Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles a…
This is a calculus-based book meant for the first semester of a first year survey course taken by engineering and physical science majors. It has a traditional order of topics whereby force is discussed before energy. It is divided into 17 chapters that cover a review of high school physics, scaling and estimation, vectors, velocity, acceleration, forces, circular motion, gravity, conservation …
The concepts and basic topics in elementary Linear Algebra and Calculus are reviewed and generalized to Linear Analysis in this first unit. In particular, the dot product, the vector space of R 2(that is, the x − y plane in Plane Geometry), and measurement of lengths of vectors in R2 , are extended to the “inner product,” the “inner-product space,” and “norm” measurement, respecti…
This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is de-signed to review mathematical concepts that are o[en stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is …
In this lecture, the professor discussed single mode light, thermal states, coherent states
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. This comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions. The term atomic physics can …
This book takes a look at fully automated, autonomous vehicles and discusses many open questions: How can autonomous vehicles be integrated into the current transportation system with diverse users and human drivers? Where do automated vehicles fall under current legal frameworks? What risks are associated with automation and how will society respond to these risks? How will the marketplace rea…
In biology, a spore is a unit of asexual reproduction that may be adapted for dispersal and for survival, often for extended periods of time, in unfavorable conditions. By contrast, gametes are units of sexual reproduction. Spores form part of the life cycles of many plants, algae, fungi and protozoa. Bacterial spores are not part of a sexual cycle but are resistant structures used for survival…
There are some key angles that have exact values in trigonometry. The ones we need to know are 0, 30, 45, 60 and 90. In this video we will discover one method of remember what these values are - by counting fingers on our hand! In the first part we discovered a different method (constructing a table) which you may prefer. Choose whichever method works best for you. SUBSCRIBE to the Fus…
A gamete (from Ancient Greek ??µ??? gamete from gamein "to marry") is a cell that fuses with another cell during fertilization (conception) in organisms that sexually reproduce. In species that produce two morphologically distinct types of gametes, and in which each individual produces only one type, a female is any individual that produces the larger type of gamete—called an ovum (or egg)…