The Fundamentals

Examples of The Fundamentals in the following topics:

• The Fundamental Theorem of Calculus

  • The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function to the concept of the integral.
  • The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function to the concept of the integral.
  • The first published statement and proof of a restricted version of the fundamental theorem was by James Gregory (1638–1675).
  • We can see from this picture that the Fundamental Theorem of Calculus works.
  • Taking the limit as $h$ tends to zero completes the proof of the Fundamental Theorem of Calculus.

• The Fundamental Theorem of Algebra

  • The fundamental theorem states that every non-constant, single-variable polynomial with complex coefficients has at least one complex root.
  • The fundamental theorem of algebra says that every non-constant polynomial in a single variable $z$, so any polynomial of the form
  • There are lots of proofs of the fundamental theorem of algebra.
  • For a general polynomial $f(x)$ of degree $n$, the fundamental theorem of algebra says that we can find one root $x_0$ of $f(x)$.
  • So an alternative statement of the fundamental theorem of algebra is:

• Standing Waves in Air Columns

  • The fundamental is the first harmonic, the first overtone is the second harmonic, and so on. shows hows the fundamental and the first three overtones (the first four harmonics) in a tube closed at one end.
  • The fundamental has =4L, and frequency is related to wavelength and the speed of sound as given by the following:
  • Here, f1 is the fundamental, f3 is the first overtone, and so on.
  • The fundamental and overtones can be present simultaneously in a variety of combinations.
  • The fundamental and three lowest overtones for a tube closed at one end.

• The Accounting Equation

  • The fundamental accounting equation, which is also known as the balance sheet equation, looks like this: $\text{assets} = \text{liabilities} + \text{owner's equity}$.
  • Or more correctly, the term "assets" represents the value of the resources of the business.
  • On the right side of the equation are claims of ownership on those assets: liabilities are the claims of creditors (those "outside" the business); and equity, or owners' equity, is the claim of the owners of the business (those "inside" the business).
  • The fundamental accounting equation is kept in balance after every business transaction because everything falls under these three elements in a business transaction.
  • Looking at the fundamental accounting equation, one can see how the equation stays is balance.

• Christian Fundamentalism

  • Christian Fundamentalism, also known as Fundamentalist Christianity, or Fundamentalism, arose out of British and American Protestantism in the late 19th and early 20th centuries among Evangelical Christians.
  • Fundamentalism has roots in British and American theology of the 19th century.
  • A third school of thought grew out of the release of a 12-volume set of 90 essays called, The Fundamentals: A Testimony to the Truth.
  • By the late 1920s the first two schools of thought – Dispensationalism and Princeton Theology – had become central to Fundamentalism.
  • Analyze the origins of Christian Fundamentalism in late 19th- and early 20th-century America

• Fundamental Theorem for Line Integrals

  • The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve.
  • It is a generalization of the fundamental theorem of calculus to any curve in a plane or space (generally $n$-dimensional) rather than just the real line.
  • Work done by conservative forces does not depend on the path followed by the object, but only the end points, as the above equation shows.
  • Here the $\cdot$ denotes the usual inner product.
  • where the definition of the line integral is used in the first equality and the fundamental theorem of calculus is used in the third equality.

• Fundamental Accounting Equation

  • The fundamental accounting equation can actually be expressed in two different ways.
  • Every transaction and all financial reports must have the total debits equal to the total credits.
  • As you can see, the total amount of the debits (the amount on the left) equal the credits (the total amount on the right).
  • The total assets listed on a company's balance sheet must equal the company's total liabilities, plus its owners' equity in the company.
  • As you can see, the business's total assets equal the company's total liabilities and equity.

• Fundamental Concepts in Accounting

  • In order to prepare the financial statements, it is important to adhere to certain fundamental accounting concepts.
  • Identifies the economic resources of an enterprise, the claims to those resources, and the effects that transactions, events, and circumstances have on those resources.
  • In order to prepare the financial statements, it is important to adhere to certain fundamental accounting concepts.
  • Going Concern, unless there is evidence to the contrary, it is assumed that a business will continue to trade normally for the foreseeable future.
  • Prudence, if there are two acceptable accounting procedures choose the one gives the less optimistic view of profitability and asset values.

• Preface

  • The book developed from an oft-reinvented course at the University of British Columbia.
  • Most of the notes were written during my first reinvention of the course, calling it "Fundamentals of Astrophysics" instead of the former "Non-Stellar Astrophysics. " The current edition is my second reinvention of the course corresponding to my second stint at teaching it.
  • It at least gave the course some context.
  • Whereas "Fundamentals of Astrophysics" sounds more impressive, it actually does not mean much in particular, except giving the connotation that the course is going to be difficult; consequently, in the interest of giving this broad and challenging subject some context, this edition will attempt to focus on a particular object — the Crab Nebula.
  • I would like to thank the first generation of victims, em, I mean, students for learning from the Crab Nebula; hopefully, it will be worthwhile.

• The Future of Religion

  • In addition to discussing secularization and how the theory has been modified due to the continued existence of religion, religious fundamentalism is briefly touched upon as it is playing a significant role in society today.
  • Fundamentalism describes a movement to return to what is considered the defining or founding principles of a religion.
  • A full analysis of what constitutes religious fundamentalism is beyond the scope of this chapter.
  • However, the interested reader is encouraged to explore this topic further by reading the Wikipedia article on fundamentalism.
  • What the future of religious fundamentalism holds for human society is unknown, but because of the impact of this particular religious approach on society today, religious fundamentalism warrants continued study.