methods static variables and class math

Ngày tải lên: 17/09/2012, 09:13

Ngày tải lên: 05/03/2014, 23:20

... collection of mathematical tools for both understanding and solving problems in robotics and computer vision Several classes at Stanford cover the topics presented in this class, and so in much ... include the following R Courant and D Hilbert, Methods of Mathematical Physics, Volume I and II, John Wiley and Sons, 1989 D A Danielson, Vectors and Tensors in Engineering and Physics, Addison-Wesley, ... black -and- white vocabulary of discrete mathematics, which is foreign to most classical models of reality, quantum physics notwithstanding This class surveys some of the key tools of applied math...

Ngày tải lên: 14/03/2014, 14:20

... assumptions and subject to change in time MATHEMATICS AND MIND 1.3 MATHEMATICS AND MIND Almost, everywhere mathematics is a very useful and powerful language in expressing the law and order in ... Brown and Churchill, and Diflerential Equations by Ross, or the contents of books like Mathematicab Methods in Physical Sciences by Boas, Mathematical Methods: f o r Students of Physics and Related ... Acknowledgments N A T U R E and M A T H E M A T I C S 1.1 Mathematics and Nature 1.2 Laws of Nature 1.3 Mathematics and Mind 1.4 Is Mathematics the Only Language f o r Nature? 1.5 Nature and Mankind L E...

Ngày tải lên: 22/03/2014, 13:20

... intermediatelevel mathematics taught by mathematicians (in the one or two additional math courses that could be fit into the crowded undergraduate chemistry curriculum) and the kinds of mathematical methods ... course Mathematics courses beyond calculus are no longer a standard part of the chemistry curriculum in the United States This is despite the fact that advanced mathematical and statistical methods ... physicist, and mathematician Isaac Newton (1642-1727) Calculus was also developed, independently and almost simultaneously, by the German philosopher, mathematician, poet, lawyer, and alchemist...

Ngày tải lên: 28/03/2014, 10:20

... Z+ , Q+ and R+ are the sets of positive integers, rationals and reals, respectively For example, Z+ = {1, 2, 3, } • Z0+ , Q0+ and R0+ are the sets of non-negative integers, rationals and reals, ... 191 198 201 Functions of a Complex Variable 7.1 Curves and Regions 7.2 The Point at Infinity and the Stereographic 7.3 Cartesian and Modulus-Argument Form 7.4 Graphing Functions of ... the grammar’s too good.) • The theorems and methods in this text are subject to change without notice • This is a chain book If you not make seven copies and distribute them to your friends within...

Ngày tải lên: 31/03/2014, 16:19

... assumptions and subject to change in time MATHEMATICS AND MIND 1.3 MATHEMATICS AND MIND Almost, everywhere mathematics is a very useful and powerful language in expressing the law and order in ... Brown and Churchill, and Diflerential Equations by Ross, or the contents of books like Mathematicab Methods in Physical Sciences by Boas, Mathematical Methods: f o r Students of Physics and Related ... Acknowledgments N A T U R E and M A T H E M A T I C S 1.1 Mathematics and Nature 1.2 Laws of Nature 1.3 Mathematics and Mind 1.4 Is Mathematics the Only Language f o r Nature? 1.5 Nature and Mankind L E...

Ngày tải lên: 27/06/2014, 05:20

... assumptions and subject to change in time MATHEMATICS AND MIND 1.3 MATHEMATICS AND MIND Almost, everywhere mathematics is a very useful and powerful language in expressing the law and order in ... Brown and Churchill, and Diflerential Equations by Ross, or the contents of books like Mathematicab Methods in Physical Sciences by Boas, Mathematical Methods: f o r Students of Physics and Related ... Acknowledgments N A T U R E and M A T H E M A T I C S 1.1 Mathematics and Nature 1.2 Laws of Nature 1.3 Mathematics and Mind 1.4 Is Mathematics the Only Language f o r Nature? 1.5 Nature and Mankind L E...

Ngày tải lên: 27/06/2014, 18:20

... 11 14 16 Vectors 2.1 Vectors 2.1.1 Scalars and Vectors 2.1.2 The Kronecker Delta and Einstein 2.1.3 The Dot and Cross Product 2.2 Sets of Vectors in n Dimensions ... a Complex Variable 7.1 Curves and Regions 7.2 The Point at Infinity and the Stereographic 7.3 A Gentle Introduction to Branch Points 7.4 Cartesian and Modulus-Argument Form 7.5 ... the grammar’s too good.) • The theorems and methods in this text are subject to change without notice • This is a chain book If you not make seven copies and distribute them to your friends within...

Ngày tải lên: 06/08/2014, 01:21

... θ is the angle from a to b and n is a unit vector that is orthogonal to a and b and in the direction such that the ordered triple of vectors a, b and n form a right-handed system 29 z z k k j ... These are called right-handed and left-handed coordinate systems See Figure 2.7 Any other labelling of the axes could be rotated into one of these configurations The right-handed system is the one ... x j x y Figure 2.7: Right and left handed coordinate systems You can visualize the direction of a × b by applying the right hand rule Curl the fingers of your right hand in the direction from...

Ngày tải lên: 06/08/2014, 01:21

... evaluates x to and is thus discontinuous at that point Since the numerator and denominator are continuous functions and the 75 denominator vanishes while the numerator does not, the left and right ... Solution Exercise 3.14 (mathematica/calculus/differential/implicit.nb) Find y (x) and y (x), given that x2 − xy + y = Hint, Solution 3.8.5 Maxima and Minima Exercise 3.15 (mathematica/calculus/differential/maxima.nb) ... interval and any positive there exists a δ > such that |f (x) − f (ξ)| < for all < |x − ξ| < δ In general, this value of δ depends on both ξ and If δ can be chosen so it is a function of alone and...

Ngày tải lên: 06/08/2014, 01:21

... 1) and |x1 − x2 | < δ Solution 3.6 √ √ √ First consider the function x Note that the function x + δ − x is a decreasing function of x and an increasing √ √ √ function of δ for positive x and ... and ∆f By definition, ∆f = f (u + ∆u) − f (u), ∆u = g(x + ∆x) − g(x), and ∆f, ∆u → as ∆x → If ∆u = then we have = ∆f df − → as ∆u → ∆u du If ∆u = for some values of ∆x then ∆f also vanishes and ... the derivative does not exist and thus x = is a critical point For x < 2, f (x) < and for x > 2, f (x) > x = is a local minimum Solution 3.16 Let r be the radius and h the height of the cylinder...

Ngày tải lên: 06/08/2014, 01:21

... of variables u = 2x + Hint 4.2 Make the change of variables u = ln x Hint 4.3 Make the change of variables u = x2 + Hint 4.4 Make the change of variables u = sin x Hint 4.5 Make the change of variables ... Hint 4.13 Let u = x, and dv = sin x dx Hint 4.14 Perform integration by parts three successive times For the first one let u = x3 and dv = e2x dx Hint 4.15 Expanding the integrand in partial fractions, ... 4.13 Let u = x, and dv = sin x dx Then du = dx and v = − cos x x sin x dx = −x cos x + cos x dx = −x cos x + sin x + C Solution 4.14 Let u = x3 and dv = e2x dx Then du = 3x2 dx and v = e2x x3...

Ngày tải lên: 06/08/2014, 01:21

... ıu1 + u2 + ku3 where u0 , u1 , u2 and u3 are real numbers and ı,  and k are objects which satisfy ı2 = 2 = k = −1, ı = k, ı = −k and the usual associative and distributive laws Show that for ... product of z = r eıθ and ζ = ρ eıφ is zζ = rρ eı(θ+φ) The length of the vector zζ is the product of the lengths of z and ζ The angle of zζ is the sum of the angles of z and ζ (See Figure 6.6.) ... quotient of z = r eıθ and ζ = ρ eıφ is z = ρ eı(θ−φ) The length of the ζ vector z is the quotient of the lengths of z and ζ The angle of z is the difference of the angles of z and ζ (See ζ ζ Figure...

Ngày tải lên: 06/08/2014, 01:21

... |ζ|2 Consider the parallelogram defined by the vectors z and ζ The lengths of the sides are z and ζ and the lengths of the diagonals are z + ζ and z − ζ We know from geometry that the sum of the squared ... complex variable z as a function of x and y or as a function of r and θ with the substitutions z = x + ıy and z = r eıθ , respectively Then we can separate the real and imaginary components or write ... θ) eıφ(r,θ) Example 7.4.1 Consider the functions f (z) = z, f (z) = z and f (z) = and y and separate them into their real and imaginary components 1−z We write the functions in terms of x f (z)...

Ngày tải lên: 06/08/2014, 01:21

... Figure 7.18 and Figure 7.19 for plots of the real and imaginary parts of the cosine and sine, respectively Figure 7.20 shows the modulus of the cosine and the sine The hyperbolic sine and cosine ... plots of the real and imaginary part of Log z -1 -2 -2 -2 y y -2 -1 -1 x -1 x -1 -2 Figure 7.21: Plots of (Log z) and -2 (Log z) The form: ab Consider ab where a and b are complex and a is nonzero ... zero at infinity and its only singularity is at z = 1, the only possibilities for branch points are at z = and z = ∞ Since log z−1 = − log(z − 1) and log w has branch points at zero and infinity,...

Ngày tải lên: 06/08/2014, 01:21

... the strip | (z)| < and of the strip < (z) < under the transformations: w = 2z 2 w = z+1 z−1 Hint, Solution 295 b a c θ φ l Figure 7.34: A linkage Exercise 7.37 Locate and classify all the singularities ... the region, x = and x = 3, are respectively mapped to the parabolas: u=4− v , 16 v ∈ R and u = − v , 36 v∈R We write the image of the mapping in set notation w = u + ıv : v ∈ R and − v < u < − ... and radius greater than unity We can either say that this path encloses the two branch points at z = ±1 and no other singularities or we can say that this path encloses the point at infinity and...

Ngày tải lên: 06/08/2014, 01:21

... branch cut beteen z = and z = 13/12 This puts a branch cut between w = ∞ and w = and thus separates the branches of the logarithm Figure 7.54 shows the branch cuts in the positive and negative sheets ... function expressed in terms of x and y, φ(x, y) We can write φ as a function of z = x + ıy and z = x − ıy f (z, z) = φ z+z z−z , ı2 We treat z and z as independent variables We find the partial derivatives ... 0, and each go to infinity We can also make the function single-valued with a branch cut that connects two of the points z = −1, 0, and another branch cut that starts at the remaining point and...

Ngày tải lên: 06/08/2014, 01:21

... partial derivatives of u and v with respect to x and y exist at z = and that ux = vy and uy = −vx there: the Cauchy-Riemann equations are satisfied at z = On the other hand, show that lim z→0 f ... equations for µ and ν are satisfied if and only if the Cauchy-Riemann equations for u and v are satisfied The continuity of the first partial derivatives of u and v implies the same of µ and ν Thus f ... equations hold and the first partial derivatives of u and v are continuous at that point (a) f (z) = x3 + y + ı0 The Cauchy-Riemann equations are ux = vy and uy = −vx 3x2 = and 3y = x = and y = The...

Ngày tải lên: 06/08/2014, 01:21