Reminder: TA’s Review session Date: July 17 (Tuesday, for all students) Time: 10 - 11:40 am Room: 304 BH.

Slides:

Advertisements

Similar presentations

Solved problems on comparison theorem for series.

Advertisements

MA Day 67 April 22, 2013 Section 13.7: Stokes’s Theorem Section 13.4: Green’s Theorem.

Engineering Mathematics Class #15 Fourier Series, Integrals, and Transforms (Part 3) Sheng-Fang Huang.

PA214 Waves and Fields Fourier Methods Blue book New chapter 12 Fourier sine series Application to the wave equation Fourier cosine series Fourier full.

Partial Differential Equations Definition One of the classical partial differential equation of mathematical physics is the equation describing the conduction.

[YEAR OF ESTABLISHMENT – 1997]

Fourier Series.

APPLICATIONS OF INTEGRATION

Binomial Theorem. Go to slide 11 Introduction Notice.

Saturday May 02 PST 4 PM. Saturday May 02 PST 10:00 PM.

The Fourier series A large class of phenomena can be described as periodic in nature: waves, sounds, light, radio, water waves etc. It is natural to attempt.

Representing Functions by Power Series. A power series is said to represent a function f with a domain equal to the interval I of convergence of the series.

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

1 Week 4 1. Fourier series: the definition and basics (continued) Fourier series can be written in a complex form. For 2π -periodic function, for example,

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

Fourier series of function with arbitrary period p=2L

f /(x) = 6x2 – 6x – 12 = 6(x2 – x – 2) = 6(x-2)(x+1).

Please open Daily Quiz 34. A scientific calculator may be used on this quiz. You can keep your yellow formula sheets out when you take the quiz. Remember.

Review Of Formulas And Techniques Integration Table.

Sinusoids and Transformations

Fourier Series and Transforms Clicker questions. Does the Fourier series of the function f converge at x = 0? 1.Yes 2.No 0 of 5 10.

From Fourier Series to Fourier Transforms. Recall that where Now let T become large... and so ω becomes small... Fourier Transform of f(x) Inverse Fourier.

Integral Transform Method CHAPTER 15. Ch15_2 Contents  15.1 Error Function 15.1 Error Function  15.2Applications of the Laplace Transform 15.2Applications.

FOURIER ANALYSIS TECHNIQUES Fourier series permit the extension of steady state analysis to general periodic signal. FOURIER SERIES.

Mathematics. Session Definite Integrals –1 Session Objectives  Fundamental Theorem of Integral Calculus  Evaluation of Definite Integrals by Substitution.

15.3 Fourier Integral. Fourier Integral In ch 12, f(x) defined in (-p,p) f(x)= FS(x) Fourier Series (periodic function) In 15.3, f(x) defined in (-infinity,

11/20/2015 Fourier Series Chapter /20/2015 Fourier Series Chapter 6 2.

Orthogonal Functions and Fourier Series

12.2 Fourier Series Trigonometric Series is orthogonal on the interval [ -p, p]. In applications, we are interested to expand a function f(x) defined on.

1 CHAPTER 5 : FOURIER SERIES  Introduction  Periodic Functions  Fourier Series of a function  Dirichlet Conditions  Odd and Even Functions  Relationship.

1 Example 2 (a) Find the range of f(x) = x 2 +1 with domain [0,2]. Solution The function f is increasing on the interval [0,2] from its smallest value.

Differential Equations Brannan Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 09: Partial Differential Equations and Fourier.

Ch 10.6: Other Heat Conduction Problems

Sheng-Fang Huang Fourier Series Fourier series are the basic tool for representing periodic functions. A function ƒ(x) is called a periodic function.

12.3 Fourier Cosine and Sine Series Odd function Even function (a) The product of two even functions is even. (b) The product of two odd functions is even.

Section 10.5 Fourier Series. Taylor Polynomials are a good approximation locally, but not necessarily globally We can use Fourier approximations –May.

Fourier Integral Fourier series of the function f [-p,p] The Fourier Integral of the function f.

Section 5.3 The Fundamental Theorem and Interpretations.

Section 5.3 The Fundamental Theorem and Interpretations.

Clicker Question 1 What is the degree 2 (i.e., quadratic) Taylor polynomial for f (x) = 1 / (x + 1) centered at 0? – A. 1 + x – x 2 / 2 – B. 1  x – C.

1 College Algebra K/DC Friday, 04 December 2015 OBJECTIVE TSW solve absolute value equations and inequalities. QUIZ: Sec. 1.6 will be given after the lesson.

Finals are just around the corner. Factor? Review Session: (all levels) Date: Monday, May 9 th When: 2:00 – 3:00pm Where: MS 413.

FOURIER SERIES EVEN AND ODD FUNCTION AND APPLICATION

Math for CS Fourier Transform

Chapter 7 Infinite Series. 7.6 Expand a function into the sine series and cosine series 3 The Fourier series of a function of period 2l 1 The Fourier.

Fourier Series What will you learn???. Contents How to determine the Periodic Functions How to determine Even and Odd Functions Fourier Series : Fourier.

Fourier analysis Periodic function: Any (“reasonable”) periodic function, can be written as a series of sines and cosines “vibrations”, whose frequencies.

Subject : Advance engineering mathematics Topic : Fourier series & Fourier integral.

Legendre Polynomials Recurrence Relation

Mathematics 2 the First and Second Lectures

Present by SUBHRANGSU SEKHAR DEY

Boyce/DiPrima 10th ed, Ch 10.4: Even and Odd Functions Elementary Differential Equations and Boundary Value Problems, 10th edition, by William E. Boyce.

Mean Value Theorem 5.4.

Boyce/DiPrima 10th ed, Ch 10.3: The Fourier Convergence Theorem Elementary Differential Equations and Boundary Value Problems, 10th edition, by William.

Ch 10.4: Even and Odd Functions

2-2 Extension Part 2: Piecewise Functions

Fourier Series Introduction Fourier sine series (square wave)

Fourier Series, Integrals, and Transforms

Chapter 11 Fourier Series.

Fourier Integrals For non-periodic applications (or a specialized Fourier series when the period of the function is infinite: L) -L L -L- L

Representation of Functions by Power Series (9.9)

Partial Differential Equations

Mean-Value Theorem for Integrals

Fourier Analysis Lecture-8 Additional chapters of mathematics

Piecewise Functions.

Reminder Second Hour Exam Date: July 9 ( Monday).

Introduction to Fourier Series

Approximation and Computing Area

FOURIER SERIES PERIODIC FUNCTIONS

Presentation transcript:

Reminder: TA’s Review session Date: July 17 (Tuesday, for all students) Time: :40 am Room: 304 BH

Final Exam Date: July 19 (Thursday) Time: 10: :30 pm Room: LC-C3 Covers: all materials I will have a review session on Wednesday

Fourier Series For a piecewise continuous function f on [-T,T], we have the Fourier series for f:

Examples Compute the Fourier series for

Convergence of Fourier Series Pointwise Convegence Theorem. If f and f are piecewise continuous on [ -T, T ], then for any x in (-T, T), we have where the a n, s and b n, s are given by the previous fomulas. It converges to the average value of the left and right hand limits of f(x). Remark on x = T, or -T.

Consider Even and Odd extensions; Definition: Let f(x) be piecewise continuous on the interval [0,T]. The Fourier cosine series of f(x) on [0,T] is: and the Fourier sine series is: Fourier Sine and Cosine series

Consider the heat flow problem:

Solution Since the boundary condition forces us to consider sine waves, we shall expand f(x) into its Fourier Sine Series with T = . Thus

With the solution