École Internationale Polytechnique de Genève (EIPG) e-Learning platform (LMS & LCMS)


The Platform supports 26 languages, it's compliant with the SCORM 1.2 and 2004 standards, and supports different didactic models, including: Blended, Self-Directed, Collaborative and even Social Learning through Chat, Wiki, Forums and other different functions.


BVMDAE(Bachelors Validation/Masters & Doctorates Access Exam)

You are in possession of Master's or Doctorate's Degrees from other institutions you still have to pass the BVMDAE.


BVMDAE examinations

Whether you studied at Oxford, Harvard, Cambridge, Yale, Open University, UNISA, SAIM, IBS, ICS, Intec, Alison, Coursera or Fun MOOC, you have to pass the BVMDAE(Bachelor's Validation/Master's & Doctorate's Access Exam). The BVMDAE will become the future Educational level Evaluation tool. The BVMDAE has for goal to keep the highest standard possible. Take note that Oxford, Harvard, Cambridge and Yale students have difficulty to pass the BVMDAE.



EIPG Online Vocational education(and what is ...) can take place at the post-secondary, further education and higher education level; and can interact with the apprenticeship system. At the post-secondary level, vocational education is often provided by highly specialized trade, Technical schools, community colleges, colleges of further education UK, Universities, Institutes of technology / Polytechnic Institutes etc.

Until recently, almost all vocational education took place in the classroom, or on the job site, with students learning trade skills and trade theory from accredited professors or established professionals. However, online vocational education has grown in popularity, and made it easier than ever for students to learn various trade skills and soft skills from established professionals in the industry.

What about Recognition ... The BVMDAE(Bachelors Validation/Masters & Doctorates Access Exam) serve as an automated recognition exam. Most Public University students fails this exam so do not take this Examination for Granted.

Faculty of Management



Doctor Of Science Business Management & Administration or D.Sc. BMA or DBMA

will be of interest to persons wanting to develop skills in Management, Administration, Managerial science and Entrepreneur in general.


    <b> Our <b>Doctor Of Science Business Management & Administration or D.Sc. BMA or DBMA</b> will be of great interest to students of Management, Administration, Managerial science and Entrepreneur in general, as well as any student wanting to expand their knowledge and understanding of Management & Administration.</b>

Management, Administration, Managerial science and Entrepreneurship.



Faculty of Medecine



Doctor Of Science Natural Medicine or D.Sc. nMed.

studing anatomy, physiology, biomedical science and medicine in general, as well as any persons wanting to expand their knowledge and understanding of Natural Medicine.


Our <b>Doctor Of Science Natural Medicine or D.Sc. nMed.</b> will be of great interest to students of anatomy, physiology, biomedical science and medicine in general, as well as any student wanting to expand their knowledge and understanding of Natural Medicine.</b>

With our vision and determination to be transparent, we develop research protocol's, with respect to animal and human life. We Elaborate protocol's in Nutrition and Medication based on plants and minerals.



Doctor Of Science Nursing, Nutrition & Naturopathy or D.Sc. nNat.

nursing students will study anatomy, physiology, biomedical science and nursing in general.


From taking our vital signs to conducting patient education and case management, nurses are the jack-of-all-trades in the medical field. Celebrated May 6-12, National Nurses Week is a time...

From taking our vital signs to conducting patient education and case management, nurses are the jack-of-all-trades in the medical field. Celebrated May 6-12, National Nurses Week is a time...



Doctor Of Science Psychiatrist & Naturopathy or D.Sc. pNat.

is a physician who specializes in psychiatry, the branch of medicine devoted to the diagnosis, prevention, study, and treatment of mental disorders.


Our <b>Doctor Of Science Psychiatrist & Naturopathy or D.Sc. pNat.</b> will be of great interest to students of Natural Medicine, Psychiatrist in general, as well as any student wanting to expand their knowledge and understanding of Psychiatrist

General psychiatrists are medically qualified doctors who contribute to the management and treatment of adults with mental health problems.



Doctor Of Science Psychology & Naturopathy or D.Sc. sNat.

... attempt to understand the role of mental functions in individual and social behavior, while also exploring the physiological and biological processes that underlie cognitive functions and behaviors.


Our <b>Doctor Of Science Psychology & Naturopathy or D.Sc. sNat.</b> will be of great interest to students of psychology, naturopathy, biomedical science and medicine in general, as well as any student wanting to expand their knowledge and understanding of Psychology

Forensic Psychology - The Judicial Error

Although crime dramas focus more on the forensic analysis of material evidence (DNA for example), the human element of the story, especially the evidence provided by the victims / witnesses , remains a determining element.



Faculty of Science



Doctor of Science Astronomy & Space Science (AS) D.Sc. AS

is the scientific study of celestial objects (such as stars, planets, comets, and galaxies) and phenomena that originate outside the Earth's atmosphere (such as the cosmic background radiation).


Our micro-satellite looks like this one (Illustrations) with our Gyroscope, Geiger Counter, Thermostat and other Scientific Instrument for Pressure / Vacuum Measurement

EIPG Orbiter II - micro-satellite

Our micro-satellite(Illustrations) with Gyroscope, Geiger Counter, Thermostat and other Scientific Instrument for Pressure / Vacuum Measurement, Electromagnetism, Gas Composition etc. Fully Designed and Developed by Prof. Horstmann and his team of researchers. Cost per unit launched into space 12 000.00€



Doctor of Science Chemistry (CY) D.Sc. CY

is the scientific discipline involved with elements and compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a reaction with other substances.


Our <b>Doctor of Science Chemistry (CY)  D.Sc. CY</b> will be of great interest to students of Chemistry, Analytical Chemistry, Biochemistry, Chemical Engineering, Food Science & Nutrition, Petroleum Chemistry, Pharmaceutical Chemistry and Pharmacovigilance.

Analytical chemistry involves the quantitative and qualitative measurement of atoms, molecules, particles, and cells. As such, all Chemists, indeed most scientists use Analytical Chemistry in some form.



Doctor of Science Ecology, Evolution & Environmental Science (EY) D.Sc. EY

Ecology is the scientific analysis and study of interactions among organisms and their environment. Environmental science is an interdisciplinary academic field that integrates physical, biological and information sciences (including ecology, biology, physics, chemistry, plant science, zoology, mineralogy, oceanography, limnology, soil science, geology and physical geography (geodesy), and atmospheric science) to the study of the environment, and the solution of environmental problems.


Our <b>Doctor of Science Ecology, Evolution & Environmental Science (EY)  D.Sc. EY</b> will be of great interest to students of ecology, environmental, sustainable development and conservation in general, as well as any student wanting to expand their knowledge and understanding of Ecology & Environmental Science.

the branch of science concerned with the physical, chemical, and biological conditions of the environment and their effect on organisms.



Doctor of Science General Science (GS) D.Sc. GS

... is science in it's basic and pure form. The science which deals with the things related to our life. It includes Biology, chemistry, physics, mathematics and environmental science.


The Splitting of Hydrogen in different strong magnetic fields.

This degree offers a solid foundation in all core areas from biology, chemistry, biochemistry, computer science, earth and environmental sciences, mathematics, physics. There is room in the degree to explore other areas of interest as well.



Doctor of Science Humanity & Social Science (HS) D.Sc. HS

... are the study of human behaviour and interaction in social, cultural, environmental, economic and political contexts.


The Splitting of Hydrogen in different strong magnetic fields.

the branch of science concerned with the human and social conditions of populations in environment and their effect globaly.



Doctor of Science Life Sciences (LS) D.Sc. LS

the life sciences or biological sciences comprise the branches of science that involve the scientific study of life and organisms – such as microorganisms, plants, and animals including human beings.


The Splitting of Hydrogen in different strong magnetic fields.

This degree offers a solid foundation in all core areas from Botany, chemistry and biochemistry, Microbiology, Zoology and Food Technology. There is room in the degree to explore other areas of interest as well.



Doctor of Science Materials Science (MS) D.Sc. MS

... an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. It includes elements of physics and chemistry, as well as chemical, mechanical, civil and electrical engineering.


Characteristics of Materials D Sided.

Resources Presentation
Material resources include wood, glass (which comes from sand), metals, edible plants, and plastics (which are made from natural chemicals). Renewable material resources, like glass, can be re-created easily.



Doctor of Science Mathematics (MA) D.Sc. MA

from Greek μάθημα máthēma, "knowledge, study, learning", includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis). It has no generally accepted definition.


will be of great interest to students of Chemistry, Engineering, Physic as well as any student wanting to expand their knowledge and understanding of Mathematics.

Vogel’s approximation method for solving transportation problems.

The Vogel Approximation Method is an improved version of the Minimum Cell Cost Method and the Northwest Corner Method that in general produces better initial basic feasible solution, which are understood as basic feasible solutions that report a smaller value in the objective (minimization) function of a balanced Transportation Problem (sum of the supply = sum of the demand).



Doctor of Science Physics (PH) D.Sc. PH

is the natural science that studies matter, its motion and behavior through space and time, and that studies the related entities of energy and force.


Our Doctor of Science Physics (PH)  D.Sc. PH will be of great interest to students of Physics, as well as any student wanting to expand their knowledge and understanding of Physics.

Standard model of physics
CERN - all of our current understanding of the universe condensed into a single infographic



Doctor of Science Statistics (ST) D.Sc. ST

... data collection, organization, analysis, interpretation and presentation. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.


Characteristics of Materials D Sided.

When census data
cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.



Faculty of Engeneering



Doctor of Science Aerospace Engineering (AE) D.Sc. AE

is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering.


EIPG Jet-h2o I - Water fueled jet Engine | EIPG Jet-h2o I - Wasserbetriebener Strahltriebwerk

1600 years before any machine could fly and before Newton announced the third mechanical law, Hero of Alexandria invented the Aeolipile. Nothing serious(just a toy) but the modern jet engine use it, same physics principle!
In Greek, the word Aeolipile means Wind Ball. How does this stuff work? A closed vessel filled with water is heating. After a few minutes, steam is produced and passes through two vertical outlets into the ball. Steam began to escape from the directional nozzle and the ball can rotate.



Liquid rocket motors


Girl in a jacket

We locked our main engine choice about a year ago. This occurred after a series of static tests with medium and large liquid propellant rocket engines using LOX (Liquid Oxygen) and ethanol / water as a propellant.



Doctor of Science Avionics Engineering (AVE) D.Sc. AVE

avionics engineers design and develop aircraft and spacecraft avionic instrumentation. They also conduct research to address problems associated with flight safety systems, landing gear and electronic navigation systems.


What is the importance of c language in agricultural engineering?

Working in the aerospace engineering subspecialty field of avionics,
avionics engineers design and develop aircraft and spacecraft avionic instrumentation.



Doctor of Science Agricultural Engineering (AG) D.Sc. AG

is the area of engineering concerned with the design, construction and improvement of farming equipment and machinery. Agricultural engineers integrate technology with farming.


What is the importance of c language in agricultural engineering?

What is the importance of c language in agricultural engineering?
As evident from the above illistration there are many applications of Software and Information technology across the main verticals of agriculture engineering. As an agricultural engineer , one is supposed to be familiar with these technologies and hence knowledge of programming is necessary.



Doctor of Science Biomedical Engineering (BE) D.Sc. BE

also referred to as Bioengineering, BioMed or BME, is a multidisciplinary STEM field that combines biology and engineering, applying engineering principles and materials to medicine and healthcare.


Synthetic Stingray May Lead To A Better Artificial Heart Using gold, silicone and heart cells from a rat. The engineering involved in propelling it could help make a heart that's more than a mechanical pump.

Synthetic Stingray May Lead To A Better Artificial Heart Using gold, silicone and heart cells from a rat. The engineering involved in propelling it could help make a heart that's more than a mechanical pump.



Doctor of Science Civil Engineering (CE) D.Sc. CE

is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built ...


will be of great interest to students of civil engineering, construction, civil engineering in general, as well as any student wanting to expand their knowledge and understanding of Construction(civil) Engineering.

Civil Engeneering Courses Masters of Engineering Concepts of Engineering Practice: It is a graduate-level category that covers the role of engineering in fashionable society. Lecture notes cowl ethics, construction and project management. Students will transfer case studies and find out about the project analysis method.



Doctor of Science Chemical Engineering (CH) D.Sc. CH

engineering is a branch of engineering that uses principles of chemistry, physics, mathematics, biology, and economics to efficiently use, produce, design, transport and transform energy and materials.


Chemical engineering is a branch of engineering that applies physical sciences (physics and chemistry), life sciences (microbiology and biochemistry), together with applied mathematics and economics to produce, transform, transport, and properly use chemicals, materials and energy. A chemical engineer designs large-scale processes that convert chemicals, raw materials, living cells, microorganisms and energy into useful forms and products.

Chemical engineering is a branch of engineering that applies physical sciences (physics and chemistry), life sciences (microbiology and biochemistry), together with applied mathematics and economics to produce, transform, transport, and properly use chemicals, materials and energy. A chemical engineer designs large-scale processes that convert chemicals, raw materials, living cells, microorganisms and energy into useful forms and products.
Chemical engineers are involved in many aspects of plant design and operation, including safety and hazard assessments, process design and analysis, control engineering, chemical reaction engineering, construction specification and operating instructions.



Doctor of Science Control & Instrumentation Engineering (CI) D.Sc. CI

Instrumentation is defined as the art and science of measurement and control of the process variables within a production or manufacturing area.


Control and Instrumentation Illustrations - Our Engineers in control and instrumentation are responsible for designing, developing, installing, managing and/or maintaining systems

Control and Instrumentation Illustrations
As Control and instrumentation engineers you are responsible for designing, developing, installing, managing and maintaining equipment which is used to monitor and control engineering systems, machinery and processes.



Doctor of Science Design Engineering (DE) D.Sc. DE

is a person who may be involved in any of various engineering disciplines including civil, mechanical, electrical, chemical, textiles, aerospace, nuclear, manufacturing, systems, and structural building/architectural.


3D Printing for the Design and Manufacturing

Design Engineer in Action.
3D Printing for the Design and Manufacturing Engineers are a must in today's fast developing society.



Doctor of Science Electronics and Communication Engineering (EC) D.Sc. EC

is the application of science and mathematics to practical problems in the field of electronics and communications. Electronics and communications engineers engage in research, design, development and testing of the electronic equipment used in various systems.


Semiconductor pn junction diagram - The junction here is drawn with photon injection condition like in a solar cell, so we use the quasi-fermi levels.

Semiconductor pn junction diagram
The junction here is drawn with photon injection condition like in a solar cell, so we use the quasi-fermi levels.



Doctor of Science Electrical & Computer Engineering (EE) D.Sc. EE

... apply electrical, electronic and magnetic theory to obtain solutions for problems related to the development, design and operation of electrical hardware and software, control systems, electrical machines and communications systems.


will be of great interest to students of electrical control systems, programmers, computer science in general, as well as any student wanting to expand their knowledge and understanding of Electrical, electronic and computer Systems.

Embedded software designs such as those for avionics and automotive systems have become highly complex to develop, test and certify. As a result, the traditional document...



Doctor of Science Engineering Sciences (ES) D.Sc. ES

is the application of scientific, economic, social, and practical knowledge in order to design, build, and maintain structures, machines, devices, systems, materials and processes.


OCEAN ENERGY OCEAN THERMAL ENERGY CONVERSION.

The Engineering Science Society
Various pathways in Engineering. You have a vast zone of Activities to choose from ...



Doctor of Science Geology and Geophysics Engineering (GE) D.Sc. GE

is the study of geologic structures such as faults and folds. Tectonics deals with large scale Earth structures such as tectonic plates and its deep interior. Geophysics is the study of the Earth by quantitative physical methods. It is an applied science and includes the Earth’s interior, crust, oceans, atmosphere and magnetosphere.


OCEAN ENERGY OCEAN THERMAL ENERGY CONVERSION.

The Geological Society
Various pathways in Geology & Geophysics. You have a vast zone of Activities to choose from ...



Doctor of Science Information Systems Engineer (IE) D.Sc. IE

design, implement, and maintain computer systems that collect, process, store, and present data.


The EIPG Mos All in One PC (21

EIPG Mos All in One PC (21") (HMT2160AGOS)
The EIPG Mos All in One PC (21") (HMT2160AGOS) Product Description Model HMT2160AGOS; Display Size 21.6 inch; Resolution 1360*768@60Hz or 1920*1080 Display Ratio 16: 9; Mother Board Intel G41 ICH7; CPU Intel Atom@ Dual Core HT E5500 2.8Hz; Memory DDR2-800, 2GB and above; Hard Disk S-ATAII 250GB/500GB/8MB/7200rpm; Graphic Card Intel Graphics Media Accelerator 3150; Network Card 1000M(Built-in wireless card); Audio Card (Realtek HD audio output) audio system; Input/Output USB2.0*4 / AUDIO / EARPHONE / MIC /RJ45 LAN / SD, MMC, MS / VGA / HDMI; Operating System: Mos64 atom version 1.0



Doctor of Science Mechanical Engineering (ME) D.Sc. ME

is the discipline that applies engineering, physics, engineering mathematics, and materials science principles to design, analyze, manufacture, and maintain mechanical systems.


If the beta is greater than 90 degrees, the pressure increases with increasing flow. Such blades are called forward curved blades.

Forward curved Blades
If the beta is greater than 90 degrees, the pressure increases with increasing flow. Such blades are called forward curved blades. If beta is less than 90 degrees. Since the second term in LHS of the head vs. flow equation is positive in this case, the pressure head decreases with increasing flow. These types of impellers are called backward curved blades. Thus backward curved blades that achieved self-stabilizing characteristics in energy consumption is the most preferred in the industry.



Doctor of Science Mining Engineering (MN) D.Sc. MN

is an engineering discipline that applies science and technology to the extraction of minerals from the earth.


Various mining resources are available exp. Gold, Silver, Diamonds, Platinum, Uranium etc.

Mining Engineer in Action.
Various mining resources are available exp. Gold, Silver, Diamonds, Platinum, Uranium etc.



Doctor of Science Metallurgical Engineering (MT) D.Sc. MT

is the study of metals. Combining theory and practice, degree programs cover the mining, extraction, design and processing of metals, as well as how metals react to environmental changes or stress.


... Nonrenewable resources Recyclable resources The degree of availability of ... Almost all home scrap, as well as a sizeable part of prompt industrial scrap, are ... etc.

Metallurgical Engineer in Action.
... Nonrenewable resources Recyclable resources The degree of availability of ... Almost all home scrap, as well as a sizeable part of prompt industrial scrap, are ... etc.



Doctor of Science Ocean & Atmospheric Engineering (OE) D.Sc. OE

... It includes the study of physical processes acting across the ocean boundaries at the sea floor, coast, and sea surface, and of the ocean's role in the Earth's climate system.


OCEAN ENERGY OCEAN THERMAL ENERGY CONVERSION.

Non-Convectional Energy Resources Presentation
Various Ocean Energy resources are available exp. Ocean Thermal Energy Conversion as illustrated above.



Doctor of Science Petroleum Engineering (PE) D.Sc. PE

is a field of engineering concerned with the activities related to the production of hydrocarbons, which can be either crude oil or natural gas.


Our Doctor of Science Petroleum Engineering (PE)  D.Sc. PE will be of great interest to students of biofuel, alternative, ecology & environmental science in general, as well as any student wanting to expand their knowledge and understanding of Bio Petrochemical Industries.

HIBPCI - Growing Algae for Biodiesel Use So, we've talked about the chemical process that takes algae and turns it into biodiesel fuel.



Doctor of Science Production and Industrial Engineering (PI) D.Sc. PI

is an interdisciplinary engineering discipline that includes manufacturing technology, engineering sciences, management science, and optimization of complex processes, systems, or organizations.


Hands on Production & Industrial engineering experience by our students, Doctor Of Science Production & Industrial Engineer or D.Sc. piEng.

EIPG Candela I - Electric Car project Hands on Production & Industrial engineering experience by our students, as part of their practical formation.



Doctor of Science Textile Engineering and Fibre Science (TF) D.Sc. TF

the application of scientific and engineering principles to the design and control of all aspects of fiber, textile, and processes, products, and machinery. ... A textile engineer therefore works with textile materials: fibers, yarns, fabrics, and finishes.


Various chemical, mechanical and physical processes are involved throughout the textile manufacturing process.

Textile Engineering
Various chemical, mechanical and physical processes are involved throughout the textile manufacturing process. Textile equipment, chemicals, fibres, polymers and other synthetic materials are involved in it. Textile engineering deals with these processes, synthetic materials, machinery and overall production. These days, computers play a prominent role in textile industry. Computers are used to design and manufacture (process control) textile products!



Doctor of Science Vehicle Engineer (VE) D.Sc. VE

is the design, manufacture and operation of motorcycles, automobiles and trucks and their respective engineering subsystems.


Customer choice upholstery/color vehicles will be build by our Students, Doctor of Science Vehicle Engineer (VE)  D.Sc. VE

EIPG Presents Candela I - Electric Car
Customer choice upholstery/color vehicles will be build by our Students, Doctor of Science Vehicle Engineer (VE) D.Sc. VE, as part of their practical experience during formation.



Faculty of Arts



Doctor of Science Architecture & Planning (AR) D.Sc. AR

is a design and planning for a building, and can contain architectural drawings, specifications of the design, calculations, time planning of the building process, and other documentation.


Architectural planning: The architect usually begins to work when the site and the type and cost of a building have been determined.

Architectural planning: The architect usually begins to work when the site and the type and cost of a building have been determined. The site involves the varying behaviour of the natural environment that must be adjusted to the unvarying physical needs of human beings; the type is the generalized form ...



Doctor of Science Archaeology & Anthropology (AA) D.Sc. AA

archaeology focuses on the study of past human cultures through research of historical sites and artifacts, such as tools, skeletal remains and structural ruins in general.


Archaeology & Anthropology.

Anthropology is a vast field that spans ethnography, genetics, media studies, culture studies, linguistics and even photography and film. ...



Faculty of Theology



Doctor of Science Theology (TH) D.Sc. TH

is the study of religion. ... While some students take theology in preparation for a career in the church, you don't have to be religious to have an interest in religion.


your gateway to an exciting, fulfilling and ... future!  Learn to apply biblical principles in a secular world,

your gateway to an exciting, fulfilling and ... future! Learn to apply biblical principles in a secular world, and help families and individuals in your community find Christ-centered solutions to difficult life issues.



Private School - Saint Amrane Of Jerusalem


From Kindergarten to 12 Grade - Homeschool for Isolated individuals



Diploma of Science High School or Dip.Sc. Hs.

High school graduation is a rite of passage in modern society. Whether you want to impress your friends, get the job of your dreams or qualify for an upcoming promotion, we can help. Saint Amrane Church of Jerusalem has partnered with EIPG Online Academy to complete your primary education with a Christian degree. Avoid the stigma attached to GEDs with a diploma that says "I finished High School."



Saint Amrane Of Jerusalem High School


High school students raising hands, in classroom with professor

EIPG for "Saint Amrane Of Jerusalem" - High school students raising hands, in classroom with professor



General Information ...


Magnesium aluminate, Synthetic spinel, accidentally produced in the mid-18th century, has been more recently described in scientific publications in 2000 and 2004. By 2015, transparent spinel was made into sheets and other forms by sintering. Synthetic spinel, which looks like glass but has a significantly higher resistance to pressure, can also have applications for military and commercial purposes.
Spinel in different Colors
At EIPG our Students produce different Turbo Machines Transparent like Glass, Light as Feathers and Hard as Tanks from Spinel(Magnesium aluminate) formula MgAl2O4.
We are at the point of realizing a 3D Printer for Simply Printing Pumps and PD Pumps(Positive Displacement Pumps) in Spinel at 650°C.

Periodic Table of Chemical Elements


Periodic Table of Chemical Elements for EIPG students


Periodic Table of Chemical Elements

Girl in a jacket

Math Equations on all webpages are now functional thanks to Prof. Horstmann's Math API integration



Beautiful Math Equations in all browsers


MathML Integral Formula

f ( a ) = 1 2 π i γ f ( z ) z a d z

or Math API Tex base ... Integral Formula

\begin{align} f(a) = \frac{1}{2\pi i} \oint_{\gamma}\frac{f(z)}{z-a}dz \end{align}

Dynamic Equations - step by step

Expand the following: \begin{align} (x 1)^2 &\cssId{Step1}{= (x 1)(x 1)}\\ &\cssId{Step2}{= x(x 1) 1(x 1)}\\ &\cssId{Step3}{= (x^2 x) (x 1)}\\ &\cssId{Step4}{= x^2 (x x) 1}\\ &\cssId{Step5}{= x^2 2x 1}\\ \end{align}

The Quadratic Formula

When \(a \ne 0\), there are two solutions to \(ax^2 bx c = 0\) and they are

\begin{align} x = {-b \pm \sqrt{b^2-4ac} \over 2a}. \end{align}

Double angle formula for Cosines

\begin{align} \cos(θ φ)=\cos(θ)\cos(φ)−\sin(θ)\sin(φ) \end{align}

Gauss' Divergence Theorem

\begin{align} \int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot ndS \end{align}

Curl of a Vector Field

\begin{align} \vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i} \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k} \end{align}

Standard Deviation

\begin{align} \sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2} \end{align}

Definition of Christoffel Symbols

\begin{align} (\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i \left( \frac{\partial Y^k}{\partial x^i} \Gamma_{im}^k Y^m \right) \end{align}

The Lorenz Equations

\begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z xy \end{align}

Cauchy's Integral Formula

\begin{align} f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz \end{align}

The Cauchy-Schwarz Inequality

\[ \left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]

A Cross Product Formula

\[ \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\ \end{vmatrix} \]

The probability of getting \(k\) heads when flipping \(n\) coins is:

\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]

An Identity of Ramanujan

\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1 \frac{e^{-2\pi}} {1 \frac{e^{-4\pi}} {1 \frac{e^{-6\pi}} {1 \frac{e^{-8\pi}} {1 \ldots} } } } \]

A Rogers-Ramanujan Identity

\[ 1 \frac{q^2}{(1-q)} \frac{q^6}{(1-q)(1-q^2)} \cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j 2})(1-q^{5j 3})}, \quad\quad \text{for $|q|<1$}. \]

Maxwell's Equations

\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, \, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}

In-line Mathematics

Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression \(\sqrt{3x-1} (1 x)^2\) is an example of an inline equation. As you see, equations can be used this way as well, without unduly disturbing the spacing between lines.

Trig Identity Formulas

Use these fundemental formulas of trigonometry to help solve problems by re-writing expressions in another equivalent form.

Basic Identities

\[\sin(x)=\frac{1}{\csc(x)}\]

\[\cos(x)=\frac{1}{\sec(x)}\]

\[\tan(x)=\frac{1}{\cot(x)}\]

\[\sec(x)=\frac{1}{\cos(x)}\]

\[\csc(x)=\frac{1}{\sin(x)}\]

\[\cot(x)=\frac{1}{\tan(x)}\]

\[\tan(x)=\frac{\sin(x)}{\cos(x)}\]

\[\sin(-x)=-\sin(x)\]

\[\cos(-x)=\cos(x)\]

\[\tan(-x)=-\tan(x)\]

Pythagorean Identities

\[\sin^2(x) \cos^2(x)=1\]

\[1 \tan^2(x)=\sec^2(x)\]

\[1 \cot^2(x)=\csc^2(x)\]

Sum and Difference Formulas

\[\sin(a b)=\sin(a)\cos(b) \cos(a)\sin(b)\]

\[\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(b)\]

\[\cos(a b)=\cos(a)\cos(b)-\sin(a)\sin(b)\]

\[\cos(a-b)=\cos(a)\cos(b) \sin(a)\sin(b)\]

\[\tan(a b)=\frac{\tan(a) \tan(b)}{1-\tan(a)\tan(b)}\]

\[\tan(a-b)=\frac{\tan(a)-\tan(b)}{1 \tan(a)\tan(b)}\]

\[\sin(x) \sin(y)=2\sin(\frac{x y}{2})\cos(\frac{x-y}{2})\]

\[\sin(x)-\sin(y)=2\cos(\frac{x y}{2})\sin(\frac{x-y}{2})\]

\[\cos(x) \cos(y)=2\cos(\frac{x y}{2})\cos(\frac{x-y}{2})\]

\[\cos(x)-\cos(y)=-2\sin(\frac{x y}{2})\sin(\frac{x-y}{2})\]

Double Angle Formulas

\[\sin(2x)=2\sin(x)\cos(x)\]

\[\cos(2x)=\cos^2(x)-\sin^2(x)=1-2\sin^2(x) = 2\cos^2(x)-1\]

Half Angle Formulas

\[\sin(\frac{x}{2})=\pm\sqrt{\frac{1-\cos(x)}{2}}\]

\[\cos(\frac{x}{2})=\pm\sqrt{\frac{1 \cos(x)}{2}}\]

\[\tan(\frac{x}{2})=\pm\sqrt{\frac{1-\cos(x)}{1 \cos(x)}}=\frac{1-\cos(x)}{\sin(x)}=\frac{\sin(x)}{1 \cos(x)}\]

Trigonometric Products

\[\sin(x)\cos(y)=\frac{\sin(x y) \sin(x-y)}{2}\]

\[\cos(x)\cos(y)=\frac{\cos(x y) \cos(x-y)}{2}\]

\[\sin(x)\sin(y)=\frac{\cos(x-y)-\cos(x y)}{2}\]

Chemical Equations on all webpages are now functional thanks to Prof. Horstmann's Chemical API integration

Beautiful Chemical Equations in all browsers

$$\ce{Zn^2 <=>[ 2OH-][ 2H ] $\underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}}$$ <=>[ 2OH-][ 2H ] $\underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}$$}$$

Organic chemistry molecule ...

$$\ce{CH3\bond{1}} {\stackrel{ \;\;\;\large\ce{CH3} }{\stackrel{|}{\underset{\underset{\huge\ce{Cl}}{|}}{\ce{C}}}}}\ce{-CH3}$$

Chemical Equations (ce) ...

$$\ce{CO2 C -> 2 CO}$$

$$\ce{Hg^2 ->[I-] HgI2 ->[I-] [Hg^{II}I4]^2-}$$

$$C_p[\ce{H2O(l)}] = \pu{75.3 J // mol K}$$

Chemical Formulae

$$\ce{H2O}$$ $$\ce{Sb2O3}$$

Charges

$$\ce{H }$$ $$\ce{CrO4^2-}$$ $$\ce{[AgCl2]-}$$

$$\ce{Y^99 }$$ $$\ce{Y^{99 }}$$

Stoichiometric Numbers

$$\ce{2 H2O}$$ $$\ce{2H2O}$$ $$\ce{0.5 H2O}$$

$$\ce{1/2 H2O}$$ $$\ce{(1/2) H2O}$$ $$\ce{$n$ H2O}$$

Isotopes

$$\ce{^{227}_{90}Th }$$ $$\ce{^227_90Th }$$ $$\ce{^{0}_{-1}n^{-}}$$ $$\ce{^0_-1n-}$$ $$\ce{H{}^3HO}$$ $$\ce{H^3HO}$$

Reaction Arrows

$$\ce{A -> B}$$     $$\ce{A <- B}$$     $$\ce{A <-> B}$$     $$\ce{A <--> B}$$     $$\ce{A <=> B}$$     $$\ce{A <=>> B}$$     $$\ce{A <<=> B}$$     $$\ce{A ->[H2O] B}$$     $$\ce{A ->[{text above}][{text below}] B}$$     $$\ce{A ->[$x$][$x_i$] B}$$

Parentheses, Brackets, Braces

$$\ce{(NH4)2S}$$ $$\ce{[\{(X2)3\}2]^3 }$$ $$\ce{CH4 2 $\left( \ce{O2 79/21 N2} \right)$}$$

States of Aggregation

$$\ce{H2(aq)}$$ $$\ce{CO3^2-_{(aq)}}$$ $$\ce{NaOH(aq,$\infty$)}$$

Crystal Systems

$$\ce{ZnS($c$)}$$ $$\ce{ZnS(\ca$c$)}$$

Variables like x, n, 2n 1

$$\ce{NO_x}$$ $$\ce{Fe^n }$$ $$\ce{x Na(NH4)HPO4 ->[\Delta] (NaPO3)_x x NH3 ^ x H2O}$$

Greek Characters

$$\ce{\mu-Cl}$$ $$\ce{[Pt(\eta^2-C2H4)Cl3]-}$$ $$\ce{\beta }$$ $$\ce{^40_18Ar \gamma{} \nu_e}$$

(Italic) Math

$$\ce{NaOH(aq,$\infty$)}$$ $$\ce{Fe(CN)_{$\frac{6}{2}$$}}$$ $$\ce{X_{$i$}^{$x$}}$$ $$\ce{X_$i$^$x$}$$

Italic Text

$$\ce{$cis${-}[PtCl2(NH3)2]}$$ $$\ce{CuS($hP12$)}$$

Upright Text, Escape Parsing

$$\ce{{Gluconic Acid} H2O2}$$ $$\ce{X_{{red}}}$$ $$\ce{{( )}_589{-}[Co(en)3]Cl3}$$

Bonds

$$\ce{C6H5-CHO}$$ $$\ce{A-B=C#D}$$ $$\ce{A\bond{-}B\bond{=}C\bond{#}D}$$ $$\ce{A\bond{1}B\bond{2}C\bond{3}D}$$ $$\ce{A\bond{~}B\bond{~-}C}$$ $$\ce{A\bond{~--}B\bond{~=}C\bond{-~-}D}$$ $$\ce{A\bond{...}B\bond{....}C}$$ $$\ce{A\bond{->}B\bond{<-}C}$$

Addition Compounds

$$\ce{KCr(SO4)2*12H2O}$$ $$\ce{KCr(SO4)2.12H2O}$$ $$\ce{KCr(SO4)2 * 12 H2O}$$

Oxidation States

$$\ce{Fe^{II}Fe^{III}2O4}$$

Unpaired Electrons, Radical Dots

$$\ce{OCO^{.-}}$$ $$\ce{NO^{(2.)-}}$$

Kröger-Vink Notation

$$\ce{Li^x_{Li,1-2x}Mg^._{Li,x}$$V'_{Li,x}Cl^x_{Cl}}$$ $$\ce{O''_{i,x}}$$ $$\ce{M^{..}_i}$$ $$\ce{$V$^{4'}_{Ti}}$$ $$\ce{V_{V,1}C_{C,0.8}$$V_{C,0.2}}$$

Equation Operators

$$\ce{A B}$$ $$\ce{A - B}$$ $$\ce{A = B}$$ $$\ce{A \pm B}$$

Precipitate and Gas

$$\ce{SO4^2- Ba^2 -> BaSO4 v}$$ $$\ce{A v B (v) -> B ^ B (^)}$$

Other Symbols and Shortcuts

$$\ce{NO^*}$$ $$\ce{1s^2-N}$$ $$\ce{n-Pr}$$ $$\ce{iPr}$$ $$\ce{\ca Fe}$$ $$\ce{A, B, C; F}$$ $$\ce{{and others}}$$

Complex Examples

$$\ce{Zn^2 <=>[ 2OH-][ 2H ] $\underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}}$$ <=>[ 2OH-][ 2H ] $\underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}$$}$$ $$K = \frac{[\ce{Hg^2 }][\ce{Hg}]}{[\ce{Hg2^2 }]}$$ $$K = \ce{\frac{[Hg^2 ][Hg]}{[Hg2^2 ]}}$$ $$\ce{Hg^2 ->[I-] $\underset{\mathrm{red}}{\ce{HgI2}}$$ ->[I-] $\underset{\mathrm{red}}{\ce{[Hg^{II}I4]^2-}}$$}$$

Physical Units (pu)

$$\pu{123 kJ}$$ $$\pu{123 mm2}$$ $$\pu{123 J s}$$ $$\pu{123 J*s}$$ $$\pu{123 kJ/mol}$$ $$\pu{123 kJ//mol}$$ $$\pu{123 kJ mol-1}$$ $$\pu{123 kJ*mol-1}$$ $$\pu{1.2e3 kJ}$$ $$\pu{1,2e3 kJ}$$ $$\pu{1.2E3 kJ}$$ $$\pu{1,2E3 kJ}$$

Crystal Systems

$$\ce{ZnS($c$)}$$ $$\ce{ZnS(\ca$c$)}$$

In-line Chemical Equations

Finally, while display equations look good for a page of samples, the ability to mix Chemical Equations and text in a paragraph is also important. This expression \(\ce{Zn^2 <=>[ 2OH-][ 2H ] $\underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}}$$ <=>[ 2OH-][ 2H ] $\underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}$$}\) is an example of an inline equation. As you see, equations can be used this way as well, without unduly disturbing the spacing between lines.