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4434Nonlinear Dynamics and Chaos
http://www.merlot.org/merlot/viewMaterial.htm?id=987443
'This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.״ The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena.The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation.'Topology
http://www.merlot.org/merlot/viewMaterial.htm?id=899275
Topology is generally considered to be one of the three linchpins of modern abstract mathematics (along with analysis and algebra). Recently, topology has an important components of applied mathematics, with many mathematicians and scientists employing concepts of topology to model and understand real-world structures and phenomena. Topology is the study of shapes:Including their properties, Deformations applied to them, Mappings between them and Configurations composed of them. Here we can learn this course with the help of provided study materialFutureLearn: Massive Open Online Courses (MOOCs)
http://www.merlot.org/merlot/viewMaterial.htm?id=899078
The Open University (UK) is forming FutureLearn: a consortium of 21 universities, as well as cultural players such as the British Museum, British Library, and British Council to provide Massive Open Online Courses (MOOCs). FutureLearn's pilot program began this Fall 2014.Beginning Algebra Module 2: Linear Equations I
http://www.merlot.org/merlot/viewMaterial.htm?id=897751
This module (eCouse) is designed to standalone as an instructional tool to cover the topic of Linear Equations from point and slope equations. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.Beginning Algebra Module 3: Linear Equations II
http://www.merlot.org/merlot/viewMaterial.htm?id=897754
This module (eCouse) is designed to stand alone as an instructional tool to cover the topic of Linear Equations II from point and slope equations. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.Beginning Algebra Module 5: Variable Expression I
http://www.merlot.org/merlot/viewMaterial.htm?id=897758
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expresions using properties of real numbers and rules of exponentiation. Learners would benefit by reviewing modules in sequence for the related course in Beginning Algebra.Beginning Algebra Module 6: Variable Expression II
http://www.merlot.org/merlot/viewMaterial.htm?id=897760
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expressions. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.Beginning Algebra Module 7: Factoring
http://www.merlot.org/merlot/viewMaterial.htm?id=897762
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of factoring polynomials. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.Beginning Algebra Module 8: Graphing Polynomial Equations
http://www.merlot.org/merlot/viewMaterial.htm?id=897764
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Graphing Polynomial Equations. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.Beginning Algebra Module 1: First Degree Equations and Inequalities with One Variable
http://www.merlot.org/merlot/viewMaterial.htm?id=893610
This eCourse (module) is designed to stand alone as an instructional tool to cover the topic of First-Degree Equations and Inequalities in Beginning Algebra. Learners would benefit by reviewing modules in sequence.