Wednesday, September 10, 2008

Meeting of AeSI alumuni in Bangalore on 14th septermber


Got this following mail regarding AeSIAA.

hi all,
There is a meeting of Aesi Alumni from all over Bangalore on 14th Sep, please come forward and join the Alumni meet. Details on http://groups.google.com/group/aesiaa
aesiaa@googlegroups.com



What is AeSIAA?

As you know we don’t have our formal Alumni Association and so have a puny presence in AeSI, even though we have our individual impact in the industry.The alumni association will have brawny presence and detection as a group in the industry as well as in AeSI. Please come forward to ensure the same.

Related: AeSI private Alumuni association initiative




Monday, September 08, 2008

3 things that Dr. Ramamuthy taught me and how they can help you learn catia or solidworks better

I did my training in NAL. I began it in my last semester. It was around the time when VMD subject took a turn around. This was the semester that AeSI folks all around saw no person passing in VMD!! So that time i joined NAL and was fortunate to be able work under Dr. S Ramamurthy, then sceintest F.

Apart from applying my aerospace knowledge there, i learnt NASTRAN, ANSYS, solidworks and many other programming languages..

Of those days i remember this 3 points that I have learnt from my mentor. This are the 3 steps that have made my learning of so many software's easy and fruitful

1. Always begin with basics. You will never get stuck. don't jump steps. Approach the problem from the root. follow all assumptions and tackle one problem one at a time. From CATIA to NASTRAN, everywhere Dr. Ramamurthy began any analysis project from the basics. he kept the focus of the basics and developed the whole thing from that point. He incrementally added the details and curved out the perfect mesh or model.

2. Work is your puja. This is the nirvana, this is the karma. If you can enjoy it and bring your passion into it you are the number one. He used to say this and this is what Dr. Ramamuthy followed. This is what he preached and followed. One glance at his desk will reveal him hunched back and playing around with his books, thesis or softwares. I still remember he was the first scientist who came to our division and the last who he left. He was very much involved in all his projects. How con he bring so much . Well his work. his passion in the subject supplied all the energy. Like Natrajan sir., his passion was his fuel.

3. Avoid shortcuts, they might be easy on the surface but they need more more work in the long run. Shortcuts can stumble you in unfamiliar territories but not the long cuts...shorts cuts are like AeSI, easy to get in But difficult to pass. He followed this in learning software too. He used file menu than relying on the shortcuts of the tool bar. For many it seemed to be a waste of time but I have seen that because he was accustomed to using the menu, he was more efficient in any machine he sat, while the lead designer in our team was great in his own customized system but his productivity decreased drastically if he sat on a different system, struggling to find the shortcut toolbars. So while learning any software, rely more on the menus and standard keyboard shortcuts than on toolbars, they might look inviting but with menus you will be more productive in the long term.

So folks what do you say? What have you learnt. Share your knowledge? Training is all about learning. So what have you learnt from your experiences.

Friday, September 05, 2008

Happy Teacher's Day


Happy teachers day folks! Always remember them they are the one whom even our ancient scriptures put ahead of God!!


Happy teacher's day!!!






The worst résumé I have ever seen of an AeSI guy


Yesterday a friend of mine who is in the process of recruiting AeSI graduates for his firm received this resume.

Take a look at the resume.








Immediately he forwarded the resume to me.

It’s the worst résumé I have ever seen.

See the structure and how it is aligned. I have deliberately distorted the names and reference but look at it and you will realize how pathetic the resume writing skills are for the guy who sends it.

If this is the standard of the resume I am sure he will be struggling to get a job for a long time. Today I am shocked but I promise to dissect this resume in weeks time and make his resume more rounded and presntable.

Point wise what are blunders he did.
  • 5 pages resume.
  • His personal profile is first thing he writes
  • Objective is the last sentence of the resume
  • Language he uses in the resume is not professional.
  • No format or standards followed


I feel so sorry for this guy and bad for myself that even though I am writing on this topic so often in this blog and still there are people in AeSI who aren’t reading any of it. A little while ago someone asked me why I promote this blog on orkut and this is the answer. I don’t want AeSI guys to be so naïve. I don’t want them to be the lowest denominators…… This is bad and what good is your degree if you lack the bare minimum of sense. So guys if you are reading this refer this resource to other AeSI folks. Lets be professional enough to be able to send a resume properly.







Wednesday, September 03, 2008

What's cool and new in solidworks 2009


For the regualr readers of this blog, its no secret that solidworks in my CAD program of choice. even though i write a lot about learning CATIA and use the name of catia a lot in this blog, but solidworks remains my passion. So what's new in solidworks! They are launching the new super fast solidowrks 2009 by the third quarter of 2008!! So i decided to take a look at what's cool and new in solid works.


solidworks 2009
There are lot of blogs and information about the reviews but i wanted a clean and clear text where they just tell me what is new in solidworks 2009 and i just got that ebook.

So if you are looking for an plain ebook on solidwroks then this ebook from Solidworks is for you.

Click here to get the book. [pdf]

This book highlights and helps you learn the new functionality of Solidworks 2009 software. It introduces concepts and provideds step-by-step examples for many new functions.

This book is intended for for experienced users of Solidworks software and assumes that they have a good working knowledge of the earlier release.

For those interested in the launch of solidworks can see look at this new website

http://www.solidworkslaunch.com/

Youtube has lot of sleek video on the new solidworks 2009. So chek them out here.

And don't forget there are tons of solidworks/CAD learning tips that are burried in this blog. So explore.


A titbit fact:
As of last count, solidworks is embraced more than a half million users at more than 97,000 companies in more than 100 countries.
Source: solidwroks





How I stayed abreast to new develoment in Aerospace while doing AeSI


A while back i present some of the steps from AIAA that presented tips and things that folks can do to stay ahead in your chosen career. The tips were very useful and among the many tip , one of them was "Stay abreast of new developments in your field....."

So how do I stayed abreast to the new developments in your field. I want to tackle this topic today.


While i was in AeSI, the resources were very limited, net access was 80 rs per hour at the cyber cafe and speeds were dismal and penetration of Indian aerospace news was nothing to talk about. But then also there were this 3 sites that i always visited to keep myself updated in what's happening in aerospace. Now my repertoire of sites has increased many fold but this sites are still relevant and are still present in my browsers address bar.

So here they are.

NAL's pasteborad.

This is only primary source that i had back then that covered indian aerospace industry. It mainly talked about NAL but also covered the various aerospace conference, events that happened in indian aerospace industry. So this was my most visited site in 1999 and early 2000. It still is as you get to know what NAL, my first place where i worked is doing. Read the development of saras, RTA, hansa and many other indian stories here. Now of course we have indianaeronews blog that religiously follows and inform us of the recent stories happening in indian aerospace.

www.NASA.gov was the next site the i regularly visited back them, now my visit to this site are quite less but back then. It excited me and i remember after every visit from cyber cafe i came with abundant enthusiasm about aerospace and at the new technology that NASA is working. As my roommates will vouch, this was only thing i talked about during those time. It was really exciting and today though my visits have decreased but i know, as i have already mentioned here, NASA is the ultimate destination for any aerospace engineer. And for those who don't know, an AeSI'ian among us is already working in NASA.


Science at NASA

Apart from the main site of NASA, the other site that i visited was its sister site named sciece.nasa.gov. It only talked about technology, about the stuff that is getting made or done. It was another source of excitement for me and i still visit this site to know about what's happening. What new material is being developed. How people will live on mars and how NASA is preparing for it....

So this are the 3 sites that made my days back when i was in AeSI. So tell me what are your aerospace sites that you visit to stay abreast in aerospace? What site you hang out to get to know what's happening in aerospace industry.

As mentioned earlier you can stay abreast with indian aerospace industry by following IndianAeroNews blog.






Kung Fu Panda advise to AeSI'ians

Last weekend I saw Kung Fu Panda finally. Was waiting for it for long. And finally fully understood the blog article that I read at youth curry. In that post, the blogger expresses her Kung Fu Panda advice. Do read it.

The one that I believe applies most to all of AeSI'ians is this one.

And this is especially relevant at a time when we are all on the quest for the Holy Grail. We believe that joining the right college, the right course or the right company is the secret ingredient which will spice up our soup - our careers, our lives.


The truth is, it's all about what you believe. The moment you join an IIT or an IIM you start believing,"Hey I am really really good". You get the confidence to take on the world, the chutzpah to say,"The world is my oyster".


Clearing these super tough exams is like running a lawnmower through your own mental garden. It crushes the weeds of self doubt and self pity which we've allowed to grow.


Exam or no exam, you can choose to yank out those weeds. Then look the guys who think they know better in the eye and declare,"My soup is as kick-ass as yours."

As she rightly points out. Its what we believe that matters ultimately. IIT, IIM only gives us that belief and self confidence. Many AeSI folks have said they are the best when they clear AeSI, which all you know is the toughest course on earth ( I know some will disagree?). Anyway believe in your degree, believe in yourself and crush those weeds of doubt and self pity!!!

Tuesday, September 02, 2008

Take pride in your AeSI degree


The moment i saw this mail and saw it was from Mr. Bishnujee. I knew i have to post it here. It needs a wider audience. It iterates the view that i have. Pride in your degree. Once you are in it. Believe in it. and Believe in yourself. As i have already pointed out here in this post that self confidence in our own degree is the need of the hour for AeSI.


Yes i do stand by the previous post of problems with AeSI degree and my unwillingness to recommend to my cousins. But i am as proud of the degree as anybody. From my experience at NAL i have told you already, AeSI guys are more than at par with the best aerospace engineers. All they lack is this belief in themselves. Many have previously pointed out this here, here and here. As i have seen this in my training days, if you are an AeSI engineer, take it to your heart that you are the best. If you have cleared AeSI honestly. You are equal to any aerospace graduate in the country or the world. And Bishnujee is the shining inspiration to us all!!!

Following is the mail of Bishnujee addressed to fellow AeSI graduates, engineers and students.


Dear AeSI Engineers & Students,
In recent times there has been sharp increase in criticism about AeSI Degree from various AeSI Engineers & Students.The pride in being AeSI Graduate is gradually fading out among newer generation of Aeronautical Engineers.I am not sure about the reasons behind it.If AeSI Graduates were not having strong Aeronautical Engineering background,they would never have received the Cayley Award 2003 from all major Industries of UK at Buckingham Palace in London on Nov 10,2003.
I know one major reason behind poor Examination result has been lack of proper training facility for AeSI students.There has not been enough pre-requisite check of students joining this programme which leads to student struggling in same.But anyway any Professional Membership Examination whether it is for AeSI or Engineering Council-UK examination for RAeS,UK where result is much lower than AeSI programme ,is never easy course work .
But as I have advised all students & Engineers coming out of AeSI to take pride in whatever you do in life.Until you take pride in whatever you do in life and feel confident that you are best in profession,you will always be lacking behind among your peers and fellow Engineers.
These are the qualities no Universities or Institutes can impart in you and you are solely responsible for developing yourself. What you learn in AeSI course work like hand calculation is the basis of Analysis of Engineering programmes which helps you decide whether the design is acceptable or not. Even if you work on Finite Element Modelling tools like Patran, Nastran,Ansys,FEMAP ,result you get should be compared using hand calculation to check whether they make sense or not and if there is any modelling error.These things you cannot do unless you are sound with you calculating and numerical skills of AeSI Course work in Solid Mechanics,Applied Mechanics,Strength of Materials,Aircraft Structures.

As I have mentioned numerous times in past that first choice after AeSI Graduation should be to work in Industry for few years,build strong foundation and based on your experience in Industry,then go for MS/MTech/ME in your career which you have been following. It helps in selecting right module which you have been working upon and you won't need further brush up while working at site or registering as Professional Engineer. Always bear in mind that AeSI Graduate with 3 years Engineering experience as full time Engineer is better than MS/MSc/MTech//ME with 1 year experience.Always Industry would prefer BE with 3 years experience in Industry first for job compared to MS or PHD with 1 or 0 year of experience.
There is no substitute for Industry experience.When I mention to you guys Industry Experience it doesn't mean working as Mechanic or Technician but only Design or Analysis Engineering whether in Aero Mechanical or Avionics Designing or Propulsion Design & testing.

Also Engineers who opting for Higher studies abroad are advised first to explore the Scholarships & Assistantship options as it might be expensive proposition doing it abroad since due differences in economy between different countries.RAeS UK administers Scholarships for MSc studies in UK.Please do bear in mind that applicants for RAeS Scholarships are not only from UK but from all across the globe with applications coming from NASA based Engineers,South African,European and Australia based Aerospace Engineers.So its highly competitive and one should be clear with his personal goals how MSc is going to benefit the Aerospace Engineer in his career.Just to mention that practical part of MSc is going to add his further knowledge acquired from AeSI won't be sufficient.Normally Industry only when its expects candidate to be very promising and excel in career is offered such competitive scholarships.Apply quite in advance before start of such course to avoid disappointment.
AIAA USA administer scholarship for MS Studies in US too.

There is no gain in criticizing AeSI Degree ,instead it would be better if you all who studying for same remain focused towards studies and do well in your exams and prospective career.Unless you have confidence and pride in yourself you will never be able to achieve any mission in life even if you get Degree from some very reputed Universities of the world leave aside AeSI.

I hope above information helps in achieving your goal.

Best wishes


As you can see he is passionate about this and i share this feeling. There's nothing wrong in expressing the wrongs of AeSI but what will ultimately matter is your pride and your self confidence. So be proud of the degree you have because if you won't then no body else will!!!






Quantity or Quality....

What's more important during training while learning design software's like catia, solidworks or analysis software like NASTRAN,ANSYS or any CAE software? What will you choose Quality or Quantity?

I'll choose Quantity? Why?

For getting the maximum out of  your training, focus on the quantity. Make a commitment that you will produce one catia model,one mesh every day.  One per day is much more effective and successful strategy than focusing on quality and trying to perfect one model or mesh for weeks. Quality is important and is an essential part but a daily commitment to quantity is the way that will help you learn and achieve more. This encourages you to experiment, to go ahead and make something, make more mistakes and learn more. so whatever you are doing strive more to produce more... quality will eventually follow!!!!

If CAD program is what you are learning, commit to produce one model everyday. Don't worry if its perfect of not but keep churning out... every single model you will produce will teach you a thing. So go ahead produce.. Same goes for NASTRAN, ANSYS, HYPERMESH or fluent or any other CAE that you are learning.

Monday, September 01, 2008

Gate preparation for aerospace and Internet

Well preparing for GATE is very different from preparing for your semester examination. Someone rightly said GATE is all about basics and how to apply those basics in practical problems. so how do you prepare for GATE 2009? What is your strategy for gate? How you plan to tackle the question. With negative marking what are your plans for uncertain answers. If Aerospace is your stream for GATE 2009, what topics you will touch and what you will leave? Do share with me? And for the people who are preparing in aerospace for GATE 2009, Here i have made links from the web that will give bit size information about all the topics. You can use this web page to learn each topic everyday. I specially made to help me have bite size preparation while working from office

FLIGHT MECHANICS FLIGHT MECHANICS FLIGHT MECHANICS

Atmosphere properties Atmosphere properties Atmosphere properties

standard atmosphere standard atmosphere standard atmosphere

Classification of aircraft Classification of aircraft Classification of aircraft

Airplane (fixed wing aircraft) configuration Airplane (fixed wing aircraft) configuration Airplane (fixed wing aircraft) configuration


various parts of aircraft. various parts of aircraft. various parts of aircraft.


alieron alieron alieron


flaps and slats of aircraft wings flaps and slats of aircraft wings flaps and slats of aircraft wings
rudder and elevator of airplane rudder and elevator of airplane rudder and elevator of airplane
fuselage fuselage fuselage

Airplane performance Airplane performance Airplane performance
Pressure altitude Pressure altitude Pressure altitude
equivalent air speed equivalent air speed equivalent air speed
calibrated air speed calibrated air speed calibrated air speed
indicated air speeds; indicated air speeds; indicated air speeds;
Primary flight instruments Primary flight instruments Primary flight instruments
Altimeter Altimeter Altimeter
Air speed indicator Air speed indicator Air speed indicator
Turn bank indicator Turn bank indicator Turn bank indicator
Drag polar Drag polar Drag polar
take off and landing performance take off and landing performance take off and landing performance
steady climb & descent steady climb & descent steady climb & descent
absolute ceiling and service ceiling; absolute ceiling and service ceiling; absolute ceiling and service ceiling;
cruise cruise cruise
cruise climb cruise climb cruise climb
endurance or loiter endurance or loiter endurance or loiter
load factor aeronautics load factor aeronautics load factor aeronautics
turning flight turning flight turning flight
VN diagram VN diagram VN diagram
Winds: head tail & cross winds Winds: head tail & cross winds Winds: head tail & cross winds

Static stability Static stability Static stability
Angle of attack Angle of attack Angle of attack
sideslip sideslip sideslip
roll roll roll
pitch & yaw controls pitch & yaw controls pitch & yaw controls
longitudinal stick fixed & free stability longitudinal stick fixed & free stability longitudinal stick fixed & free stability
horizontal tail position and size horizontal tail position and size horizontal tail position and size
directional stability directional stability directional stability
vertical tail position and size vertical tail position and size vertical tail position and size
dihedral stability dihedral stability dihedral stability
Wing dihedral Wing dihedral Wing dihedral
sweep & position sweep & position sweep & position
hinge moments hinge moments hinge moments
stick forces stick forces stick forces

Dynamic stability Dynamic stability Dynamic stability
Euler angles Euler angles Euler angles
Equations of motion Equations of motion Equations of motion
aerodynamic forces and moments aerodynamic forces and moments aerodynamic forces and moments
stability & control derivatives stability & control derivatives stability & control derivatives
decoupling of longitudinal and lat directional dynamics decoupling of longitudinal and lat directional dynamics decoupling of longitudinal and lat directional dynamics
longitudinal modes longitudinal modes longitudinal modes
lateral directional modes. lateral directional modes. lateral directional modes.

SPACE DYNAMICS SPACE DYNAMICS SPACE DYNAMICS
Central force motion, Central force motion, Central force motion,
determination of trajectory and orbital period determination of trajectory and orbital period determination of trajectory and orbital period
Orbit transfer in plane and out of plane Orbit transfer in plane and out of plane Orbit transfer in plane and out of plane
Elements of rocket motor performance. Elements of rocket motor performance. Elements of rocket motor performance.

AERODYNAMICS AERODYNAMICS AERODYNAMICS
Basic Fluid Mechanics Basic Fluid Mechanics Basic Fluid Mechanics
Incompressible irrotational flow Incompressible irrotational flow Incompressible irrotational flow
Helmholtz and Kelvin theorem Helmholtz and Kelvin theorem Helmholtz and Kelvin theorem
singularities and superposition singularities and superposition singularities and superposition
viscous flows viscous flows viscous flows
boundary layer on a flat plate boundary layer on a flat plate boundary layer on a flat plate

Airfoils and wings Airfoils and wings Airfoils and wings
Classification of airfoils Classification of airfoils Classification of airfoils
aerodynamic characteristics aerodynamic characteristics aerodynamic characteristics
high lift devices high lift devices high lift devices
Kutta Joukowski theorem Kutta Joukowski theorem Kutta Joukowski theorem
lift generation lift generation lift generation
thin airfoil theory thin airfoil theory thin airfoil theory
wing theory wing theory wing theory
induced drag induced drag induced drag
qualitative treatment of low aspect ratio wings qualitative treatment of low aspect ratio wings qualitative treatment of low aspect ratio wings

Viscous Flows Viscous Flows Viscous Flows
Flow separation Flow separation Flow separation
introduction to turbulence introduction to turbulence introduction to turbulence
transition transition transition
structure of a turbulent boundary layer. structure of a turbulent boundary layer. structure of a turbulent boundary layer.

Compressible Flows Compressible Flows Compressible Flows
Dynamics & Thermodynamics of ID flow Dynamics & Thermodynamics of ID flow Dynamics & Thermodynamics of ID flow
isentropic flow isentropic flow isentropic flow
normal shock normal shock normal shock
oblique shock oblique shock oblique shock
Prandtl Meyer flow Prandtl Meyer flow Prandtl Meyer flow

flow in nozzles and diffusers flow in nozzles and diffusers flow in nozzles and diffusers
inviscid flow in a cd nozzle inviscid flow in a cd nozzle inviscid flow in a cd nozzle
flow in diffusers flow in diffusers flow in diffusers
subsonic and supersonic airfoils subsonic and supersonic airfoils subsonic and supersonic airfoils
compressibility effects on lift and drag compressibility effects on lift and drag compressibility effects on lift and drag
critical and drag divergence Mach number critical and drag divergence Mach number critical and drag divergence Mach number
wave drag wave drag wave drag

Wind Tunnel Testing Wind Tunnel Testing Wind Tunnel Testing
Measurement and visualisation techniques Measurement and visualisation techniques Measurement and visualisation techniques

STRUCTURES STRUCTURES STRUCTURES
Stress and Strain Stress and Strain Stress and Strain
Equations of equilibrium Equations of equilibrium Equations of equilibrium
constitutive law constitutive law constitutive law
strain displacement relationship strain displacement relationship strain displacement relationship
compatibility equations compatibility equations compatibility equations
plane stress and strain plane stress and strain plane stress and strain
Airy's stress function Airy's stress function Airy's stress function

Flight Vehicle Structures Flight Vehicle Structures Flight Vehicle Structures
Characteristics of aircraft structures and materials Characteristics of aircraft structures and materials Characteristics of aircraft structures and materials
torsion torsion torsion
bending and flexural shear bending and flexural shear bending and flexural shear
Flexural shear flow in thin walled sections Flexural shear flow in thin walled sections Flexural shear flow in thin walled sections
Buckling Buckling Buckling
Failure theories Failure theories Failure theories
Loads on aircraft Loads on aircraft Loads on aircraft

Structural Dynamics Structural Dynamics Structural Dynamics
Free and forced vibration of discrete systems Free and forced vibration of discrete systems Free and forced vibration of discrete systems
Damping and resonance Damping and resonance Damping and resonance
Dynamics of continuous systems Dynamics of continuous systems Dynamics of continuous systems

PROPULSION PROPULSION PROPULSION
Thermodynamics of Aircraft Gas Turbine engines Thermodynamics of Aircraft Gas Turbine engines Thermodynamics of Aircraft Gas Turbine engines
thrust and thrust augmentation thrust and thrust augmentation thrust and thrust augmentation
Turbomachinery: Turbomachinery: Turbomachinery:
Axial compressors Axial compressors Axial compressors
Axial turbines Axial turbines Axial turbines
centrifugal pumps centrifugal pumps centrifugal pumps
Centrifugal compressors Centrifugal compressors Centrifugal compressors

Aerothermodynamics of non rotating propulsion components Aerothermodynamics of non rotating propulsion components Aerothermodynamics of non rotating propulsion components
Intakes Intakes Intakes
combustor and nozzle combustor and nozzle combustor and nozzle
Thermodynamics of ramjets and scramjets Thermodynamics of ramjets and scramjets Thermodynamics of ramjets and scramjets
ramjets ramjets ramjets
scramjets scramjets scramjets
Elements of rocket propulsion Elements of rocket propulsion Elements of rocket propulsion


Matrix algebra Matrix algebra Matrix algebra
systems of linear equations systems of linear equations systems of linear equations
eigen values and eigen vectors eigen values and eigen vectors eigen values and eigen vectors
Functions of single variable Functions of single variable Functions of single variable
limit limit limit
continuity and differentiability continuity and differentiability continuity and differentiability
mean value theorems mean value theorems mean value theorems
evaluation of definite and improper integrals evaluation of definite and improper integrals evaluation of definite and improper integrals
partial derivatives partial derivatives partial derivatives
total derivative, maxima and minima total derivative, maxima and minima total derivative, maxima and minima
gradient gradient gradient
divergence and curl divergence and curl divergence and curl
vector identities vector identities vector identities
directional derivatives directional derivatives directional derivatives
line line line
surface and volume integrals surface and volume integrals surface and volume integrals
Theorems of Stokes Theorems of Stokes Theorems of Stokes
Gauss and Green. Gauss and Green. Gauss and Green.

First order linear and nonlinear equations First order linear and nonlinear equations First order linear and nonlinear equations
higher order linear ODEs with constant coefficients higher order linear ODEs with constant coefficients higher order linear ODEs with constant coefficients
Cauchy and Euler equations Cauchy and Euler equations Cauchy and Euler equations


initial and boundary value problems initial and boundary value problems initial and boundary value problems
Laplace transforms. Laplace transforms. Laplace transforms.
Partial differential equations and separation of variables methods. Partial differential equations and separation of variables methods. Partial differential equations and separation of variables methods.
Numerical solution of linear and nonlinear algebraic equations Numerical solution of linear and nonlinear algebraic equations Numerical solution of linear and nonlinear algebraic equations
integration by trapezoidal and Simpson rule integration by trapezoidal and Simpson rule integration by trapezoidal and Simpson rule
single and multi step methods for differential equations single and multi step methods for differential equations single and multi step methods for differential equations

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