We express the exponential function of an imaginary variable in terms of sine and cosine. The "complex exponentials" that result trace out a circle in the complex plane. Pointing to one of the positions in the complex plane, we obtain the identity exp(i pi) = -1.

In the first video segment, we introduce Euler's number by considering the problem of interest compounded continuously. After we obtain the power-series representation for exp(x), we explore its properties, in the next four video segments, to convince ourselves that exp(x) is literally an exponential function, meaning a number, approximately 2.71828, taken to the power x. In the final two segments, we present the natural logarithm and demonstrate that it is the anti-derivative of 1/x.

In the first video segment, we analyze the population dynamics for a test-tube of cells that affect each others' likelihoods of replication when they collide. The particular example we use is a prisoner's dilemma, which has the almost paradoxical property that survival of the relatively most fit leads overall fitness to decrease. In the second video segment, we suggest that the population dynamics from the first segment can be related to an analysis that uses payoff matrices found in traditional game theory.

Ontwerpen is een combinatie van logisch redeneren en het creatief combineren van bestaande technieken om tot nieuwe, innovatieve ideeen te komen. Een goede werktuigkundig ontwerper put zijn creativiteit uit kennis van een groot aantal bestaande werktuigbouwkundige systemen. Hoe groter die kennis, hoe groter de kans dat nieuwe, innovatieve ontwerpconcepten ontstaan. Vooral kennis over niet-conventionele techniek bevordert dit creatieve ontwerpproces.

Het doel van het vak Evolving Design is om studenten de onderhavige werkprincipes te tonen van een grote hoeveelheid niet-conventionele werktuigbouwkundige systemen. Er wordt hierbij zowel gekeken naar bijzondere ontdekkingen uit het verleden als uit het heden, met een blik op de toekomst. De ontwerpprincipes worden niet simpelweg opgesomd, maar geplaatst in hun fascinerende, historische ontwikkeling om te laten zien hoe de ontwerpers hun creativiteit en vernuft gebruik(t)en om goedwerkende oplossingen te vinden binnen de beperkingen van de beschikbare fabricageprocessen en beschermingsmogelijkheden (patenten). Veel oplossingen uit het verleden zijn klaar om te worden toegepast in de technologie van de toekomst!

Het vak richt zich primair op het kwalitatief beschrijven van de werkprincipes van bestaande technologieen, met de nadruk op bewegende mechanische constructies. Hoewel het kwantatief, in detail uitwerken van de kracht-bewegingsvergelijkingen niet het hoofddoel van het vak is, zijn mechanische vergelijkingen wel essentieel als zij leiden tot een beter begrip.

Financial institutions are a pillar of civilized society, supporting people in their productive ventures and managing the economic risks they take on. The workings of these institutions are important to comprehend if we are to predict their actions today and their evolution in the coming information age. The course strives to offer understanding of the theory of finance and its relation to the history, strengths and imperfections of such institutions as banking, insurance, securities, futures, and other derivatives markets, and the future of these institutions over the next century.

This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra.
All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile.
Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text.
Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.

The course "Fluid Flow, Heat and Mass Transfer," course number ta3220, is third-year BSc course in the program of Applied Earth Sciences at Delft University of Technology. Students in this class have already taken a course in "Transport Phenomena" in the second year, and "Fluid Flow Heat and Mass Transfer" is designed as a follow-up to that class, with an emphasis on topics of importance in applied earth sciences, and in particular to Petroleum Engineering, groundwater flow and mining.
In practice, however I start over again with first principles with this class, because the initial concepts of the shell balance are difficult for students to grasp and can always use a second time through. The course covers simple fluid mechanics problems (rectilinear flow) using shell balances, for Newtonian and power-law fluids and Bingham plastics. Turbulence for Newtonian fluids is covered in the context of friction factors for flow in pipes, flow around spheres and flow in packed beds.

This course covers the emergence of modern France. Topics include the social, economic, and political transformation of France; the impact of France's revolutionary heritage, of industrialization, and of the dislocation wrought by two world wars; and the political response of the Left and the Right to changing French society.

This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.

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Contributors on page 169. The licenses GPL, LGPL and GFDL are included in chapter Licenses on
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General Biology is intended to leave the student with an integrated view of the living world including the nature of sciences, evolution of biological organization, composition and organization of living substances, metabolism, control, reproduction, heredity and ecological relationships. This class meets the A.A. degree lab science requirement in the State of Washington.Login: guest_oclPassword: ocl

A three-quarter general chemistry sequence primarily for science, pre-professional, and engineering students. The CHEM& 161/162/163 series introduces the basic concepts of chemistry: atomic structure and bonding, periodicity, physical measurement, quantitative relationships, chemical reactivity, oxidation and reduction, stoichiometry, ideal gas laws, aqueous solutions, colligative properties, intermolecular forces, structure of matter, equilibrium, acid/base topics, kinetics, thermodynamics, electrochemistry, nuclear chemistry, qualitative analysis, d-block metals and coordination chemistry, and an introduction to organic chemistry.Login: guest_oclPassword: ocl

Geo-information has proven to be extremely helpful in many aspects of risk and disaster management: locational and situational awareness, monitoring of hazards, damage detection, sharing of information, defining vulnerability areas, etc. This course aims to provide knowledge on risk and disaster management activities, demonstrate use of geo-information technologies in emergency response, outline current challenges and motivate young geo-specialist to seek for advanced solutions. The course is organised as lectures and practicals. The practicals will be in the form of group assignments. Some excursions and guest lectures will be organised as well.

In the first part of this video, we review the idea of flat space and the Pythagorean theorem. The second part of the video reviews ideas from trigonometry including the unit circle, sine, cosine, and pi. We conclude with a proof of an angle-sum identity.

These materials include background for the instructor and a lab that engages student in an analysis of global inequality while learning and using the R language (a programming language for statistics). Students obtain data on the US and two other countries (one more developed and one less developed).

These materials include background for the instructor and a lab that engages student in an analysis of global inequality while learning and using the R language (a programming language for statistics). Students ultimately write a function to access country level data from the CIA World Factbook.

This course examines major works by Hemingway, Fitzgerald, and Faulkner, exploring their interconnections on three analytic scales: the macro history of the United States and the world; the formal and stylistic innovations of modernism; and the small details of sensory input and psychic life. WARNING: Some of the lectures in this course contain graphic content and/or adult language that some users may find disturbing.

"The Human Controller" presents and discusses design and evaluation issues of human-machine interaction. The focus is on understanding human perception-action couplings (limitations, preferences, adaptation) and on quantifying control behavior of humans in the direct manual control loop of vehicles, robots or other man-made tools. Case studies from automotive, aviation, medical and tele-operation applications are discussed, with a special focus on the importance of including and enhancing haptics (=the sense of touch) during manual control.

This course addresses essential learning outcomes in normal growth, development and nutrition across the lifespan, inclusive of aging. Its focus is on normal function rather than disease.

Includes lectures, handouts, schedules, and student notes.