'General solution' presentation slideshows

Algebra II

Algebra II. Series of parameter driven, algebra exercises involving factoring polynomial expressions, quadratic equation, and using radical expressions involving square and cube roots. Algebra 101.

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Impossible, Imaginary, Useful Complex Numbers

Seventy-twelve. Impossible, Imaginary, Useful Complex Numbers. By:Daniel Fulton. Eleventeen. Why imagine the imaginary. Where did the idea of imaginary numbers come from Descartes, who contributed the term "imaginary" Euler called sqrt(-1) = i Who uses them

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Sec. 4.1 Antiderivatives and Indefinite Integration

Sec. 4.1 Antiderivatives and Indefinite Integration. By Dr. Julia Arnold. Antidifferentiation is the art of finding the function F(x) whose derivative would be the given function F / (x). Antidifferentiation is also called: Indefinite Integration.

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Complex eigenvalues

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Exponential Growth and Decay

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Solving the algebraic equations

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Lecture #9

Lecture #9. OUTLINE Continuity equations Minority carrier diffusion equations Minority carrier diffusion length Quasi-Fermi levels Read: Sections 3.4, 3.5. Derivation of Continuity Equation. Consider carrier-flux into/out-of an infinitesimal volume:. Area A , volume Adx. J N ( x ).

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PROBLEM SOLVING

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Binary Space Partition Trees

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Binary Space Partition Trees

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Section 1.8

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Supporting Collaborative Learning Activities with SCORM

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Strength of Materials I EGCE201 ?????????? 1

Strength of Materials I EGCE201 ?????????? 1. Instructor: ??.???????? ????????? ( ? . ?? ) ????????? : 6391 ??????????????????? E-mail: egwpr@mahidol.ac.th ???????? : 66(0) 2889-2138 ??? 6391. Columns. Members that support axial loads. Columns fail as a result of an instability .

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Ch 5.3: Series Solutions Near an Ordinary Point, Part II

Ch 5.3: Series Solutions Near an Ordinary Point, Part II. A function p is analytic at x 0 if it has a Taylor series expansion that converges to p in some interval about x 0 The point x 0 is an ordinary point of the equation

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Ch 7.4: Basic Theory of Systems of First Order Linear Equations

Ch 7.4: Basic Theory of Systems of First Order Linear Equations. The general theory of a system of n first order linear equations parallels that of a single n th order linear equation. This system can be written as x ' = P ( t ) x + g ( t ), where. Vector Solutions of an ODE System.

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Driven Oscillator

Driven Oscillator. One simple driving force is sinusoidal oscillation. Inhomogeneous equation Complex solution (real part). Sinusoidal Drive. Try a solution. Im. r. ir sin q. q. Re. r cos q. The solution given was a particular solution. Steady state solution

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Differential Equations

Differential Equations. Sec 6.3: Separation of Variables. Separation of Variables. all x terms can be collected with dx, and all y terms with dy, and a solution can be obtained by integration.

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Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients

Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients. The method of undetermined coefficients can be used to find a particular solution Y of an n th order linear, constant coefficient, nonhomogeneous ODE provided g is of an appropriate form.

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Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients

Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients. The method of undetermined coefficients can be used to find a particular solution Y of an n th order linear, constant coefficient, nonhomogeneous ODE provided g is of an appropriate form.

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Phase planes for linear systems with real eigenvalues

Phase planes for linear systems with real eigenvalues. SECTION 3.3. Summary. Suppose Y (t) = e ? t V is a straight-line solution to a system of DEs. What happens to Y (t) = (x(t), y(t)) as t ??? How does your answer depend on the sign of ??

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