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Wednesday, August 27, 2008

How Light Enters the Eye

Wednesday, August 27, 2008
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Refraction of Light

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Refraction is the change in direction of a wave due to a change in its speed. This is most commonly seen when a wave passes from one medium to another. Refraction of light is the most commonly seen example, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium into another or when water waves move into water of a different depth. In optics,...

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Laws of reflection

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Reflection is the change in direction of a wave front at an interface between two different media so that the wave front returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves.Reflection of light may be specular (that is, mirror-like) or diffuse (that is, not retaining the image, only the energy) depending on the nature of the interface....

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Prism

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Prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use "prism" usually refers to this type. Some types of optical prism are not in fact in the shape of geometric prisms....

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SPECTRUM

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A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by analogy to many fields. Thus one might talk about the spectrum of political opinion,...

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Sunday, August 24, 2008

Modern Physics: Special Relativity

Sunday, August 24, 2008
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Special relativity (SR) (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after considerable contributions of Hendrik Lorentz and Henri Poincaré) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity – that all uniform motion is relative,...

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Wednesday, August 20, 2008

Resolution - Refutation Proofs

Wednesday, August 20, 2008
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Thursday, August 14, 2008

Programming Paradigms

Thursday, August 14, 2008
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Computer architecture by discussing function call and return in further depth as well as introducing the swap function in relation to C++ c...

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computer architecture function call and returns in relation to C code.

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Computer architecture and the Assembly programming language

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Heap segments and their use in the C programming language

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HEap Swgment is a segment of memory claimed by a program. Within the heap, pieces of memory can be used and freed as needed. Depending on usage, heaps can become fragmented as small pieces of memory are used and freed. In formal computer science terms, a heap is the same as a partially ordered tr...

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C programming language and generic stacks

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Programming Paradigms-C language programming by focusing on different forms of stack.

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Linear Dynamical Systems Lecture 20-Observability and State Estimation

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Lecture 19 Controllability and State Transfer and their uses in modern electrical engineering

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Linear Dynamical Systems Lecture 18 -Applications of SVD, Controllability,and State Transfer in Electrical Engineering

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Linear Dynamical Systems Lecture 17-Applications of single value decomposition in LDS and electrical engineering

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Singular value decomposition (SVD) is an important factorization of a rectangular real or complex matrix, with several applications in signal processing and statistics. Applications which employ the SVD include computing the pseudoinverse, least squares fitting of data, matrix approximation, and determining the rank, range and null space of a matr...

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Linear Dynamical Systems Lecture 16- Use of symmetric matrices, quadratic forms, matrix norm, and SVDs in LDS

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Linear Dynamical Systems Lecture 15-Inputs and Outputs of symmetric matrices

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Linear Dynamical Systems Lecture 14- Applications of Jordan Canonical Form in LDS and Electrical Engineering

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Linear Dynamical Systems Lecture 13-generalized eigenvectors, diagonalization, and Jordan canonical form

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Jordan normal form (often called Jordan canonical form) shows that a given square matrix M over a field K containing the eigenvalues of M can be transformed into a certain normal form by changing the basis. This normal form is almost diagonal in the sense that its only non-zero entries lie on the diagonal and the superdiagonal. This is made more precise in the Jordan-Chevalley decomposition. One can...

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Linear Dynamical Systems Lecture12-Matrix exponentials,Eigenvectors,and Diagonalization and their uses in LDS

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Matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e. if there exists an invertible matrix P such that P −1AP is a diagonal...

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Linear Dynamical Systems Lecture 11-LaPlace transform use of matrix exponentials

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Matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.Laplace transform is one of the best known and widely used integral transforms. It is commonly used to produce an easily solvable algebraic equation from an ordinary differential...

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Linear Dynamical Systems Lecture 9&10 -Autonomous linear dynamical systems

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Linear Dynamical Systems Lecture 8-Least Norm solutions of undetermined equations

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Linear Dynamical Systems Lecture 7-Regularized least squares and the Gauss-Newton method

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Gauss–Newton algorithm is a method used to solve non-linear least squares problems. It can be seen as a modification of Newton's method for finding a minimum of a function. Unlike Newton's method, the Gauss–Newton algorithm can only be used to minimize a sum of squared function values, but it has the advantage that second derivatives, which can be challenging to compute, are not required.Non-linear...

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Linear Dynamical Systems Lecture 6-Applications of least squares

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Linear Dynamical Systems Lecture 5- QR Factorization and least squares

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The method of least squares is used to solve overdetermined systems. Least squares is often applied in statistical contexts, particularly regression analysis.Least squares can be interpreted as a method of fitting data. The best fit in the least-squares sense is that instance of the model for which the sum of squared residuals has its least value, a residual being the difference between an observed...

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Linear Dynamical Systems lecture 4-Orthonormal sets of vectors and QR factorization

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In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and both of unit length. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal bas...

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Linear Dynamical Systems Lecture 3-Linear algebra

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Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation...

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Linear Dynamical Systems Lecture 2 -Linear functions

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A linear function is a real or complex function f with the functional equation y=f(x)=m⋅x+b, where m and b are real (or complex) numbers. The equation y=f(x)=m⋅x+b is called (general) linear equation. The graph of a real linear function is a straight li...

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Introduction to Linear Dynamical Systems Lecture 1

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Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical...

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Monday, August 11, 2008

Convex Optimization II

Monday, August 11, 2008
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Knowledge Based Systems: Logic and Deduction

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Convex Optimization

Convex optimization is a subfield of mathematical optimization. Given a real vector space together with a convex, real-valued functiondefined on a convex subset of , the problem is to find the point in for which the number is smallest, i.e., the point such that for all .The convexity of and make the powerful tools of convex analysis applicable: the Hahn–Banach theorem and the theory of subgradients...

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Thursday, August 7, 2008

Programming Abstractions

Thursday, August 7, 2008
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The computing environment of tomorrow will not be anything like the stand-alone environment of yesterday. Computing infrastructure is changing drastically, presenting unique opportunities as well as challenges for applications and application scientists. Despite the rapid onset of distributed infrastructure, the majority of scientists still use the same programming methods that they are accustomed...

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Friday, August 1, 2008

Special Relativity Lecture

Friday, August 1, 2008
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Special relativity (SR) (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after considerable contributions of Hendrik Lorentz and Henri Poincaré) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity – that all uniform motion is relative,...

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Thursday, July 31, 2008

Searching Game Trees

Thursday, July 31, 2008
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In combinatorial game theory, a game tree is a directed graph whose nodes are positions in a game and whose edges are moves. The complete game tree for a game is the game tree starting at the initial position and containing all possible moves from each position.The diagram shows the first two levels, or ply, in the game tree for tic-tac-toe. We consider all the rotations and reflections of positions...

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Problem Reduction Search: AND/OR Graphs

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Sometimes problems only seem hard to solve. A hard problem may be one that can be reduced to a number of simple problems...and, when each of the simple problems is solved, then the hard problem has been solved. This is the basic intuition behind the method of problem reduction. We will have much more to say about this method of search when we cover problem solving and planning in the second half...

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Heuristic Search A* and Beyond

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Heuristic algorithm or simply a heuristic is an algorithm that gives up finding the optimal solution for an improvement in run time.Two fundamental goals in computer science are finding algorithms with provably good run times and with provably good or optimal solution quality. A heuristic is an algorithm that abandons one or both of these goals; for example, it usually finds pretty good solutions,...

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Wednesday, July 30, 2008

Programming Paradigms

Wednesday, July 30, 2008
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A programming paradigm is a fundamental style of computer programming. (Compare with a methodology, which is a style of solving specific software engineering problems).A programming language can support multiple paradigms. For example programs written in C++ or Object Pascal can be purely procedural, or purely object-oriented, or contain elements of both paradigms. Software designers and programmers...

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Tuesday, July 29, 2008

Introduction to Robotics Lecture 16

Tuesday, July 29, 2008
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Introduction to Robotics Lecture 15

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Introduction to Robotics Lecture 14

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Introduction to Robotics Lecture 13

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Introduction to Robotics Lecture 12

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Introduction to Robotics Lecture 11

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Introduction to Robotics Lecture 10

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Introduction to Robotics Lecture 9

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Introduction to Robotics Lecture 8

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Introduction to Robotics lecture 7

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Introduction to Robotics Lecture 6

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Introduction to Robotics Lecture 5

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Introduction to Robotics lecture 4

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Introduction to Robotics Lecture 3

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Introduction to Robotics Lecture 2

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Introduction to Robotics

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Robotics is the science and technology of robots, their design, manufacture, and application. Robotics requires a working knowledge of electronics, mechanics and software, and is usually accompanied by a large working knowledge of many subjects. A person working in the field is a roboticist.The structure of a robot is usually mostly mechanical and can be called a kinematic chain (its functionality...

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Machine Learning lecture 20

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Machine Learning Lecture 19

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Machine learning lecture 18

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Machine Learning lecture 17

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Machine learning lecture 16

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Machine Learning lecture 15

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Machine learning lecture 14

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Machine learning lecture 13

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Machine learning Lecture 12

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Machine learning lecture 11

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Machine Learning Lecture 10

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Machine Learning lecture 9

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Machine Learning lecture 8

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Machine Learning lecture 7

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Machine Learning Lecture 6

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Machine Learning Lecture 5

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Machine Learning Lecture 4 |

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Machine Learning lecture 3

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This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include supervised learning, unsupervised learning, learning theory, reinforcement learning and adaptive control. Recent applications of machine learning, such as to robotic control, data mining, autonomous navigation, bioinformatics, speech recognition, and text and web data processing are also...

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Machine Learning lecture 2

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Linerar regression,gradient descent,normal equati...

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Machine Learning lecture

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Machine learning is concerned with the design and development of algorithms and techniques that allow computers to "learn". At a general level, there are two types of learning: inductive, and deductive. Inductive machine learning methods extract rules and patterns out of massive data sets.The major focus of machine learning research is to extract information from data automatically, by computational...

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Artificial Intelligence:Informed State Space Search

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Artificial Intelligence-Searching with Costs

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Artificial Intelligence-Problem Solving by Search

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Index Properties and Classification of Soils

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Sampling and Non - Intrusive Methods

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Introduction to Subsurface Exploration

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Fluid Mechanics

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Artificial Intelligence

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Sediment Transport and Deposition

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Monday, July 28, 2008

The New Food Wars: Globalization GMOs and Biofuels

Monday, July 28, 2008
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The New Food Wars: Globalization GMOs and Biofu...

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Advanced Concepts of Gravity

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Advanced Concepts of Grav...

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Weathering

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Metamorphic Rocks

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Sedimentary Rocks

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Igneous Rocks lecture

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Origin And Types of Soils

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Origin And Types of Rocks

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Sunday, July 27, 2008

Chemical Characteristics of Minerals

Sunday, July 27, 2008
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Minerals may be classified according to chemical composition. They are here categorized by anion group. The list below is in approximate order of their abundance in the Earth's crust. The list follows the Dana classification system.Silicate classThe largest group of minerals by far are the silicates (most rocks are ≥95% silicates), which are composed largely of silicon and oxygen, with the addition...

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Crystallography and Optical Properties

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Physical Properties of Minerals

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Remote Sensing in Engineering Geology

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Geologic Maps and Stratigraphic Sections

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Geologic Structures

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Structural geology is the study of the three dimensional distribution of rock bodies and their planar or folded surfaces, and their internal fabrics.Structural geology includes features of and overlaps with facets of geomorphology, metamorphism and geotechnical studies. By studying the three dimensional structure of rocks and regions, inferences on tectonic history, past geological environments and...

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Saturday, July 26, 2008

Introduction to Engineering Geology

Saturday, July 26, 2008
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