4. Complex integration: Cauchy integral theorem and …
4. 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.
Download 4. Complex integration: Cauchy integral theorem and …
Information
Domain:
Source:
Link to this page:
Documents from same domain
5. Taylor and Laurent series Complex sequences and series
www.math.hkust.edu.hk5. Taylor and Laurent series Complex sequences and series An infinite sequence of complex numbers, denoted by {zn}, can be considered as a function defined on a set of positive integers into the unextended complex plane. For example, we take zn= n+ 1 2n so that the complex sequence is {zn} = ˆ1 + i 2, 2 + i 22, 3 + i 23 ...
Matrix Algebra for Engineers - Hong Kong University of ...
www.math.hkust.edu.hkThe mathematics in this matrix algebra course is at the level of an advanced high school student, but typically students would take this course after completing a university-level single variable calculus course. There are no derivatives and integrals in this course, but student’s are expected to …
Differential Equations - Department of Mathematics, HKUST
www.math.hkust.edu.hkused textbook “Elementary differential equations and boundary value problems” by Boyce & DiPrima (John Wiley & Sons, Inc., Seventh Edition, c 2001). Many of the examples presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven
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,
Differential Equations for Engineers
www.math.hkust.edu.hkequations 1. By checking all that apply, classify the following differential equation: d3y dx3 +y d2y dx2 = 0 a)first order b)second order c)third order d)ordinary e)partial f)linear g)nonlinear 2. By checking all that apply, classify the following differential equation: 1 x2 d dx x2 dy dx = e y a)first order b)second order c)ordinary d ...
Portfolio Selection Harry Markowitz The Journal of Finance ...
www.math.hkust.edu.hkvary with risk. The hypothesis (or maxim) that the investor does (or should) maximize discounted return must be rejected. If we ignore market im- perfections the foregoing rule never implies that there is a diversified portfolio which is preferable to all non-diversified portfolios. Diversi-
Numerical Methods for Engineers - Hong Kong University of ...
www.math.hkust.edu.hk44 Cubic spline interpolation (Part A)115 45 Cubic spline interpolation (Part B)117 46 Interpolation in Matlab 121 47 Project IV: Bessel functions and their zeros123 V Ordinary Differential Equations125 48 Euler method 129 49 Modified Euler method131 50 Runge-Kutta methods133 51 Second-order Runge-Kutta methods135 52 Higher-order Runge-Kutta ...
(2.1) Markowitz’s mean-variance formulation (2.2) Two …
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 ...
www.math.hkust.edu.hkIn MATLAB, single(224) has the same value as single(224 +1). Since single(224 +1) is exactly halfway between the two consecutive machine numbers 224 and 224 +2, MATLAB rounds to the number with a final zero-bit in f, which is 224. 1.10Machine epsilon Machine epsilon (e mach) is the distance between 1 and the next largest number. If
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 …
Related documents
Simpson 3/8 Rule for Integration - MATH FOR COLLEGE
mathforcollege.comThe main objective this chapter is to develop appropriateof formulas for approximating the integral of the form =∫ b a I f (x)dx (1) Most (if not all) of the developed formulas for integration based on a simple concept of are approximating a given function . f (x)by a simpler function (usually a polynomial function) f
Lecture 21 Integration: Left, Right and Trapezoid Rules
www.ohiouniversityfaculty.comIntegration: Left, Right and Trapezoid Rules The Left and Right endpoint rules In this section, we wish to approximate a de nite integral Z b a f(x)dx; where f(x) is a continuous function. In calculus we learned that integrals are (signed) areas and can be approximated by sums of smaller areas, such as the areas of rectangles. We begin by ...
6 Numerical Integration - Department of Mathematics
www2.math.umd.educal integration formulas are also referred to as integration rules or quadratures, and hence we can refer to (6.3) as the rectangular rule or the rectangular quadrature. The points x 0,...x n that are used in the quadrature formula are called quadrature points. a b f(a) f(b) x f(x) Figure 6.1: A rectangular quadrature
Mathematical Formula Handbook
homepage.ntu.edu.twEquation of a plane A point r (x, y, z)is on a plane if either (a) r bd= jdj, where d is the normal from the origin to the plane, or (b) x X + y Y + z Z = 1 where X,Y, Z are the intercepts on the axes. Vector product A B = n jAjjBjsin , where is the angle between the vectors and n is a unit vector normal to the plane containing A and B in the direction for which A, B, n form a right-handed …
Integral Calculus Formula Sheet
mslc.osu.eduIntegration by Parts: Knowing which function to call u and which to call dv takes some practice. Here is a general guide: u Inverse Trig Function (sin ,arccos , 1 xxetc) Logarithmic Functions (log3 ,ln( 1),xx etc) Algebraic Functions (xx x3,5,1/, etc)
Formulas and tables for the calculation of the inductance ...
nvlpubs.nist.govGrover} IvductanceofPolygonalCoils. 739 althoughtheplanofcalculationhereadopteddiffersfromthat ofNiwa. Itisatonceevidentthatinthelimitingcaseofanextremely ...
Differentiation Formulas Integration Formulas
www.pas.rochester.eduIntegration Formulas Z dx = x+C (1) Z xn dx = xn+1 n+1 +C (2) Z dx x = ln|x|+C (3) Z ex dx = ex +C (4) Z ax dx = 1 lna ax +C (5) Z lnxdx = xlnx−x+C (6) Z sinxdx = −cosx+C (7) Z cosxdx = sinx+C (8) Z tanxdx = −ln|cosx|+C (9) Z cotxdx = ln|sinx|+C (10) Z secxdx = ln|secx+tanx|+C (11) Z cscxdx = −ln |x+cot +C (12) Z sec2 xdx = tanx+C (13 ...
4.4 Composite Numerical Integration
www3.nd.edu4.4 Composite Numerical Integration . Motivation: 1) on large interval, use low order -Cotes formulas Newton are not accurate. 2) on large interval, interpolation using high degree polynomial is unsuitable because of oscillatory nature of high degree polynomials.