Example: stock market
Differential Equations
Chapter 0 A short mathematical review A basic understanding of calculus is required to undertake a study of differential equations. This zero chapter presents a short review.
Information
Domain:
Source:
Link to this page:
Documents from same domain
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 …
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 ...
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 ...
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.
(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
15.Applications of Differentiation (A)
irp-cdn.multiscreensite.comderivative is negative. While this method is quite efficient, it can become quite a task to find the second derivative when the first derivative is an extremely complex function. In such a case we use Method 1 to determine the nature of the stationary points. dy dx 2 0.6 12( 0.6) 6( 0.6) 6 1.92 0 x dy dx =-æö ç÷=- -- -= > èø 2 0.4 12( 0.4 ...
Adaptive Control: Introduction, Overview, and Applications
www.cds.caltech.eduRobust and Adaptive Control Workshop Adaptive Control: Introduction, Overview, and Applications Lyapunov Functions • Definition: If in a ball B R the function V(x) is positive definite, has continuous partial derivatives, and if its time derivative along any state trajectory of the system is negative semi-definite, i.e., then V(x)
The Second Derivative - Open Computing Facility
www.ocf.berkeley.eduSolution By repeated applications of the power rule, we find that f0(x) = 3x2, and f00(x) = 6x. For all x, the first derivative f0(x) > 0, so the function f(x) is always increasing.Considering the second derivative, we see that for x < 0 we have f00(x) < 0, so f(x) is concave down.For x > 0
CHAPTER 4 FLUID KINEMATICS
www2.et.byu.eduFluid Mechanics: Fundamentals and Applications Third Edition Yunus A. Çengel & John M. Cimbala McGraw-Hill, 2013 CHAPTER 4 ... Analysis Derivative operator d is a total derivative, ... 0.781 4.67 3.54 4.67 ...
Applications of Geographic Information Systems
www.eolss.net4.3.1. Trends 4.3.2. Perspectives 5. GIS Applications 5.1. General 5.2. Environmental Planning and Management 5.3. Hydrology and Water Resources 5.4. Urban Planning and Socioeconomics ... well as derivative map outputs. Although GIS has been around since the 1960s, applications have expanded in the 1990s. Many software systems have now been ...
Lecture 3 Properties of MLE: consistency,
ocw.mit.edu0 0.5 1 1.5 2 2.5 3 3.5 4 ϕˆ ϕ Figure 3.1: Maximum Likelihood Estimator (MLE) Suppose ... if we take derivatives of this equation with respect to ϕ (and interchange derivative and integral, which can usually be done) we will get, 2 ...
Iterative Reweighted Least Squares
cedar.buffalo.edu•Derivative has the form •Setting equal to zero and solving we get Machine Learning Srihari 4 y(x,w)=w j ... 3.Gradient 4.Hessian 5.Newton-Raphsonupdate …
Applications of Integration - Whitman College
www.whitman.edu194 Chapter 9 Applications of Integration 11. y = x3/2 and 2/3 ⇒ 12. y = x2 −2and ⇒ The following three exercises expand on the geometric interpretation of the hyperbolic functions. Refer to section 4.11 and particularly to figure 4.11.2 and exercise 6 in section 4.11. 13. Compute Z p