PS 190 Cedar Crest College Moha Mini Jung Spiritual Aim Questions Mini-Jung Assignment DUE: Tuesday, April 28 by 1pm (submit to Canvas via link on Homepag

PS 190 Cedar Crest College Moha Mini Jung Spiritual Aim Questions Mini-Jung Assignment

DUE: Tuesday, April 28 by 1pm (submit to Canvas via link on Homepage or Assignments

Directions:

Please read the article found on the following link

https://www.thesap.org.uk/resources/articles-on-jungian-psychology-2/about-analysis-and-therapy/spirituality-and-religion/

Copy and Paste each question and type answer below.

Answer all questions in complete sentences and in your own words. Be careful not to lift phrases or sentences from the original work or this will result in point deductions.

Each answer should be at least 1-2 paragraphs in length (4-6 sentences per para.)

Each answer is worth roughly 15 points.

Questions:

1.a) What does Jung say is our greatest spiritual aim as humans? And, how do we achieve it?

b)How can this (our spiritual aim) sometimes “go astray” and lead to negative outcomes rather than positive ones?

2.What do you see as the difference between being spiritual and being religious? Please answer in your own words.

3.Why do you think Jung considered fundamentalism as a “danger in the path to spiritualism,” and in opposition to individualism?

4.a) Why does Jung believe that in order to achieve individuation people will need ego-strength?

b) What’s involved in ego-strength, and why might some people have it while others don’t?

5.Read the following excerpt from the reading: “So the self-sacrifice of Jesus in his death is eternally present in this timeless dimension of our lives, and so is always powerfully available as a symbol with immediate and current relevance – the death of the ego and the resurrection of a new ‘I’ (which no-one recognizes at first, as none of the disciples immediately recognized the risen Christ), the death in seeming failure and the resurrection in new hope and a new way of life, the ending of all familiar security and then the coming, after a descent into Hell / despair, of something recognizably the same yet amazingly new and different– we have all had such experiences on a smaller or a larger scale.”

a)According to Jung, how would it be possible to achieve such an experience? That is, what process must we go through?

b) Can you recall such an experience in your own life? Please provide a few details. (*It does not have to be a religious experience.)

6.The conclusion of the article reads as follows: “For Jung, it is the internal life of the psyche not external events which are of paramount importance (MDR, Prologue). We may think this is too one-sided, and that our external life has its own equal importance. But for Jung, the external forms of religion are one means to follow our true spiritual path, which he saw as individuation, and in this quest all external events can be understood symbolically.”

a) Would Behaviorists agree with Jung’s analysis as reflected in this quote?

b)Given what you know about Jung’s theory, how can external events be important to us if Jung says our internal life is “way more important” than external events? (Be sure to include some specific Jungian concepts/language in your answer.)

c)How do you think Jung views the role of organized religion in a person’s life? July 24, 2012 17:50
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Elementary Differential
Equations
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TENTH
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EDITION
Elementary Differential
Equations
William E. Boyce
Edward P. Hamilton Professor Emeritus
Richard C. DiPrima
formerly Eliza Ricketts Foundation Professor
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
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To Elsa and in loving memory of Maureen
To Siobhan, James, Richard, Jr., Carolyn, and Ann
And to the next generation:
Charles, Aidan, Stephanie, Veronica, and Deirdre
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The Authors
William E. Boyce received his B.A. degree in Mathematics from Rhodes College,
and his M.S. and Ph.D. degrees in Mathematics from Carnegie-Mellon University.
He is a member of the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. He is
currently the Edward P. Hamilton Distinguished Professor Emeritus of Science Education (Department of Mathematical Sciences) at Rensselaer. He is the author
of numerous technical papers in boundary value problems and random differential
equations and their applications. He is the author of several textbooks including
two differential equations texts, and is the coauthor (with M.H. Holmes, J.G. Ecker,
and W.L. Siegmann) of a text on using Maple to explore Calculus. He is also coauthor (with R.L. Borrelli and C.S. Coleman) of Differential Equations Laboratory
Workbook (Wiley 1992), which received the EDUCOM Best Mathematics Curricular Innovation Award in 1993. Professor Boyce was a member of the NSF-sponsored
CODEE (Consortium for Ordinary Differential Equations Experiments) that led to
the widely-acclaimed ODE Architect. He has also been active in curriculum innovation and reform. Among other things, he was the initiator of the “Computers in
Calculus” project at Rensselaer, partially supported by the NSF. In 1991 he received
the William H. Wiley Distinguished Faculty Award given by Rensselaer.
Richard C. DiPrima (deceased) received his B.S., M.S., and Ph.D. degrees in
Mathematics from Carnegie-Mellon University. He joined the faculty of Rensselaer
Polytechnic Institute after holding research positions at MIT, Harvard, and Hughes
Aircraft. He held the Eliza Ricketts Foundation Professorship of Mathematics at
Rensselaer, was a fellow of the American Society of Mechanical Engineers, the
American Academy of Mechanics, and the American Physical Society. He was also
a member of the American Mathematical Society, the Mathematical Association of
America, and the Society for Industrial and Applied Mathematics. He served as the
Chairman of the Department of Mathematical Sciences at Rensselaer, as President
of the Society for Industrial and Applied Mathematics, and as Chairman of the Executive Committee of the Applied Mechanics Division of ASME. In 1980, he was the
recipient of the William H. Wiley Distinguished Faculty Award given by Rensselaer.
He received Fulbright fellowships in 1964–65 and 1983 and a Guggenheim fellowship in 1982–83. He was the author of numerous technical papers in hydrodynamic
stability and lubrication theory and two texts on differential equations and boundary
value problems. Professor DiPrima died on September 10, 1984.
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P R E FAC E
This edition, like its predecessors, is written from the viewpoint of the applied
mathematician, whose interest in differential equations may be sometimes quite
theoretical, sometimes intensely practical, and often somewhere in between. We
have sought to combine a sound and accurate (but not abstract) exposition of the
elementary theory of differential equations with considerable material on methods
of solution, analysis, and approximation that have proved useful in a wide variety of
applications.
The book is written primarily for undergraduate students of mathematics, science,
or engineering, who typically take a course on differential equations during their
first or second year of study. The main prerequisite for reading the book is a working
knowledge of calculus, gained from a normal two- or three-semester course sequence
or its equivalent. Some familiarity with matrices will also be helpful in the chapters
on systems of differential equations.
To be widely useful, a textbook must be adaptable to a variety of instructional
strategies. This implies at least two things. First, instructors should have maximum
flexibility to choose both the particular topics they wish to cover and the order in
which they want to cover them. Second, the book should be useful to students who
have access to a wide range of technological capability.
With respect to content, we provide this flexibility by making sure that, so far as
possible, individual chapters are independent of each other. Thus, after the basic
parts of the first three chapters are completed (roughly Sections 1.1 through 1.3, 2.1
through 2.5, and 3.1 through 3.5), the selection of additional topics, and the order and
depth in which they are covered, are at the discretion of the instructor. Chapters 4
through 8 are essentially independent of each other, except that Chapter 7 should
precede Chapter 9. This means that there are multiple pathways through the book,
and many different combinations have been used effectively with earlier editions.
ix
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Preface
With respect to technology, we note repeatedly in the text that computers are extremely useful for investigating differential equations and their solutions, and many
of the problems are best approached with computational assistance. Nevertheless,
the book is adaptable to courses having various levels of computer involvement,
ranging from little or none to intensive. The text is independent of any particular
hardware platform or software package.
Many problems are marked with the symbol
to indicate that we consider them
to be technologically intensive. Computers have at least three important uses in a
differential equations course. The first is simply to crunch numbers, thereby generating accurate numerical approximations to solutions. The second is to carry out
symbolic manipulations that would be tedious and time-consuming to do by hand.
Finally, and perhaps most important of all, is the ability to translate the results of
numerical or symbolic computations into graphical form, so that the behavior of
solutions can be easily visualized. The marked problems typically involve one or
more of these features. Naturally, the designation of a problem as technologically
is intended only as a guide.
intensive is a somewhat subjective judgment, and the
Many of the marked problems can be solved, at least in part, without computational help, and a computer can also be used effectively on many of the unmarked
problems.
From a student’s point of view, the problems that are assigned as homework and
that appear on examinations drive the course. We believe that the most outstanding
feature of this book is the number, and above all the variety and range, of the problems that it contains. Many problems are entirely straightforward, but many others
are more challenging, and some are fairly open-ended and can even serve as the basis
for independent student projects. There are far more problems than any instructor
can use in any given course, and this provides instructors with a multitude of choices
in tailoring their course to meet their own goals and the needs of their students.
The motivation for solving many differential equations is the desire to learn something about an underlying physical process that the equation is believed to model.
It is basic to the importance of differential equations that even the simplest equations correspond to useful physical models, such as exponential growth and decay,
spring–mass systems, or electrical circuits. Gaining an understanding of a complex
natural process is usually accomplished by combining or building upon simpler and
more basic models. Thus a thorough knowledge of these basic models, the equations
that describe them, and their solutions is the first and indispensable step toward the
solution of more complex and realistic problems. We describe the modeling process
in detail in Sections 1.1, 1.2, and 2.3. Careful constructions of models appear also in
Sections 2.5 and 3.7 and in the appendices to Chapter 10. Differential equations resulting from the modeling process appear frequently throughout the book, especially
in the problem sets.
The main reason for including fairly extensive material on applications and mathematical modeling in a book on differential equations is to persuade students that
mathematical modeling often leads to differential equations, and that differential
equations are part of an investigation of problems in a wide variety of other fields.
We also emphasize the transportability of mathematical knowledge: once you master a particular solution method, you can use it in any field of application in which an
appropriate differential equation arises. Once these points are convincingly made,
we believe that it is unnecessary to provide specific applications of every method
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xi
of solution or type of equation that we consider. This helps to keep this book to
a reasonable size, and in any case, there is only a limited time in most differential
equations courses to discuss modeling and applications.
Nonroutine problems often require the use of a variety of tools, both analytical
and numerical. Paper-and-pencil methods must often be combined with effective
use of a computer. Quantitative results and graphs, often produced by a computer,
serve to illustrate and clarify conclusions that may be obscured by complicated analytical expressions. On the other hand, the implementation of an efficient numerical
procedure typically rests on a good deal of preliminary analysis—to determine the
qualitative features of the solution as a guide to computation, to investigate limiting or special cases, or to discover which ranges of the variables or parameters may
require or merit special attention. Thus, a student should come to realize that investigating a difficult problem may well require both analysis and computation; that good
judgment may be required to determine which tool is best suited for a particular task;
and that results can often be presented in a variety of forms.
We believe that it is important for students to understand that (except perhaps
in courses on differential equations) the goal of solving a differential equation is
seldom simply to obtain the solution. Rather, we seek the solution in order to obtain
insight into the behavior of the process that the equation purports to model. In
other words, the solution is not an end in itself. Thus, we have included in the text
a great many problems, as well as some examples, that call for conclusions to be
drawn about the solution. Sometimes this takes the form of finding the value of the
independent variable at which the solution has a certain property, or determining
the long-term behavior of the solution. Other problems ask for the effect of variations
in a parameter, or for the determination of a critical value of a parameter at which
the solution experiences a substantial change. Such problems are typical of those
that arise in the applications of differential equations, and, depending on the goals
of the course, an instructor has the option of assigning few or many of these problems.
Readers familiar with the preceding edition will observe that the general structure
of the book is unchanged. The revisions that we have made in this edition are in
many cases the result of suggestions from users of earlier editions. The goals are
to improve the clarity and readability of our presentation of basic material about
differential equations and their applications. More specifically, the most important
revisions include the following:
1. Sections 8.5 and 8.6 have been interchanged, so that the more advanced topics appear at
the end of the chapter.
2. Derivations and proofs in several chapters have been expanded or rewritten to provide
more details.
3. The fact that the real and imaginary parts of a complex solution of a real problem are also
solutions now appears as a theorem in Sections 3.2 and 7.4.
4. The treatment of generalized eigenvectors in Section 7.8 has been expanded both in the
text and in the problems.
5. There are about twenty new or revised problems scattered throughout the book.
6. There are new examples in Sections 2.1, 3.8, and 7.5.
7. About a dozen figures have been modified, mainly by using color to make the essential feature of the figure more prominent. In addition, numerous captions have been
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Preface
expanded to clarify the purpose of the figure without requiring a search of the
surrounding text.
8. There are several new historical footnotes, and some others have been expanded.
The authors have found differential equations to be a never-ending source of interesting, and sometimes surprising, results and phenomena. We hope that users of
this book, both students and instructors, will share our enthusiasm for the subject.
William E. Boyce
Grafton, New York
March 13, 2012
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Preface
xiii
Supplemental Resources for Instructors and Students
An Instructor’s Solutions Manual, ISBN 978-0-470-45834-1, includes solutions for all
problems not contained in the Student Solutions Manual.
A Student Solutions Manual, ISBN 978-0-470-45833-4, includes solutions for selected problems in the text.
A Book Companion Site, www.wiley.com/college/boyce, provides a wealth of resources for students and instructors, including
• PowerPoint slides of important definitions, examples, and theorems from the
book, as well as graphics for presentation in lectures or for study and note taking.
• Chapter Review Sheets, which enable students to test their knowledge of key
•
•
concepts. For further review, diagnostic feedback is provided that refers to pertinent sections in the text.
Mathematica, Maple, and MATLAB data files for selected problems in the text
providing opportunities for further exploration of important concepts.
Projects that deal with extended problems normally not included among traditional topics in differential equations, many involving applications from a variety
of disciplines. These vary in length and complexity, and they can be assigned as
individual homework or as group assignments.
A series of supplemental guidebooks, also published by John Wiley & Sons, can be
used with Boyce/DiPrima in order to incorporate computing technologies into the
course. These books emphasize numerical methods and graphical analysis, showing
how these methods enable us to interpret solutions of ordinary differential equations (ODEs) in the real world. Separate guidebooks cover each of the three major
mathematical software formats, but the ODE subject matter is the same in each.
• Hunt, Lipsman, Osborn, and Rosenberg, Differential Equations with MATLAB,
3rd ed., 2012, ISBN 978-1-118-37680-5
• Hunt, Lardy, Lipsman, Osborn, and Rosenberg, Differential Equations with
•
Maple, 3rd ed., 2008, ISBN 978-0-471-77317-7
Hunt, Outing, Lipsman, Osborn, and Rosenberg, Differential Equations with
Mathematica, 3rd ed., 2009, ISBN 978-0-471-77316-0
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Preface
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