quantifier elimination for Presburger arithmetic
... Minimalistic Language of Presburger Arithmetic. Consider L = {+} and consider as I the set of all interpretations with domain N = {0, 1, 2, . . .} where + is interpreted as addition of natural numbers (these interpretations differ only in values for free variables). This is one definition of Presbur ...
... Minimalistic Language of Presburger Arithmetic. Consider L = {+} and consider as I the set of all interpretations with domain N = {0, 1, 2, . . .} where + is interpreted as addition of natural numbers (these interpretations differ only in values for free variables). This is one definition of Presbur ...
Mathematics-Paper-4-Important Questions
... 1.Deriv e Regula Falsi Formula to find the root of the equation. 2.Find the cube root of 30 using bisection method. 3.Using Muller’s method ,find the root of the equations cosx=xex,x3-x2-x1=0 4.Find the Newton- Raphson method, a root of the equations x3-5x+3=0, 3x-cosx+1=0. 5.Find the root of a equa ...
... 1.Deriv e Regula Falsi Formula to find the root of the equation. 2.Find the cube root of 30 using bisection method. 3.Using Muller’s method ,find the root of the equations cosx=xex,x3-x2-x1=0 4.Find the Newton- Raphson method, a root of the equations x3-5x+3=0, 3x-cosx+1=0. 5.Find the root of a equa ...
Variation - Alamo Colleges
... Step 2: Substitute the given values into the formula from step 1, and solve for k. The given values of this problem are: d = 5 inches, f = 50 lbs. Substituted into the problem yields: d=kf 5 = k (50) ...
... Step 2: Substitute the given values into the formula from step 1, and solve for k. The given values of this problem are: d = 5 inches, f = 50 lbs. Substituted into the problem yields: d=kf 5 = k (50) ...
AP_Calculus_Study_Sheet_BC_2013
... Interpretation of the Derivative If y = f(x) 1. m=f’(x) is ____________ 2. f’(a) is also called the _______________ ...
... Interpretation of the Derivative If y = f(x) 1. m=f’(x) is ____________ 2. f’(a) is also called the _______________ ...
slides
... pattern unification, an algorithm more powerful than Robinson’s (but still decidable) Variant: Constraint Logic Programming uses different proof-search algorithm, with specific treatment of some sub-formulae (constraints) in a particular theory (e.g. reals) All Turing-complete (not more: cf. Churc ...
... pattern unification, an algorithm more powerful than Robinson’s (but still decidable) Variant: Constraint Logic Programming uses different proof-search algorithm, with specific treatment of some sub-formulae (constraints) in a particular theory (e.g. reals) All Turing-complete (not more: cf. Churc ...
06.01-text.pdf
... 4. Integration by parts is a systematic method for finding antiderivatives of some of the functions that fit the criterion of Question 3 (i.e., ones whose antiderivatives were not presented in Chapters 1–5). Write down at least 3 examples of simple-looking functions whose antiderivatives are not obv ...
... 4. Integration by parts is a systematic method for finding antiderivatives of some of the functions that fit the criterion of Question 3 (i.e., ones whose antiderivatives were not presented in Chapters 1–5). Write down at least 3 examples of simple-looking functions whose antiderivatives are not obv ...
Mathematics 111, Spring Term 2010
... 7. Use the definition of the derivative (limit process) to compute h (x) , where h( x) 1 / x . Then find the equation of the line tangent to the graph at the point (2, 1/2). 8. Sketch a graph of a single function f with the following properties: f(0) = 1, f(1) = 4, f(-2) = 0; f(x) < 0 for x < -2 and ...
... 7. Use the definition of the derivative (limit process) to compute h (x) , where h( x) 1 / x . Then find the equation of the line tangent to the graph at the point (2, 1/2). 8. Sketch a graph of a single function f with the following properties: f(0) = 1, f(1) = 4, f(-2) = 0; f(x) < 0 for x < -2 and ...
ln x
... Using the function y = ln x, make a table of values for x that would be useful to estimate the derivative of y = ln x at x = 1 and then estimate the derivative. x ...
... Using the function y = ln x, make a table of values for x that would be useful to estimate the derivative of y = ln x at x = 1 and then estimate the derivative. x ...
a reciprocity theorem for certain hypergeometric series
... by direct applications of Stirling’s formula. The examination of f (−z) on γn is similar. However, in this case, if Re xj < 0, we can apply Stirling’s formula directly to each quotient Γ(1 − xj z) ...
... by direct applications of Stirling’s formula. The examination of f (−z) on γn is similar. However, in this case, if Re xj < 0, we can apply Stirling’s formula directly to each quotient Γ(1 − xj z) ...
Automatic differentiation
In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational differentiation, is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.) and elementary functions (exp, log, sin, cos, etc.). By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be computed automatically, accurately to working precision, and using at most a small constant factor more arithmetic operations than the original program.Automatic differentiation is not: Symbolic differentiation, nor Numerical differentiation (the method of finite differences).These classical methods run into problems: symbolic differentiation leads to inefficient code (unless carefully done) and faces the difficulty of converting a computer program into a single expression, while numerical differentiation can introduce round-off errors in the discretization process and cancellation. Both classical methods have problems with calculating higher derivatives, where the complexity and errors increase. Finally, both classical methods are slow at computing the partial derivatives of a function with respect to many inputs, as is needed for gradient-based optimization algorithms. Automatic differentiation solves all of these problems.