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본문내용
CHAPTER 1 First-Order ODEs
Major Changes
There is more material on modeling in the text as well as in the problem set.
Some additions on population dynamics appear in Sec. 1.5.
Electric circuits are shifted to Chap. 2, where second-order ODEs will be available.
This avoids repetitions that are unnecessary and practically irrelevant.
Team Projects, CAS Projects, and CAS Experiments are included in most problem sets.
SECTION 1.1. Basic Concepts. Modeling, page 2
Purpose. To give the students a first impression what an ODE is and what we mean by
solving it.
Background Material. For the whole chapter we need integration formulas and
techniques, which the student should review.
General Comments
This section should be covered relatively rapidly to get quickly to the actual solution
methods in the next sections.
Equations (1)–(3) are just examples, not for solution, but the student will see that
solutions of (1) and (2) can be found by calculus, and a solution y ex of (3) by inspection.
Problem Set 1.1 will help the student with the tasks of
Solving y ƒ(x) by calculus
Finding particular solutions from given general solutions
Setting up an ODE for a given function as solution
Gaining a first experience in modeling, by doing one or two problems
Gaining a first impression of the importance of ODEs
without wasting time on matters that can be done much faster, once systematic methods
are available.
Major Changes
There is more material on modeling in the text as well as in the problem set.
Some additions on population dynamics appear in Sec. 1.5.
Electric circuits are shifted to Chap. 2, where second-order ODEs will be available.
This avoids repetitions that are unnecessary and practically irrelevant.
Team Projects, CAS Projects, and CAS Experiments are included in most problem sets.
SECTION 1.1. Basic Concepts. Modeling, page 2
Purpose. To give the students a first impression what an ODE is and what we mean by
solving it.
Background Material. For the whole chapter we need integration formulas and
techniques, which the student should review.
General Comments
This section should be covered relatively rapidly to get quickly to the actual solution
methods in the next sections.
Equations (1)–(3) are just examples, not for solution, but the student will see that
solutions of (1) and (2) can be found by calculus, and a solution y ex of (3) by inspection.
Problem Set 1.1 will help the student with the tasks of
Solving y ƒ(x) by calculus
Finding particular solutions from given general solutions
Setting up an ODE for a given function as solution
Gaining a first experience in modeling, by doing one or two problems
Gaining a first impression of the importance of ODEs
without wasting time on matters that can be done much faster, once systematic methods
are available.
추천자료
- 가격3,000원
- 페이지수26페이지
- 등록일2011.03.30
- 저작시기2011.3
- 파일형식압축파일(zip)
- 자료번호#661635
본 자료는 최근 2주간 다운받은 회원이 없습니다.
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