Math 126 Week 3 Assignment Pro

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Solar Power

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Wind Power

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Wind energy has been converted to other forms of useful energy, especially mechanical form even long time back. Energy stored in Wind is used to turn a windmill and then to used to grind grains and other stuff.

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Hydro Power

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Just like Wind Power, people from ancient world knew how to use the power of flowing water to do something useful.

like turning a waterwheel and grinding their grains. Hydropower today though is mainly discussed with electricity generation. There are thousands and thousands of dams built around the world to convert energy stored in water flow into electricity.

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Geothermal Power

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Earth crust is heated and its molten rocks forms lava. This heat is a great energy source. Earth’s heat is available regardless of the place, and it is available 24 hours a day and 7 days a week. This makes geothermal energy a great reliable renewable energy source.

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Biomass is the most commonly used source of renewable energy. Even the ancient man knew how to use wood to cook their food using firewood. But today, biomass energy mainly refers to burning or using materials like wood and different types of seeds to produce electricity.

Biomass has created a separate market by substituting the traditional oil with the biofuel or biodiesel. This energy sector is becoming. Ability to make your own biodiesel in your own backyard is another reason for the resent popularity behind biodiesel.

There are diverse opinions about using biomass excessively. We have discussed them on this site as well as on the renewable energy guide. You can see our biomass section for more details. You can download our free eBook renewable energy guide for even more information.

Tidal Energy:

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Tides are a great source of renewable energy. Tides are created due to gravitational pull of earth, moon and sun. This is a complex natural behavior. Rising water levels provides a great opportunity to generate reliable renewable energy.

Unlike other sources, tidal waves can produce large amount of electricity with a high degree of reliability. This makes tidal energy a key competitor in commercial renewable energy sector. Building a tidal renewable energy plant needs large sums of capital. Also the technology is costly and relatively new.

Tidal waves are only one form of ocean energy. There are other ways we can use the vast amount of energy hidden in the oceans. These are discussed in our free eBook renewable energy guide. You may download this by following this link. You can learn more about the tidal waves by reaching our tidal energy archive.

There are more renewable energy sources emerging. But what listed above are more stable technologies.

In summary, we have many options open to go green with renewable energy. We can save lots of money if we tap into these alternative energy sources. In addition we will find solutions for the global environmental problems we are facing today.

Today, we have an option to use these alternative sources to produce energy. But tomorrow, we will not have an option; we will have to optin to renewable energy sources whether we like it or not. Ever decreasing oil and coal reserves and environmental crisis we are facing even today will leave us no other option. So act today, go green.

Math 126 - Introduction to PDEs - Fall 2014
Instructor:    Jason Murphy   (for contact info click here)

Lecture:   MWF 3:10–4pm in          Barrows 20

Office hours:   Tues. 2–3:30pm and Fri. 1:30–3pm in 857 Evans

RRR week office hours:   Monday, Tuesday, Wednesday from 1–3pm in Moffitt 102

Piazza:   For discussion boards etc. you can find a Piazza signup link here.

Course control number:    54227

Prerequisites:    Math 53, Math 54

Textbook:   Partial Differential Equations, An Introduction, Walter Strauss
Additional reference:   Partial Differential Equations, Lawrence C. Evans

Both of these books are on reserve in the Mathematics Statistics Library.

Syllabus:    The official course description includes the following topics: waves and diffusion,
initial value problems for hyperbolic and parabolic equations, boundary value problems for
elliptic equations, Green's functions, maximum principles, a priori bounds, Fourier transform.

We will cover these topics and more. A rough outline is as follows:
  • Introduction/background
  • Laplace/heat/wave equations
  • Methods
  • Topics/applications
Grading:   Grades will be determined using the following:
  • Homework - eleven assignments, lowest score dropped
  • Midterm 1 - in class, Monday October 6
  • Midterm 2 - in class, Monday November 10
  • Final exam - Tuesday, December 16 at 7pm
Your grade will be computed by using the best of the following schemes:
  • Homework (20%), Midterm 1 (20%), Midterm 2 (20%), Final (40%)
  • Homework (20%), Midterm 1 (20%), Final (60%)
  • Homework (20%), Midterm 2 (20%), Final (60%)
  • Homework (20%), Final (80%)
Course policies:   It is your responsibility to know the policies stated below.
  • You cannot pass this course without taking the final exam.
  • Any conflicts due to religious creed or extra-curricular activities must be addressed
    by the end of week two (September 12, 2014).
  • No make-up exams will be given for missed midterms.
  • You are free to collaborate on homework assignments and/or seek outside sources;
    however, in order to receive credit you must write up solutions in your own words and
    cite any sources you use. (Read this handout for a discussion of academic honesty.)
  • Questions or complaints regarding the grading of an assignment or midterm must be
    addressed within two weeks of the date the assignment or midterm is returned to the class.
  • Late homework assignments will not be accepted.
Contact info: The best way to reach me is by email — murphy (at) math (dot) berkeley (dot) edu.
Please check the course webpage for information before writing.

Class notes:   I will maintain some notes here, which will supplement the material presented in class.
It may be better not to print the notes, as they will be updated often and early versions may contain typos.

Class schedule:    The following table will be updated throughout the semester.

Date  Lecture   Topics   References   Remarks  
8/29 1 Introduction (derivation of some common PDE) 
9/3 2 Background (calculus, topology)   Strauss A.1, A.3  
Evans C.2, C.3
9/5 Background (convolution, distributions)  Strauss 12.1 
9/8 Laplace/Poisson (fundamental solution)  Strauss 6.1, 7.2,  
Evans 2.2.1
9/10 Laplace/Poisson (Green's functions) Strauss 7.3
Evans 2.2.4
Homework 1 Due 
9/12 Laplace/Poisson (Green's functions, mean value property)  Strauss 7.4, 7.1  
Evans 2.2.4, 2.2.2  
9/15 7   Laplace/Poisson (maximum principle, uniqueness)  Strauss 6.1, 7.1
Evans 2.2.3 (a)  
9/178  Heat Equation (fundamental solution)   Strauss 2.4
Evans 2.3.1  
Homework 2 Due  
9/19 Heat Equation (mean value property)   Evans 2.3.2    
9/22 10   Heat Equation (maximum principle, uniqueness)   Strauss 2.3
Evans 2.3.3  
9/24 11  Wave Equation (fundamental solution in 1d)  Strauss 2.1, 2.2
Evans 2.4.1  
Homework 3 Due 
9/26 12  Wave Equation (solution in 3d)  Strauss 9.1, 9.2
Evans 2.4.1 
9/29 13  Wave Equation (solution in 2d) Strauss 9.1
Evans 2.4.1, 2.4.3 
10/1 14  Wave Equation (energy methods)  Evans 2.4.3   
10/3   Review    Homework 4 Due  
10/6  Midterm 1     Midterm 1 
10/8 15  Separation of variables, Fourier series  Strauss 1.4, 4.1, 4.2    
10/10 16  Separation of variables, Fourier series   Strauss 5.1, 5.2, 5.3, 5.4   
10/1317  Separation of variables, Fourier series   Strauss 5.1, 5.2, 5.3, 5.4   
10/15 18  Fourier transform   Strauss 12.3
Evans 4.3.1 
Homework 5 Due 
10/17 19  Fourier transform   Strauss 12.3
Evans 4.3.1 
10/20 20  Fourier transform   Strauss 12.3, 12.4
Evans 4.3.1 
10/2221   Tempered distributions   Strauss 12.1, 12.3  Homework 6 Due 
10/24 22 Duhamel's principle  Strauss 3.4    
10/2723   Method of characteristics  Evans 3.2    
10/2924   Method of characteristics
Scalar conservation laws 
Evans 3.2, 3.4,
Strauss 14.1  
Homework 7 Due  
10/31 25  Scalar conservation laws  Evans 3.4,
Strauss 14.1 
11/3 26  Calculus of variations  Strauss 7.1, 11.1, 14.3
Evans 8.1  
11/5 27  Calculus of variations  Strauss 7.1, 11.1, 14.3
Evans 8.1  
11/7  Review     Homework 8 Due 
11/10   Midterm 2     Midterm 2 
11/12 28  Numerical methods   Strauss 8.1, 8.2   
11/14 29   Numerical methods   Strauss 8.3, 8.5    
11/17 30  Classical mechanics      
11/1931   Quantum mechanics   Strauss 9.4, 9.5  Homework 9 Due 
11/2132   Quantum mechanics   Strauss 9.4, 9.5   
11/24 33   Quantum mechanics  Strauss 10.3, 10.6   
11/26 34   Quantum mechanics  Strauss 10.3, 10.6  Homework 10 Due 
12/1 35  Electromagnetism   Strauss 13.1   
12/3 36  Elementary particles  Strauss 13.5    
12/5  Conclusion and review    
12/8  RRR Office hours   Moffitt 102, 1–3pm
Homework 11 Due  
12/9  RRR Office hours  Moffitt 102, 1–3pm
12/10  RRR Office hours  Moffitt 102, 1–3pm

Homework assignments:
  • Homework 1 - due Wednesday, 09/10
  • Homework 2 - due Wednesday, 09/17
  • Homework 3 - due Wednesday, 09/24
  • Homework 4 - due Friday, 10/03
  • Homework 5 - due Wednesday, 10/15
  • Homework 6 - due Wednesday, 10/22
  • Homework 7 - due Wednesday, 10/29
  • Homework 8 - due Friday, 11/07
  • Homework 9 - due Wednesday, 11/19
  • Homework 10 - due Wednesday, 11/26
  • Homework 11 - due Monday, 12/08
Exam review problems:


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