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Differential Equations
the slope of the tangent line to the curve y = f(x) at the point (x,y). This slope is obtained by a limit, and is defined as f′(x) = lim h→0 f(x +h)−f(x) h. (1) 0.4Differentiating a combination of functions 0.4.1The sum or difference rule The derivative of the sum of f(x) and g(x) is (f + g)′= f′+ g′. Similarly, the derivative of ...
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Vector Calculus for Engineers - Hong Kong University of ...
www.math.hkust.edu.hkThese are the lecture notes for my online Coursera course,Vector Calculus for Engineers. Students who take this course are expected to already know single-variable differential and integral calculus to the level of an introductory college calculus course. Students should also be familiar with matrices,
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Differential Equations for Engineers
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Numerical Methods for Engineers - Hong Kong University of ...
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4. Complex integration: Cauchy integral theorem and …
www.math.hkust.edu.hk4. Complex integration: Cauchy integral theorem and Cauchy integral formulas Definite integral of a complex-valued function of a real variable Consider a complex valued function f(t) of a real variable t: f(t) = u(t) + iv(t), which is assumed to be a piecewise continuous function defined in the closed interval a ≤ t ≤ b.
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www.math.hkust.edu.hkfrontier portfolios need only invest in combinations of these two funds. Remark Any convex combination (that is, weights are non-negative) of ef-ficient portfolios is an efficient portfolio. Let αi ≥ 0 be the weight of Fund i whose rate of return is Ri f. Since E h Ri f i …
Numerical Methods - Hong Kong University of Science and ...
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Systems of Linear Equations - Hong Kong University of ...
www.math.hkust.edu.hkSystems of Linear Equations Beifang Chen 1 Systems of linear equations Linear systems A linear equation in variables x1;x2;:::;xn is an equation of the form a1x1 +a2x2 +¢¢¢+anxn = b; where a1;a2;:::;an and b are constant real or complex numbers. The constant ai is called the coe–cient of xi; and b is called the constant term of the equation. A system of linear equations …
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