SMA 335: Ordinary Differential Equation I Notes

KES 150

Secure M-PESA Paybill • Instant digital delivery

View all Notes.

692 Views

4 Purchases

View Schemes of Work View Lesson Plans

Summary

DIFFERENTIAL EQUATIONS OF THE FIRST ORDER
1.1 Definitions
Any relation between the variables x, y and the derivatives dy/dx, d2y/dx2, ... is called an ordinary differential equation. The term ordinary distinguishes it from a partial differential equation which involves partial derivatives.
The order of a differential equation is that of the highest derivative occurring in it; the degree of a differential equation is that to which the derivative of the highest order is raised when the equation is expressed in a rational integral form.
Throughout this chapter we shall frequently write y' and y" for dy/dx and d2y/dx2 respectively.
1.2 Formation and solution of differential equations
The equation x2+y2=c2••• (i)
where c is an arbitrary constant or parameter, represents a family of concentric circles with centres at the origin; c is constant for each circle but varies from circle to circle. Differentiating (i) with respect to x, we have
2x+2y y'=0,
y'= -x/y (ii)
This is the differential equation of the family of circles given by (i). It expresses a property common to all the members of the family, viz. that the tangent at the point P(x, y) on anyone of them is perpen¬dicular to the radius which passes through P. The differential equation is of the first order.
If we start with a relation Such as
y=ax+b/x (iii)
which contains two arbitrary constants a and b, it is necessary to differentiate twice before we can eliminate the constants.
We have y' =a-b/x2 (iv)
y" =2b/x3 (v)
and eliminating a and b between (iii), (iv) and (v) We obtain the second order differential equation
x2y"+xy'=y.
The process of finding a relation from which a given differential equation is derived is known as solving (or integrating) the differential equation. The above examples suggest that the differential equation obtained from a relation involving n arbitrary constants will be of the nth order. Conversely, it may be expected that if we can solve a different equation of the nth order. the most general solution (or integral) will contain n arbitrary constants. Such a solution is termed the general solution or the complete primitive. There may, however, be other solutions in addition to the complete primitive.
................

You’re viewing a preview. Buy now to unlock the full document and download instantly after M-PESA payment.

........

This is the end of this document preview. Buy to download the complete document.

More Resources

Notes for ECO 210: Intermediate Microeconomics 2nd Year
CHAPTER ONE 1.0 Introduction Economics is the science of scarce resource allocation to meet endless human desires. The modern economics science has two major branches i.e. Micro-economics and...

Price: KES : 260
AEC 201 Intermediate Microeconomics Notes
The above document contains detailed notes which cover the unit, Intermediate Microeconomics comprehensively. It has worked examples an graphs are also included for illustrations. Please buy the...

Price: KES : 350
AEC 205 Intermediate Macroeconomics Notes
The above document contains a detailed note which covers the unit, Intermediate Macroeconomics comprehensively. Please buy the above notes to make your grades better. Brief Overview: Definition:...

Price: KES : 250
ECO 201: Intermediate Microeconomics Notes
These notes are about a very important unit,the Intermediate Micro Economics.It brings out all the basic concepts of the Intermediate Micro Economics and Explains various theorems in the students...

Price: KES : 100
HBC 2201: Intermediate Accounting 1 Notes
Jomo Kenyatta University of Agriculture and Technology Bachelor of Commerce HBC 2201: Intermediate Accounting 1 Notes HBC 2201 INTERMEDIATE ACCOUNTING 1 Preamble Welcome to this course HBC...

Price: KES : 200
HBC 2205: Intermediate Microeconomics Notes
Jomo Kenyatta University of Agriculture and Technology Bachelor of Commerce HBC 2205: Intermediate Microeconomics Notes HBC 2205: INTERMEDIATE MICROECONOMIC Course Description Introduction:...

Price: KES : 200
HBC 2208: Intermediate Accounting II Notes
Brief Overview: 1.1. Liabilities It is an obligation of an enterprise arising from past transactions or events, the settlement of which may result in the transfer of assets, provision of services...

Price: KES : 200
BBM 225: Intermediate Macroeconomics Notes
This document is Intermediate Macroeconomics notes,Mount Kenya University,Thika Main Campus. ~Business Management Course. ~Bachelor's degree second year learner. The purpose of this document is to...

Price: KES : 100
HE/CU/HR/CR/02/5/A Medical Terminology I Notes
COURSE OUTLINE. 1. INTRODUCTION TO MEDICAL TERMINOLOGY. • Definition of medical terminology. • Importance of medical terminology. • Origin/ history of medical terminology. 2. ACRONYMS AND...

Price: KES : 350
Certificate in Plumbing Complete Notes
Certificate in Plumbing Complete Notes INTRODUCTION TO PLUMBING Specific objective a. Narrate the history of plumbing trade b. State relationship existing between plumbing and other building...

Price: KES : 100
Clinical Medicine: General Surgery Complete Notes
Download complete Clinical Medicine General surgery complete notes SURGERY MODULE 1 SURGERY 1 It has three units: 1. General introduction to surgery 2. Soft tissue...

Price: KES : 200
Digital Literacy Complete Notes
Enhance your digital literacy with comprehensive notes. Purchase now and receive instant delivery via WhatsApp, email, or direct download. 1.1 Determine concepts of ICT in accordance with computer...

Price: KES : 250
ISC 207 Management Information Systems Notes
Full notes on management of information systems. Get the full notes here Brief Overview: System Concept A system is an organized, purposeful structure regarded as a whole and consisting of...

Price: KES : 200
Laboratory Manual on the Determination of Electrical Conductivity and Salinity of Water
This is a laboratory manual on the determination of electrical conductivity and salinity of water Experiment: Determination of the conductivity and salinity of water Introduction Conductivity is a...

Price: KES : 500
Kenyatta University EMP 201: Curriculum Development Notes
Document Length: 9 pages. The notes are all about curriculum Implementation and Teacher education, the definition of Curriculum Implementation, Strategies for Curriculum Implementation, Agencies of...

Price: KES : 150
Internet and Networking Revision Notes: Module III diploma in ICT
These are revision questions and answers for module III diploma in ICT. They are very understandable Q&A for exam preparation. DATA COMMUNICATION AND NETWORKS 1. Define the term Computer...

Price: KES : 200
TPR 202 Ethics/Introduction to Ethics Notes
These are the ethics notes from a researched background and they help one understand about social science. Please read and at the end of it you will benefit, am sure. TPR 202 ETHICS/ INTRODUCTION...

Price: KES : 150
Sociology Notes: Scope of Sociology
Sociological theory: A theory refers to a statement of general principles which try to explain the nature of things. A sociological theory is, therefore, a branch of sociology that attempts to...

Price: KES : 200
Conflict of Laws With Regard to Marriage
Introduction According to Fawcett, private international law (Conflict of Laws) is that part of domestic law which comes into operation whenever the court is faced with a claim that contains...

Price: KES : 1500
CLS 401: Professional Ethics Notes
Notes on Professional Ethics and practice for Law students, neatly summarized for easier reading and understanding. Each topic is outlined clearly. The notes cover most topics taught in professional...

Price: KES : 2000
EMA 412: Economics and Planning of Education Notes 4th year
These are lectures note for EMA412:ECONOMICS AND PLANING OF EDUCATION for 4th year for education students. Brief Overview: Educational Planning Is a conscious and deliberate Government effort...

Price: KES : 300
EMA 411: Educational Management and Administration Notes
These are lecture notes of EMA 411.EDUCATIONAL MANAGEMENT AND ADMINISTRATION for 4th year students for teaching and reading. Brief Overview: Organization – refers to the structure and...

Price: KES : 200
AEC 418: Project Appraisal and Evaluation - Introduction to Project Appraisal Notes
Content: This is an introduction to project appraisal and evaluation. 1. Introduction A project appraisal should entail the following: 1) A presentation and discussion of the socio-economic...

Price: KES : 300
AEC 418: Project Appraisal and Evaluation - Financial Appraisal Notes
This is a well illustrated topic about financial appraisal in the course project appraisal and evaluation. This topic has the following subtopics: (i) Total investments costs (ii) Fixed...

Price: KES : 50
ENS 2100: Urbanization and environment Notes (One Sub-topic)
This contains only one sub-topic about the environment and urbanization well written and summarized Brief Overview: URBANIZATION AND ENVIRONMENT. In this paper we are going to discuss the...

Price: KES : 10
Professional Theory and Practice
This work gives the definition, history, concepts, nature, the empirical formulation, value & ethics, practice model, perspectives and practical interventions of behavioral theory. It gives clear...

Price: KES : 200
AEC 418 Project Appraisal and Evaluation - Economic Analysis of Projects
This is a topic about economic analysis of projects. it is an important topic in project appraisal and evaluation. It has the following sub topics (i) conversion of markets to accounting prices (ii)...

Price: KES : 200
AEC 418 Project Appraisal and Evaluation - Risk Assessment of Projects
This document is about the topic 'Risk assessment of projects'. Assessment of projects is a very important thing in project evaluation. The following are the key subtopics which are highlighted. (i)...

Price: KES : 100
EPY 110: Maseno University Introduction to Educational Psychology Notes
This is full notes for the students taking Education.Introduction to psychology comes in simple and easy to understand notes placed in point form. All the theories are described in a simple way and...

Price: KES : 50
Applied Stochastic processes: Branching Process Notes
The notes are based on discrete branching process and provides a deeper understanding of the probability distributions of each population generation and introduces the concept of probability of...

Price: KES : 100

What Our Users Say

Good Work

Joseph

"Your work guys is good. I've recommended your website to many teachers so far."

I will recommend you to parents

Jared

"Thanks I will recommend you to parents for learning content."

Your schemes are very good

Margaret

"Your schemes are very good and well planned am happy to be your customer."

Great problem solving skill

Babyghurl

"Thanks so much for your kindness ...This is a great problem solving skill."

Thanks for great care

Jelva

"Thanks for great care. I shall remain to be member more to introduce my colleagues."

You are doing a great job

Njoroge

"You are doing a great job."

Helpful website

Happy Teacher

"Hello. We appreciate your effort in updating the website, it's very helpful to teachers."

My issue has been solved

Henry

"My issue has been solved and thanks for being honest, I will continue getting materials from your website, it has a lot more that I need. Be Blessed."

Your service is exemplary

Robin

"Much appreciated.....your service is exemplary🙏🏽"

I will refer my friends

Milka

"Be blessed I will refer my friends. Good job."