Fourier Series - QUIZ Team A questions in white

Slides:

Advertisements

Similar presentations

4.4 Rational Root Theorem.

Advertisements

Lesson 7-1 Integration by Parts.

P.3: Part 2 Functions and their Graphs. Transformations on Parent Functions: y = f(x): Parent Functions y = f(x – c) y = f(x + c) y = f(x) – c y = f(x)

Wavelets and Data Compression

Sec. 4.5: Integration by Substitution. T HEOREM 4.12 Antidifferentiation of a Composite Function Let g be a function whose range is an interval I, and.

Copyright © 2005 Pearson Education, Inc. Chapter 4 Graphs of the Circular Functions.

Techniques in Signal and Data Processing CSC 508 Frequency Domain Analysis.

Math Review with Matlab:

Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.

8.2 Integration By Parts.

EXAMPLE 4 Use Descartes’ rule of signs Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for f (x) = x 6.

EXAMPLE 4 Use Descartes’ rule of signs Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for f (x) = x 6.

1 Review of Fourier series Let S P be the space of all continuous periodic functions of a period P. We’ll also define an inner (scalar) product by where.

Lesson 7-2 Hard Trig Integrals. Strategies for Hard Trig Integrals ExpressionSubstitutionTrig Identity sin n x or cos n x, n is odd Keep one sin x or.

This is the graph of y = sin xo

Lecture 7 Fourier Series Skim through notes before lecture Ask questions in lecture After lecture read notes and try some problems See me in E47 office.

CHAPTER Continuity Integration by Parts The formula for integration by parts  f (x) g’(x) dx = f (x) g(x) -  g(x) f’(x) dx. Substitution Rule that.

2-2 HW = Pg #12-50 e, HW Continued.

Integration by parts Product Rule:. Integration by parts Let dv be the most complicated part of the original integrand that fits a basic integration Rule.

5.4 Exponential Functions: Differentiation and Integration The inverse of f(x) = ln x is f -1 = e x. Therefore, ln (e x ) = x and e ln x = x Solve for.

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.

Basic signals Why use complex exponentials? – Because they are useful building blocks which can be used to represent large and useful classes of signals.

Lecture 6 Intro to Fourier Series Introduction to Fourier analysis Today I’m now setting homework 1 for submission 31/10/08.

Limits. What is a Limit? Limits are the spine that holds the rest of the Calculus skeleton upright. Basically, a limit is a value that tells you what.

Substitution Rule. Basic Problems Example (1)

Today in Pre-Calculus Go over homework Notes: (need calculator & book)

Periodic driving forces

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

Integrals Related to Inverse Trig, Inverse Hyperbolic Functions

The General Power Formula Lesson Power Formula … Other Views.

Integration by Substitution

Graphs of Polynomial Functions. Parent Graphs  Quadratic Cubic Important points: (0,0)(-1,-1),(0,0),(1,1)  QuarticQuintic  (0,0) (-1,-1),(0,0),(1,1)

The Original f(x)=x 3 -9x 2 +6x+16 State the leading coefficient and the last coefficient Record all factors of both coefficients According to the Fundamental.

Simple Trigonometric Equations The sine graph below illustrates that there are many solutions to the trigonometric equation sin x = 0.5.

ZEROS=ROOTS=SOLUTIONS Equals x intercepts Long Division 1. What do I multiply first term of divisor by to get first term of dividend? 2. Multiply entire.

Graded Warm Up  Complete the graded warm up on your desk by yourself. There should be no talking.

Quadratic Functions (4) What is the discriminant What is the discriminant Using the discriminant Using the discriminant.

Chapter 4: Polynomial and Rational Functions. Warm Up: List the possible rational roots of the equation. g(x) = 3x x 3 – 7x 2 – 64x – The.

Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =

Polynomials of Higher Degree 2-2. Polynomials and Their Graphs  Polynomials will always be continuous  Polynomials will always have smooth turns.

Chapter 4: Polynomial and Rational Functions. Determine the roots of the polynomial 4-4 The Rational Root Theorem x 2 + 2x – 8 = 0.

This is JEOPARDY!!! It would be wise to be attentive, take appropriate notes, and ask questions.

Functions. Objectives: Find x and y intercepts Identify increasing, decreasing, constant intervals Determine end behaviors.

By Dr. Safa Ahmed El-Askary Faculty of Allied Medical of Sciences Lecture (7&8) Integration by Parts 1.

Integration Techniques, L’Hôpital’s Rule, and Improper Integrals 8 Copyright © Cengage Learning. All rights reserved.

TRASHKETBALL PRECALCULUS CHAPTER 2 QUIZ. WHAT IS THE VERTEX AND WHAT ARE THE INTERCEPTS?

Section 3.5 Trigonometric Functions Section 3.5 Trigonometric Functions.

Algebra Rational Functions. Introduction  Rational Function – can be written in the form f(x) = N(x)/D(x)  N(x) and D(x) are polynomials with.

Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.

Warmup 11/30/15 How was your Thanksgiving? What are you most thankful for in your life? To define the definite integralpp 251: 3, 4, 5, 6, 9, 11 Objective.

Mathematics 2 the First and Second Lectures

Today in Pre-Calculus Go over homework Notes: (need calculator & book)

FOURIER SERIES PREPARD BY: TO GUIDED BY:-

Algebra 2/Trigonometry Name __________________________

Warmup 3-7(1) For 1-4 below, describe the end behavior of the function. -12x4 + 9x2 - 17x3 + 20x x4 + 38x5 + 29x2 - 12x3 Left: as x -,

Section Euler’s Method

Algebra 2/Trigonometry Name __________________________

Integrals Related to Inverse Trig, Inverse Hyperbolic Functions

Fourier Series: Examples

Periodic Function Repeats a pattern at regular intervals

End Behaviors Number of Turns

Section 6.3 Integration by Parts.

73 – Differential Equations and Natural Logarithms No Calculator

5.3 Polynomial Functions By Willis Tang.

2 Activity 1: 5 columns Write the multiples of 2 into the table below. What patterns do you notice? Colour the odd numbers yellow and the even numbers.

Activity 1: 5 columns Write the multiples of 3 into the table below. What patterns do you notice? Colour the odd numbers yellow and the even numbers blue.

Activity 1: 5 columns Write the multiples of 9 into the table below. What patterns do you notice? Colour the odd numbers yellow and the even numbers blue.

Presentation transcript:

Fourier Series - QUIZ Team A questions in white Team B questions in red 1. What is when n = 3 ? 2. What is when n = 52 ? 3. What is when n = 1 ? 4. What is when n = 17 ? 5. What is when n = 52 ? 6. What is when n = 1 ? 7. What is when n = 4 ?

Fourier Series - QUIZ 8. Team B: What is ?

Fourier Series - QUIZ 9. Team A: What is ?

Fourier Series - QUIZ 10. Team B: Describe the following step function in terms of f(x) and x ?

Fourier Series - QUIZ 11. Team A: What is ?

Fourier Series - QUIZ 12. Team B: Describe the following step function over one period in terms of f(x) and x ?

Fourier Series - QUIZ 13. Team A: What is the integral of f(x) over one period ?

Fourier Series - QUIZ 14. Team B: Describe the following step function over one period in terms of f(x) and x ?

Fourier Series - QUIZ 15. Team A: What is the integral of f(x) over one period ?

Fourier Series - QUIZ Fourier series 16. Team B: If we were to represent the function below as a Fourier series what could you say about the value of a0 ? a0 is baseline shifter. Half way between 20 and 70 is 45. So ao = 90

Fourier Series - QUIZ Fourier series 17. Team A: If we were to represent the function below as a Fourier series what could you say about the values of the an terms ? odd function so all an terms are zero

Fourier Series - QUIZ Fourier series 18. Team B: If we were to represent the function below as a Fourier series what could you say about the sign of the b1 term ?

Fourier Series - QUIZ Fourier series 18. Team B: If we were to represent the function below as a Fourier series what could you say about the value of the b1 term ? It would have a negative amplitude

Finding coefficients of the Fourier Series - QUIZ Find Fourier series to represent this repeat pattern. Steps to calculate coefficients of Fourier series 1. Write down the function f(x) in terms of x. What is period? Period is 2p 2. Use equation to find a0? 3. Team A find coefficients an? 4. Team B find coefficients bn?

Finding coefficients of the Fourier Series - QUIZ Find Fourier series to represent this repeat pattern. Period is 2p 3. Team A find coefficients an? Integrate by parts so set u = x and cos (nx) dx = dv and du = dx n=1 n=2 n=3 n=4 n=5

Finding coefficients of the Fourier Series - QUIZ Find Fourier series to represent this repeat pattern. Period is 2p 4. Team B find coefficients bn? Integrate by parts so set u = x and sin (nx) dx = dv du = dx n=1 n=2 n=3 n=4 n=5