Curvature and the Notion of Space

Rushdl

Description

• leçon - matière potentielle : the clock at sea
• cours magistral
• leçon - matière potentielle : selection
• cours - matière potentielle : differential geometry
• leçon - matière potentielle : selec - tion

3Curvature and the Notion of Space 3.1 Introduction On June 10, 1854, at the University of Gottingen, in a lecture that nearly did not occur, Georg Friedrich Bernhard Riemann (1826–1866) proposed a vision- ary concept for the study of space [223, pp. 132–133]. To obtain the position of an unsalaried lecturer (Privatdozent) in the German university system, Riemann was required to submit an inaugural paper (Habilitationsschrift) as well as to present an inaugural lecture (Habilitationsvortrag).

• detailed study of the axiomatic geometry
• pendulum clock
• dimensional manifolds
• manifold
• curvature
• geometry
• space
• circle
• surface
• work

Sujets

• Cours magistral
• Sélection
• Differential geometry
• Jean-Baptiste Marie Meusnier de La Place
• Schumacher
• Rodrigues
• Clairaut
• Board of Longitude

Informations

• Publié par: natoc
• Nombre de lectures: 7
• Langue: English

Extrait

Chemistry
Workbook


Summer
2011
The University of Texas at Austin
College of Natural Sciences
Welcome!
Welcome to the college prep materials for Chemistry. This workbook is provided to help
you level out and level up on select high school chemistry topics ranging from exponent
math to limiting reactants and molarity. Afterall, the more you know about these topics
before college classes begin, the more you can focus on new college-level items of
interest.

We have created this workbook to be used in tandem with our online videos located at
http://www.chemprep.cm.utexas.edu or on Quest. Additional tutorials are available
through ALEKS. This booklet is not intended to teach material from scratch. Its purpose
is to review the main points of select topics in order to refresh your memory. For more
information on a given topic than is shown here, refer to a chemistry textbook such as
(shown alphabetically by first author):
Atkins, Chemical Principles: The Quest for Insight
Whitten, Davis, Peck, General Chemistry
Zumdahl, Chemical Principles
Or other chemistry textbook of your choosing

The information herein is arranged by Units:
Please note that these categories differ slightly from those in ALEKS. Refer to the
website (above) to view the videos arranged according to ALEKS’ categories.
Unit01: Math
Unit02: Math - Measurement
Unit03: Matter
Unit04: Atoms, Ions, and Molecules
Unit05: Stoichiometry – Moles and Molar Mass
Unit06: Stoichiometry - Reactions
Unit07: Stoichiometry - Molarity

A few additional comments:
In many cases, we have prepared a video to provide explanation to a problem or to
give brief review of a topic. In such a case, we provide an icon (shown at left) to let
you know that a video is available at our ChemPrep website.
(http://www.chemprep.cm.utexas.edu)

For those who would like to know which topics our instructors consider prior knowledge
for their college-level classes, please refer to the ALEKS list of learning objectives in the
Appendix.

Let’s get started!
UT Austin College of Natural Sciences:
Prep Materials for College Level Chemistry

Table of Contents

Welcome! ........................................................................................................... 3 
Periodic Table ......................................................................................................... 6 
Commit to Memory ................................................................................................. 8 
Unit 00: Refresher .................................................................................................. 9 
Unit01: Math ........................................................................................................ 10 
The Power Rule and Negative Exponents ............................................................. 10 
The Distributive Property.................................................................................... 10 
Multiplying Monomials ........................................................................................ 11 
Working with Percentages .................................................................................. 11 
Mini-Lecture: Slope of a Line .............................................................................. 12 
Mini-Lecture: Graphing a Line in Slope-Intercept Form ......................................... 13 
Graphing a Line – Standard Form Equation .......................................................... 14 
More Practice Graphing Lines ............................................................................. 15 
Unit02: Math - Measurement ................................................................................. 17 
Significant Figures (Significant Digits) .................................................................. 17 
Scientific Notation.............................................................................................. 19 
English-Metric Conversions and Other Values Considered “Common Knowledge” .... 19 
Temperature Conversions .................................................................................. 19 
Table of Metric Prefixes ...................................................................................... 20 
Metric Prefixes .................................................................................................. 21 
Practice Problems: Interconversion of Prefixed and Based SI Units ........................ 22 
Unit03: Matter ...................................................................................................... 23 
Periodic Table ................................................................................................... 23 
More on Periodic Table ...................................................................................... 24 
Unit04: Atoms, Ions, and Molecules ....................................................................... 25 
The Atom and Subatomic Particles ...................................................................... 25 
Mini-lecture: Atoms and Isotopes – Counting Protons, Neutrons and Electrons ...... 25 
Practice Problems: Counting Protons, Neutrons and Electrons ............................... 26 
Periodic Table showing Ionic Charge ................................................................... 27 
Predicting Ions .................................................................................................. 28 
Naming Ions ..................................................................................................... 28 
Table of Polyatomic Ions .................................................................................... 29 
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UT Austin College of Natural Sciences:
Prep Materials for College Level Chemistry
Special Metal Ions ............................................................................................. 29 
Table of Prefixes for Naming Binary Molecules ..................................................... 30 
Naming Binary Molecules ................................................................................... 30 
Naming Ionic Compounds .................................................................................. 31 
Nomenclature: Compounds Involving Polyatomic Ions .......................................... 31 
Nomenclature: Acids I ........................................................................................ 32 
Nomenclature: Acids II (with oxoanions) ............................................................. 32 
The 7 Strong Acids ............................................................................................ 33 
Creating (or Breaking) Ionic Compounds 34 
Naming Organic Hydrocarbons ........................................................................... 35 
Unit05: Stoichiometry – Moles and Molar Mass ........................................................ 37 
Molecular Mass, Avogadro’s Number, and the Mole .............................................. 37 
Avogadro’s Number and “The Mole” (Part II) ....................................................... 38 
Working with Moles ........................................................................................... 38 
Mastering Molecular Weights .............................................................................. 39 
Interpreting Chemical Formulas (Chemical Stoichiometry) ..................................... 40 
Mole Ratios and Chemical Formulas .................................................................... 40 
Mass Per Cent ................................................................................................... 41 
Unit06: Stoichiometry – Reactions ......................................................................... 43 
Solubility Rules .................................................................................................. 43 
Table of Reaction Types ..................................................................................... 44 
Reaction Types .................................................................................................. 45 
Mini-Lecture: Limiting Reactant and Percent Yield ................................................ 46 
Acids ................................................................................................................ 47 
Unit07: Stoichiometry - Molarity ............................................................................. 49 
Molarity ............................................................................................................ 49 
Practice Problems - Molarity ............................................................................... 50 
Molarity: Dilution ............................................................................................... 51 : Dilution (Type 2) ................................................................................. 52 
Now Your Turn: Molarity and Limiting Reactant.................................................... 52 

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