Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Topics in physical therapyPhysical therapy (PT), also known as physiotherapy, is one of the allied health professions. It is provided by physical therapists who promote, maintain, or restore health through physical examination, diagnosis, management, prognosis, patient education, physical intervention, rehabilitation, disease prevention, and health promotion. Physical therapists are known as physiotherapists in many countries. The career has many specialties including musculoskeletal, orthopedics, cardiopulmonary, neurology, endocrinology, sports medicine, geriatrics, pediatrics, women's health, wound care and electromyography.
Topics in quantum mechanicsQuantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.
Topics in macroeconomicsMacroeconomics is a branch of economics that deals with the performance, structure, behavior, and decision-making of an economy as a whole—for example, using interest rates, taxes, and government spending to regulate an economy's growth and stability. This includes regional, national, and global economies. Macroeconomists study topics such as GDP (Gross Domestic Product), unemployment (including unemployment rates), national income, price indices, output, consumption, inflation, saving, investment, energy, international trade, and international finance.
Abrahamic religionsThe Abrahamic religions are a group of religions centered around the worship of the God of Abraham. Abraham, a Hebrew patriarch, is extensively mentioned throughout the Abrahamic religious scriptures of the Quran, and the Hebrew and Christian Bibles. Jewish tradition claims that the Twelve Tribes of Israel are descended from Abraham through his son Isaac and grandson Jacob, whose sons formed the nation of the Israelites in Canaan (or the Land of Israel); Islamic tradition claims that twelve Arab tribes known as the Ishmaelites are descended from Abraham through his son Ishmael in the Arabian Peninsula.
Early modern periodThe early modern period of modern history spans the period after the Late Middle Ages of the post-classical era (1400–1500) to the beginning of the Age of Revolutions (1800). Although the chronological limits of this period are open to debate, the timeframe is variously demarcated by historians as beginning with the fall of Constantinople in 1453, the Renaissance period in Europe and Timurid Central Asia, the end of the Crusades, the Age of Discovery (especially the voyages of Christopher Columbus beginning in 1492 but also Vasco da Gama's discovery of the sea route to India in 1498), and ending around the French Revolution in 1789, or Napoleon's rise to power.
Algebraic geometryAlgebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.
Geography of North AmericaNorth America is the third largest continent, and is also a portion of the third largest supercontinent if North and South America are combined into the Americas and Africa, Europe, and Asia are considered to be part of one supercontinent called Afro-Eurasia. With an estimated population of 580 million and an area of 24,709,000 km2 (9,540,000 mi2), the northernmost of the two continents of the Western Hemisphere is bounded by the Pacific Ocean on the west; the Atlantic Ocean on the east; the Caribbean Sea on the south; and the Arctic Ocean on the north.
Liver diseaseLiver disease, or hepatic disease, is any of many diseases of the liver. If long-lasting it is termed chronic liver disease. Although the diseases differ in detail, liver diseases often have features in common. File:Ground glass hepatocytes high mag cropped 2.jpg|Ground glass hepatocytes File:Primary biliary cirrhosis intermed mag much cropping.jpg|Primary biliary cirrhosis File:Buddchiari2.PNG|Budd-chiari syndrome File:Non-alcoholic_fatty_liver_disease1.
EquationsIn mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
