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Modern Introductory Analysis, by Mary P. Dolciani
Download Modern Introductory Analysis, by Mary P. Dolciani
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Most helpful customer reviews
8 of 8 people found the following review helpful.
Grade-12 Text...
By A Customer
Miracle! I finally got a copy of Dolciani's "MODERN INTRODUCTORY ANALYSIS", and it is everything I remembered it to be thirty three years ago in my 12th grade College Prep (CP-12) Math course. I still endorse this text as 5-stars! MN
5 of 5 people found the following review helpful.
Review of the 1964 and 1967 editions
By Jimmy "Handyman" Jones
"Modern Introductory Analysis" was published in four different versions:
1. Teacher's Manual ("Teacher's Edition" is printed on the spine) - This has a separate teacher's manual (usually on green paper) at the beginning of the book along with teacher notes throughout the rest of the student text. In particular, short answers are provided as dialog to the pedagogical (Why?), which is encountered continuously in the student text. Answers to exercises are in the back of the book.
2. Student Version ("With Odd-Numbered Answers" is printed on the spine) - Answers to odd-numbered exercises are in the back of the book.
3. Student Version ("With Answers" is printed on the spine) - Answers to odd and even-numbered exercises are in the back of the book.
4. Student Version (no additional annotation on the spine) - No answers to exercises.
However, those answers in the back exclude both graphs and proofs. If you desire answers for graphs and proofs, they are included in a separate publication, viz., "Solution Key for Modern Introductory Analysis." Nota bene: the "1980 Impression" (reprint) of the Solution Key, ISBN: 0395255554, is compatible with the 1964 and 1967 editions of the text.
Though its title may suggest otherwise, "Modern Introductory Analysis" does not concern itself with epsilon-delta calculus proofs. Rather, it is a kind of pre-calculus text originally intended for high school seniors who had completed a course in Algebra II and Trigonometry in the previous year. It was the follow-on book to Dolciani's "Modern Algebra and Trigonometry Structure and Method Book 2." There is substantial overlap in the topics of these two books, although "Modern Introductory Analysis" covers them at a higher level. Other topics in "Modern Introductory Analysis" are new material, for example, mathematical induction, vectors, limits, derivatives, transformations and polar coordinates. There are > 4400 exercises. Most of the exercise sets contain at least a handful of proofs to whet your appetite. Considerable added insight is gained by doing these proofs, which serve to extend the basic material. The presentation is axiomatic. Yet, you will find a fair amount of intuitive development preceding the theorems. Some of the theorems are stated without proof, either left as exercises, or with a citation (in the Teacher's Manual) to another book containing a proof.
The 1964 and 1967 editions of the book are nearly identical. The 1964 ed. has several easy-to-spot errors that are fixed in the 1967 ed. However, be advised of certain less obvious errata in the 1964 ed. You may wish to revise your 1964 ed. as follows:
1) Exercise 36, P. 182, "T - S and P - S" should read "T - P and S - P"
2) Exercise 11, P. 312, "the length" should read "a function whose minimum is the length"
3) Exercise 12, P. 312, "what is" should read "let L be" and "(-2, 5)?" should read "(-2, 5). Find a function whose minimum is L."
4) Exercise 13, P. 312, "which for a fixed volume requires the least material (surface area)" should read "of greatest volume having a total surface area of 96π sq. cm."
5) Exercise 18, P. 313, should read "Solve Exercise 17 if triangle POQ has minimum area."
6) Exercise 34, P. 327, "b = 1" should read "b ≠ 1"
7) Exercise 14, P. 362, "log 2 (base e)" should read "log 4 (base e)"
8) Exercise 23, P. 362, "b = √a " should read "b = a� "
9) Exercise 24, P. 362, "b = �√a " should read "b = a� "
10) Exercise 42, P. 424, "csc θ" should read "-csc θ"
11) Exercise 47, P. 424, "sin X1 - sin X2" should read "sin X1 + sin X2"
12) Exercise 41, P. 441, "0 < x < π/2" should read "π < x < 3π/2"
13) P. 451 (also 1967 ed.), "y' = acos x" should read "y' = acos ax " and "y' = -asin x" should read "y' = -asin ax"
14) Exercise 20, P. 453, "a sin(ax + b)" should read "-a sin(ax + b)"
15) P. 461, incorrectly drawn graph. Point A should be in the fourth quadrant.
16) Exercise 18, P. 472, "8 m.p.h." should read "2 m.p.h."
17) Exercise 21, P. 472, "2r(180/n)�" should read "2r sin(180/n)�"
18) Exercise 13, P. 481, "bearing 250�" should read "bearing 265�" and "B and 265�" should read "B and 250�"
19) Exercise 30, P. 493, change ending to "... such that r* = f(θ*) and for some integer n, either r* = g(θ* + 2nπ) or -r* = g(θ* + π + 2nπ).
20) Exercise 26, P. 502, "θ1 = θ2." should read "θ1 = θ2 + 2nπ for some integer n."
21) Exercise 29, P. 524, " 5x� - 4y� " should read " 3x� - y� "
22) Exercise 11, P. 536, " 9x� + 24xy + 6y� = 0; θ = Sin‾� (-4/5)" should read " 2x� + 3xy + 2y� = 7; φ = π/4"
23) Exercise 4, P. 541, " x� - 3xy + 3y� + 6y = 7" should read " 7x� + 6xy + 15y� = 144"
24) Exercise 5, P. 541, " y� - 4xy - 4y + 8x = 0" should read " 8y� + 6xy - 26y -12x + 11 = 0"
25) Exercise 6, P. 541, " x� - xy - x + y - 2 = 0" should read " x� + xy + y� = 8"
26) Exercise 16, P. 546 (also 1967 ed.), change to " 20x� - 24xy + 27y� + 20x - 55y - (4615 / 396) = 0"
27) Exercise 33, P. 568, "rv = vr" should read "If rv = vs and v ≠ 0, then r = s."
28) Exercise 7, P. 616, "n - 1" should read "r - 1"
29) Exercise 14, P. 616, "12 or more." should read "12 or more balls."
---
Contents:
Ch 1 Statements and Sets in Mathematics
Ch 2 Ordered Fields
Ch 3 Mathematical Induction - Sequences and Series
Ch 4 The Algebra of Vectors
Ch 5 Plane Analytic Geometry of Points and Lines
Ch 6 Functions
Ch 7 The Field of Complex Numbers
Ch 8 Graphs of Polynomial Functions
Ch 9 Exponential and Logarithmic Functions
Ch 10 The Circular Functions and Trigonometry
Ch 11 Properties of Circular Trigonometric Functions
Ch 12 Vectors, Trigonometry and Complex Numbers
Ch 13 Analytic Geometry and Matrices
Ch 14 Space Geometry
Ch 15 Probability
Appendix (1967 edition) Area Under a Curve
12 of 12 people found the following review helpful.
Great Series
By Ex-Buyer
This text, along with all the Dolciani books by Houghton Mifflin were the corner stones of any high school math program in the 60's-70's and early 80's. This book particularly was the book that I learned pre-calculus from, and made me become a math major. The books were literate in their context, never watered down, but not so abstract that a high school student couldn't read and follow. What makes this book so unique is the fact that mathematical induction is introduced in Chapter 3 and is carried throughout the book. No other precalculus book prior or since has used this approach. Mathematical induction is a proof driven treatment for the topics which follow. It makes the students think in a logical manner and enables them, by proof, to understand the full argument of why certain "things happen" in math as they do. The Teacher's Edition's were the best of any series (until Houghton Mifflin changed the format, and made them less teacher friendly). I still have 2 TE's of this book and the solutions key, and still refer to it when I need to...it beats any precalculus book out today. Once Dr. Dociani passed away, the entire Houghton Mifflin series went down the tubes, their current texts DO NOT hold muster to this old classic!!!
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