Applied Symbolic Computation (CS 680/480) Lecture 6: Integer Multiplication, Interpolation, and the Chinese Remainder Theorem. Jeremy R. Johnson May 9, 2001. Introduction.

ByThe Fundamental Theorem of Algebra. Lesson 4.5. Example. Consider the solution to Note the graph No intersections with x-axis Using the solve and csolve functions. Fundamental Theorem of Algebra. A polynomial f(x) of degree n ≥ 1 has at least one complex zero

ByDivision of Polynomials. Division by a Monomial. When dividing monomials with Exponential expressions, use the Quotient Rule of Exponents:. if x = 0. When subtracting exponents, you might get a zero or a negative exponent.

ByAlgebra II. 4.1: Graphing Polynomial Functions Objective: To identify polynomials, and to use several techniques to get rough sketches. Vocabulary. What is a monomial? An expression that is either a number, a variable, or the product of a number and one or more variables. Vocabulary.

ByIntroduction to Algorithms NP-Complete. CSE 680 Prof. Roger Crawfis. Polynomial Time. Most (but not all) of the algorithms we have studied so far are easy, in that they can be solved in polynomial time, be it linear, quadratic, cubic, etc.

BySolving Polynomial Inequalities. Factor & Solve!!. Solving Polynomial Inequalities. Place the inequality in standard form . Factor the polynomial completely. Find the zeros of the polynomial and sketch a graph using end behavior and your zeros. **Look for bounces**

ByChapter 6. Polynomials and Polynomial Functions. 6.1 Using Properties of Exponents. Properties of Exponents. Let a and b be real numbers and let m and n be integers. PRODUCT OF POWERS PROPERTY a m • a n = a m+n POWER OF A POWER PROPERTY ( a m ) n = a mn

ByPower and Polynomial Functions. College Algebra. Power Function. A power function is a function that can be represented in the form where k and p are real numbers, and k is known as the coefficient . Example : consider functions for area or volume.

ByDesign and Analysis of Computer Algorithm Lecture 10. Pradondet Nilagupta Department of Computer Engineering. Acknowledgement.

ByNUMERICAL DIFFERENTIATION. The derivative of f (x) at x 0 is:. An approximation to this is:. for small values of h. Forward Difference Formula. Find an approximate value for . The exact value of . Assume that a function goes through three points:. Lagrange Interpolating Polynomial.

ByPolynomial Functions and Models. Lesson 4.2. Review. General polynomial formula a 0 , a 1 , … ,a n are constant coefficients n is the degree of the polynomial Standard form is for descending powers of x a n x n is said to be the “leading term”. •. •.

ByCSE 20 Lecture 13: Analysis of Recursive Functions. CK Cheng. 3. Analysis . 3.1 Introduction 3.2 Homogeneous Linear Recursion. 3.1 Introduction. Derive the bound of functions or recursions Estimate CPU time and memory allocation Eg. PageRank calculation

ByGeostatistic Analysis. Topic 5 Starting 2/27/2007. Purposes. Estimating or interpolating values at unsampled sites within the area covered by existing observations Visiting every location is usually difficult or expensive.

By6.5 Theorems About Roots of Polynomial Equations. Imaginary Roots. POLYNOMIALS and THEOREMS Theorems of Polynomial Equations. There are 4 BIG Theorems to know about Polynomials Rational Root Theorem Irrational Root Theorem Imaginary Root Theorem Descartes Rule. Example (Imag RT).

By6.7 Multiplying a Polynomial by a Monomial. CORD Math Mrs. Spitz Fall 2006. Objectives:. After studying this lesson, you should be able to: Multiply a polynomial by a monomial, and Simplify expressions involving polynomials. Assignment. 6.7 Worksheet. Application.

By5.2 Polynomial & Linear Factors. Learning goals graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases

ByCreating Polynomials Given the Zeros. What do we already know about polynomial functions?. They are either ODD functions. They are either EVEN functions. Linear y = 4x - 5. Cubic y = 4x 3 - 5. Quadratics y = 4x 2 - 5. Quadratics y = 4x 2 - 5. Fifth Power y = 4x 5 –x + 5.

ByPOLYNOMIALS – Monomial Times a Polynomial When multiplying a monomial and a polynomial, multiply the monomial by EACH term in the polynomial. It’s called the Distributive Property. POLYNOMIALS – Monomial Times a Polynomial

By4.1 Exponents. n is your power; x is your base Read x to the nth power 3 factors of x, 5 factors of y xxxyyyyy What is the coefficient for the above term? What is the power on this term? 3x . Rules of Exponents:. Product Rule :

ByImage filtering. Hybrid Images, Oliva et al., http://cvcl.mit.edu/hybridimage.htm. Slides from Steve Seitz and Rick Szeliski. Image filtering. Hybrid Images, Oliva et al., http://cvcl.mit.edu/hybridimage.htm. What is an image?. Images as functions.

ByView Polynomial PowerPoint (PPT) presentations online in SlideServe. SlideServe has a very huge collection of Polynomial PowerPoint presentations. You can view or download Polynomial presentations for your school assignment or business presentation. Browse for the presentations on every topic that you want.