on one of the most ambitious theories ever proposed: superstring theory. String theory, as it is often called, is the key to the Unified Field Theory that eluded Einstein for more than thirty years. Finally, the century-old antagonism between the large and the small-General Relativity and Quantum Theory-is resolved. String theory proclaims that all of the wondrous happenings in the universe, from the frantic dancing of subatomic quarks to the majestic swirling of heavenly galaxies, are reflections of one grand physical principle and manifestations of one single entity: microscopically tiny vibrating loops of energy, a billionth of a billionth the size of an atom. In this brilliantly articulated and refreshingly clear book, Greene relates the scientific story and the human struggle behind twentieth-century physics' search for a theory of everything.
Through the masterful use of metaphor and analogy, The Elegant Universe makes some of the most sophisticated concepts ever contemplated viscerally accessible and thoroughly entertaining, bringing us closer than ever to understanding how the universe works.
Radiation: What could go wrong? In short, plenty. From Marie Curie carrying around a vial of radium salt because she liked the pretty blue glow to the large-scale disasters at Chernobyl and Fukushima, dating back to the late nineteenth century, nuclear science has had a rich history of innovative exploration and discovery, coupled with mistakes, accidents, and downright disasters.
In this lively book, long-time advocate of continued nuclear research and nuclear energy James Mahaffey looks at each incident in turn and analyzes what happened and why, often discovering where scientists went wrong when analyzing past meltdowns. Every incident, while taking its toll, has led to new understanding of the mighty atom—and the fascinating frontier of science that still holds both incredible risk and great promise.
If you ever regretted not taking physics in college--or simply want to know how to think like a physicist--this is the book for you. In this bestselling introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Challenging, lucid, and concise, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.
“The amazing story of an unbelievable boy . . . The world that opens up to us through his story is both fascinating and slightly terrifying . . . but in a good way. You won’t be able to walk away from this tale.” — Elizabeth Gilbert, author of Eat, Pray, Love
“Imagine if cartoon whiz kid Jimmy Neutron were real and had a brainchild with MacGyver and his adolescence got told as a rollicking bildungsroman about American prodigies and DIY nuclear reactors—well, that’s this book.” —Jack Hitt, author of Bunch of Amateurs
By the age of nine, Taylor Wilson had mastered the science of rocket propulsion. At eleven, his grandmother’s cancer diagnosis inspired him to investigate new ways to produce medical isotopes. And by fourteen, Wilson had built a 500-million-degree reactor and become the youngest person in history to achieve nuclear fusion. How could someone so young achieve so much, and what can Wilson’s story teach parents and teachers about how to support high-achieving kids?
In The Boy Who Played with Fusion, science journalist Tom Clynes narrates Taylor’s extraordinary journey—from his Arkansas home, to a unique public high school just for academic superstars, to the present, when Wilson is designing devices to prevent terrorists from shipping radioactive material and inspiring a new generation to take on the challenges of science.
“Clynes guides us on an engrossing journey to the outer realms of science and parenting. The Boy Who Played with Fusion is a fascinating exploration of ‘giftedness’ and all its consequences.” —Paul Greenberg, author of Four Fish and American Catch
“An essential contribution to our understanding of the most important underlying questions about the development of giftedness, talent, creativity, and intelligence.” —Psychology Today
"What time is it?" That simple question is probably asked more often in contemporary society than ever before. In our clock-studded world, the answer is never more than a glance away, and so we can blissfully partition our days into ever smaller increments for ever more tightly scheduled tasks. Modern scientific revelations about time, however, make the question endlessly frustrating. If we seek a precise knowledge of the time, the infinitesimal flash of now dissolves into a scattering flock of nanoseconds. Because we are bound by the speed of light and the velocity of nerve impulses, our perception of the "present" reflects the world as it occurred an instant ago – for all that human consciousness pretends otherwise, we can never catch up. Even in principle, perfect synchronicity escapes us. Relativity dictates that, like a strange syrup, time flows slower on moving trains than in the stations and faster in the mountains than in the valleys. The time for our wristwatch is not exactly the same as the time for our head. This eBook, A Question of Time, summarizes what science has discovered about how time permeates and guides both our physical world and our inner selves. That knowledge should enrich the imagination and provide practical advantages to anyone hoping to beat the clock, or at least to stay in step with it. Synchronize your watches...
Now updated with 30% new material, Roark Formulas for Stress and Strain, Seventh Edition, is the ultimate resource for designers, engineers, and analysts who need to calculate loads and stress. This landmark reference from Warren Young and Richard Budynas provides you with equations and diagrams of structural properties in an easy-to-use, thumb-through format. Updated, with a user-friendly page layout, this new edition includes expanded coverage of joints, bearing and shear stress, experimental stress analysis, and stress concentrations, as well as material behavior coverage and stress and strain measurement. You’ll also find expanded tables and cases; improved notations and figures in the tables; consistent table and equation numbering; and verification of correction factors.
In The Radioactive Boy Scout, veteran journalist Ken Silverstein recreates in brilliant detail the months of David’s improbable nuclear quest. Posing as a physics professor, David solicited information on reactor design from the U.S. government and from industry experts. (Ironically, the Nuclear Regulatory Commission was his number one source of information.) Scavenging antiques stores and junkyards for old-fashioned smoke detectors and gas lanterns—both of which contain small amounts of radioactive material—and following blueprints he found in an outdated physics textbook, David cobbled together a crude device that threw off toxic levels of radiation. His unsanctioned and wholly unsupervised project finally sparked an environmental catastrophe that put his town’s forty thousand residents at risk and caused the EPA to shut down his lab and bury it at a radioactive dumpsite in Utah.
An outrageous account of ambition and, ultimately, hubris that sits comfortably on the shelf next to such offbeat science books as Driving Mr. Albert and stories of grand capers like Catch Me If You Can, The Radioactive Boy Scout is a real-life adventure with the narrative energy of a first-rate thriller.
From the Hardcover edition.
In telling the story of what is perhaps the most anticipated experiment in the history of science, Amir D. Aczel takes us inside the control rooms at CERN at key moments when an international team of top researchers begins to discover whether this multibillion-euro investment will fulfill its spectacular promise. Through the eyes and words of the men and women who conceived and built CERN and the LHC—and with the same clarity and depth of knowledge he demonstrated in the bestselling Fermat’s Last Theorem—Aczel enriches all of us with a firm grounding in the scientific concepts we will need to appreciate the discoveries that will almost certainly spring forth when the full power of this great machine is finally unleashed.
Will the Higgs boson make its breathlessly awaited appearance, confirming at last the Standard Model of particles and their interactions that is among the great theoretical achievements of twentieth-century physics? Will the hidden dimensions posited by string theory be revealed? Will we at last identify the nature of the dark matter that makes up more than 90 percent of the cosmos? With Present at the Creation, written by one of today’s finest popular interpreters of basic science, we can all follow the progress of an experiment that promises to greatly satisfy the curiosity of anyone who ever concurred with Einstein when he said, “I want to know God’s thoughts—the rest is details.”
From the Hardcover edition.
Beginning with simple theoretical models and experimental techniques, the book develops the complete repertoire of theoretical principles and experimental techniques necessary for understanding and implementing the most sophisticated NMR experiments.
Important new techniques and applications of NMR spectroscopy have emerged since the first edition of this extremely successful book was published in 1996. This updated version includes new sections describing measurement and use of residual dipolar coupling constants for structure determination, TROSY and deuterium labeling for application to large macromolecules, and experimental techniques for characterizing conformational dynamics. In addition, the treatments of instrumentation and signal acquisition, field gradients, multidimensional spectroscopy, and structure calculation are updated and enhanced.
The book is written as a graduate-level textbook and will be of interest to biochemists, chemists, biophysicists, and structural biologists who utilize NMR spectroscopy or wish to understand the latest developments in this field.Provides an understanding of the theoretical principles important for biological NMR spectroscopyDemonstrates how to implement, optimize and troubleshoot modern multi-dimensional NMR experimentsAllows for the capability of designing effective experimental protocols for investigations of protein structures and dynamicsIncludes a comprehensive set of example NMR spectra of ubiquitin provides a reference for validation of experimental methods
Drawing on physics and mechanical engineering, Steven Vogel looks at how animals swim and fly, modes of terrestrial locomotion, organism responses to winds and water currents, circulatory and suspension-feeding systems, and the relationship between size and mechanical design. He also investigates links between the properties of biological materials--such as spider silk, jellyfish jelly, and muscle--and their structural and functional roles. Early chapters and appendices introduce relevant physical variables for quantification, and problem sets are provided at the end of each chapter. Comparative Biomechanics is useful for physical scientists and engineers seeking a guide to state-of-the-art biomechanics. For a wider audience, the textbook establishes the basic biological context for applied areas--including ergonomics, orthopedics, mechanical prosthetics, kinesiology, sports medicine, and biomimetics--and provides materials for exhibit designers at science museums.Problem sets at the ends of chapters Appendices cover basic background information Updated and expanded documentation and materials Revised figures and text Increased coverage of friction, viscoelastic materials, surface tension, diverse modes of locomotion, and biomimetics
Helps Students Better Understand Numerical Methods through Use of MATLAB®
The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions.
All the Material Needed for a Numerical Analysis Course
Based on the authors’ own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. Students can download MATLAB code from www.crcpress.com, enabling them to easily modify or improve the codes to solve their own problems.
The most valuable and reader-friendly reference available for engineers concerned with the optimization of liquid transportation through pipelines
About the authors . . .
D. M. PIRRO is the Equipment Builder and OEM Manager, ExxonMobil Corporation, Fairfax, Virginia. The author or contributing editor of several scholarly articles on synthetic lubes, environmental awareness applications, grease technology, lubricant interchangeability, and oil analysis, Mr. Pirro is a Certified Lubrication Specialist and a member of the Society of Tribologists and Lubrication Engineers and the Association of Manufacturing Technology. He received the B.S. degree (1978) in mechanical engineering and the B.A. degree (1978) in business administration from Rutgers University, New Brunswick, New Jersey.
A. A. WESSOL is a part-time Lubrication Consultant for the ExxonMobil Corporation in Manassas, Virginia. Mr. Wessol retired from the Mobil Corporation after 24 years in various advanced technical positions. The author or coauthor of numerous professional papers on the environmental aspects of lubrication, plant engineering, hydraulics, and pneumatics, he received the B.S. degree (1972) in mathematics, physics, and chemistry from the University of Pittsburgh, Pennsylvania.
The movements of each of the 507 mechanisms are depicted in drawings on the left-hand page, and the facing page presents a brief description of the item's use and operation. Ranging from simple to intricately complex, the mechanisms offer a fascinating view of the variety of small components that constitute complex machinery. A detailed index provides easy reference to specific mechanisms.
Inventors, tinkerers, and anyone with an interest in the history of invention and technology will find this volume a treasury of information and inspiration.
Reviews of the First Edition
“For anyone wishing to know what really goes on in their NMR experiments, I would highly recommend this book” – Chemistry World
“…I warmly recommend for budding NMR spectroscopists, or others who wish to deepen their understanding of elementary NMR theory or theoretical tools” – Magnetic Resonance in Chemistry
It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived.
As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.
Taking the bang-whiz-thud approach, Denny first talks about internal ballistics—Bang!—from before gunpowder to the development of modern firearms. External ballistics—Whiz!—are next, with discussions about short- and long-range trajectories. Denny’s lesson ends with a Thud!—an explanation of terminal ballistics.
Throughout, Denny conveys applicable physics principles in a way that will appeal to technology buffs and ballistics enthusiasts alike. His fun and factual explanations are free of complicated equations; notes cover the key aspects of ballistics physics for the more technically inclined.
Denny has perfected this engaging balance of science and story. For study or hobby, Their Arrows Will Darken the Sun is an entertaining guide to the world of ballistics.
* The first reference work on named reactions to present colored schemes for easier understanding
* 250 frequently used named reactions are presented in a convenient two-page layout with numerous examples
* An opening list of abbreviations includes both structures and chemical names
* Contains more than 10,000 references grouped by seminal papers, reviews, modifications, and theoretical works
* Appendices list reactions in order of discovery, group by contemporary usage, and provide additional study tools
* Extensive index quickly locates information using words found in text and drawings
Finite Element Modeling and Simulation with ANSYS Workbench combines finite element theory with real-world practice. Providing an introduction to finite element modeling and analysis for those with no prior experience, and written by authors with a combined experience of 30 years teaching the subject, this text presents FEM formulations integrated with relevant hands-on applications using ANSYS Workbench for finite element analysis (FEA). Incorporating the basic theories of FEA and the use of ANSYS Workbench in the modeling and simulation of engineering problems, the book also establishes the FEM method as a powerful numerical tool in engineering design and analysis.
Include FEA in Your Design and Analysis of Structures Using ANSYS Workbench
The authors reveal the basic concepts in FEA using simple mechanics problems as examples, and provide a clear understanding of FEA principles, element behaviors, and solution procedures. They emphasize correct usage of FEA software, and techniques in FEA modeling and simulation. The material in the book discusses one-dimensional bar and beam elements, two-dimensional plane stress and plane strain elements, plate and shell elements, and three-dimensional solid elements in the analyses of structural stresses, vibrations and dynamics, thermal responses, fluid flows, optimizations, and failures. Contained in 12 chapters, the text introduces ANSYS Workbench through detailed examples and hands-on case studies, and includes homework problems and projects using ANSYS Workbench software that are provided at the end of each chapter.Covers solid mechanics and thermal/fluid FEA Contains ANSYS Workbench geometry input files for examples and case studies Includes two chapters devoted to modeling and solution techniques, design optimization, fatigue, and buckling failure analysis Provides modeling tips in case studies to provide readers an immediate opportunity to apply the skills they learn in a problem-solving context
Finite Element Modeling and Simulation with ANSYS Workbench benefits upper-level undergraduate students in all engineering disciplines, as well as researchers and practicing engineers who use the finite element method to analyze structures.
Dynamics of Mechanical Systems provides a vehicle for mastering all of this. Focusing on the fundamental procedures behind dynamic analyses, the authors take a vector-oriented approach and lead readers methodically from simple concepts and systems through the analysis of complex robotic and bio-systems. A careful presentation that balances theory, methods, and applications gives readers a working knowledge of configuration graphs, Euler parameters, partial velocities and partial angular velocities, generalized speeds and forces, lower body arrays, and Kane's equations.
Evolving from more than three decades of teaching upper-level engineering courses, Dynamics of Mechanical Systems enables readers to obtain and refine skills ranging from the ability to perform insightful hand analyses to developing algorithms for numerical/computer analyses. Ultimately, it prepares them to solve real-world problems and make future advances in mechanisms, manipulators, and robotics.
Helping you overcome these hurdles, Hydraulic Power System Analysis demonstrates modern computer-aided analytical techniques used to model nonlinear, dynamic fluid power systems. Following an overview of fluid power, the authors examine various relevant fluid properties, energy calculations, and steady state and dynamic analysis along with a review of automatic control theory. Turning to modeling, the next few chapters address valves and motors and then apply dynamic modeling to examples relating to pumps, hydrostatic transmissions, and valves. The book includes a unique chapter showing how to combine flow resistance equations with the differential equations governing dynamic system performance. The final chapter translates electrical circuit theory concepts to noise attenuation in fluid power systems.
Illustrated with many equations, practical computer modeling examples, and exercises, Hydraulic Power System Analysis provides a much-needed modernization of dynamic modeling for fluid power systems using powerful computational tools.
Chapter 1 of this book deals with the extraordinary physico-chemical properties of the water molecule while Chapter 2 provides insight on theories regarding the origin of water on Earth. In the third chapter, the author focuses on the chemical composition of the main water reservoirs of our planet. Chapters 4 and 5 discuss water’s relationship with plate tectonics and life, respectively. The sixth and final chapter uses stable isotope tracking to look into the water cycle and past climates.
1. Water: A Molecule Endowed with Extraordinary Physicochemical Properties.
2. Theories about the Origin of Water on Earth.
3. The Main Water Reservoirs on Earth and their Chemical Composition.
4. Water and Plate Tectonics.
5. Water and Life.
6. Stable Isotope Tracking: Water Cycles and Climates of the Past.
The presence of water on Earth is discussed on the basis of the various theories about its origin such as a massive degassing of the primitive parent bodies that built our planet as well as a late addition from comets that collided with its surface. The extraordinary physico-chemical properties of the water molecule combined with its abundance and distribution over the Earth’s surface have contributed to regulating the global climate and favoring the evolution of species for more than 4 billion years. The early emergence of life in the deep ocean and its further diversification were closely linked to the global water cycle whose dynamics result from the energy balance between solar radiation and the internal heat flux of the Earth.
Infrared (IR) Spectroscopy deals with the infrared part of the electromagnetic spectrum. It measure the absorption of different IR frequencies by a sample positioned in the path of an IR beam. Currently, infrared spectroscopy is one of the most common spectroscopic techniques used in the food industry. With the rapid development in infrared spectroscopic instrumentation software and hardware, the application of this technique has expanded into many areas of food research. It has become a powerful, fast, and non-destructive tool for food quality analysis and control.
Infrared Spectroscopy for Food Quality Analysis and Control reflects this rapid technology development. The book is divided into two parts. Part I addresses principles and instruments, including theory, data treatment techniques, and infrared spectroscopy instruments. Part II covers the application of IRS in quality analysis and control for various foods including meat and meat products, fish and related products, and others.
*Explores this rapidly developing, powerful and fast non-destructive tool for food quality analysis and control
*Presented in two Parts -- Principles and Instruments, including theory, data treatment techniques, and instruments, and Application in Quality Analysis and Control for various foods making it valuable for understanding and application
*Fills a need for a comprehensive resource on this area that includes coverage of NIR and MVA
Principle, experimental set ups, parameters and interpretation rules of several advanced IR-based techniques; application to biointerface characterisation through the presentation of recent examples, will be given in this book. It will describe how to characterise amino acids, protein or bacterial strain interactions with metal and oxide surfaces, by using infrared spectroscopy, in vacuum, in the air or in an aqueous medium. Results will highlight the performances and perspectives of the technique.Description of the principles, expermental setups and parameter interpretation, and the theory for several advanced IR-based techniques for interface characterisationContains examples which demonstrate the capacity, potential and limits of the IR techniquesHelps finding the most adequate mode of analysisContains examplesContains a glossary by techniques and by keywords
A discussion is then presented on carbon-13 NMR, detailing its pros and cons and showing how it can be used in conjunction with proton NMR via the pivotal 2-D techniques (HSQC and HMBC) to yield vital structural information. Some of the more specialist techniques available are then discussed, i.e. flow NMR, solvent suppression, Magic Angle Spinning, etc. Other important nuclei are then discussed and useful data supplied. This is followed by a discussion of the neglected use of NMR as a tool for quantification and new techniques for this explained. The book then considers the safety aspects of NMR spectroscopy, reviewing NMR software for spectral prediction and data handling and concludes with a set of worked Q&As.
The coverage of the book includes 13 topics relevant to classical mechanics, such as integration of one-dimensional equations of motion; the Hamiltonian equations of motion; and adiabatic invariants.
The book will be of great use to physics students studying classical mechanics.
Divided into five parts, the book begins with discussions on group and field theories. The second part summarizes the standard model of particle physics and includes some extensions to the model, such as neutrino masses and CP violation. The next section focuses on grand unified theories and supersymmetry. The book then discusses the general theory of relativity, higher dimensional theories of gravity, and superstring theory. It also introduces various novel ideas and models with extra dimensions and low-scale gravity. The last part of the book deals with astroparticle physics. After an introduction to cosmology, it covers several specialized topics, including baryogenesis, dark matter, dark energy, and brane cosmology.
With numerous equations and detailed references, this lucid book explores the new physics beyond the standard model, showing that particle and astroparticle physics will together reveal unique insights in the next era of physics.
This book guides the reader through the mathematics, physics and practical techniques needed to use telescopes (from small amateur models to the larger instruments installed in many colleges) and to observe objects in the sky. Mathematics to around Advanced Placement standard (US) or A level (UK) is assumed, although High School Diploma (US) or GCSE-level (UK) mathematics plus some basic trigonometry will suffice most of the time. Most of the physics and engineering involved is described fully and requires no prior knowledge or experience.
This is a ‘how to’ book that provides the knowledge and background required to understand how and why telescopes work. Equipped with the techniques discussed in this book, the observer will be able to operate with confidence his or her telescope and to optimize its performance for a particular purpose. In principle the observer could calculate his or her own predictions of planetary positions (ephemerides), but more realistically the observer will be able to understand the published data lists properly instead of just treating them as ‘recipes.’ When the observer has obtained measurements, he/she will be able to analyze them in a scientific manner and to understand the significance and meaning of the results.
“Telescopes and Techniques, 3rd Edition” fills a niche at the start of an undergraduate astronomer’s university studies, as shown by it having been widely adopted as a set textbook. This third edition is now needed to update its material with the many new observing developments and study areas that have come into prominence since it was published. The book concentrates on the knowledge needed to understand how small(ish) optical telescopes function, their main designs and how to set them up, plus introducing the reader to the many ways in which objects in the sky change their positions and how they may be observed. Both visual and electronic imaging techniques are covered, together with an introduction to how data (measurements) should be processed and analyzed. A simple introduction to radio telescopes is also included. Brief coverage of the most advanced topics of photometry and spectroscopy are included, but mainly to enable the reader to see some of the developments possible from the basic observing techniques covered in the main parts of the book.
Mechanics Principles V10. eBook covers all the topics of this popular software title used in schools and colleges worldwide for over twenty years.
See Additional Notes for instructions to download the highly interactive PC software. Used in thousands of schools and colleges worldwide the software is designed to work as a traditional textbook on your PC screen.
Comprising hundreds of menu selected colourful topics where the graphic images (from your eBook) are brought to life for every value change along with many additional learning software features.
A combined eBook and educational software package at a tiny fraction of the previously published price.
Features of FREE Software (Incl. Physically Disabled Users) to accompany your eBook: Last published 2010 - All Windows platforms including Windows 8 - Hundreds of color fully interactive images where every value change updates the graphics and calculations - Explanatory text - Related topics are presented together in single windows - Default typical values - Full color printing single page with image for user values, text, calculations and graphs if part of topic - Copy & Paste (a feature that was used to construct all the accompanying eBook content) - Ideal for teachers making student hand-outs and assignments - Calculations and graphing widows open independently to check students calculations - Full screen whiteboard technology for whole class teaching (teachers packs eBooks and School Site Licence) - Self-Assessment questions with random values with multiple choice answers - Electronics and maths Toolbox (electronics and STEM titles) as used by professionals to quickly make all those standard calculations without having to remember the formula - For Business Studies Students there are additional features to interactively explore Break-Even charts and Supply & Demand curves - Drop down menus with topic search - Click forward and back through topics makes revision more enjoyable -Specialist Editors for equations, logic, graphs, statistics and algebra enable calculations and equations from any standard textbook to be inserted and explored changing just one value or variable at a time - BASIC programmer with full instructions to learn in minutes using statement wizards - For physically disabled users software can be operated independently of the keyboard using mouse clicks only or other voice, sight or wind activated pointing devices to choose topics and change values.
* Mechanics topics will be found in the software title Electrical, Mechanics and Maths V10 Educational Software package. Introduction, Basic Electronics, Conductors and Insulators, Resistor Value Test, Simple DC Circuits, Types of Switching, Variable Voltages, Ohm's Law, DC Voltage, DC Current, Series/Parallel Resistors, AC Measurements, AC Voltage and Current, AC Theory, RCL Series Circuits, RCL Parallel Circuits, Capacitance, Capacitors, Inductance, Inductors, Impedance, Circuit Theorems, Complex Numbers, DC Power, AC Power, Silicon Controlled Rectifier, Power Supplies, Voltage Regulation, Magnetism, Electric Machines, Transformers, Three Phase Systems, Energy Transfer and Cost, Atomic Structures, Diode Theory, Diode Applications, Transistor Theory, Bipolar Transistor, Transistor Configurations, Active Transistor Circuits, Field Effect Transistors, Analogue Multi-meter, Component Testing. Mathematics. Number Systems, Number Conversion, Number Types, Compound Measures, Roots, Angles and Parallels, Triangle Ratios, Triangle Angles, Percentages, Ratios, Fractions, Vectors, Laws, Algebra 0., Algebra 1., Algebra 2., Mathematical Rules, Powers and Indices, Simplifying, Linear Equations, Graphing, Slope and Translation, Curves and Angle Conversion, Personal Finance, Data Analysis.