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Cracking the GRE Math

by: LEDUC, STEVE

Cracking the GRE Math

by: LEDUC, STEVE

ISBN 13:
9780375753992
ISBN 10:
0375753990
Format: Trade Paper
Copyright: 01/01/2000
Publisher: Princeton Review
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Summary

PROVEN TECHNIQUES FOR SCORING HIGHER FROM THE WORLD'S #1 TEST-PREP COMPANY We Know the GRE Math Subject Test The experts at The Princeton Review study the GRE Math Test to make sure you get the most up-to-date, thoroughly researched book possible. We Know Students Each year we help more than two million students score higher with our courses, bestselling books, and award-winning software. We Get Results Students who take our six-week GRE course have an average score increase of 212 points (verified by International Communications Research). The proven techniques we teach in our courses are in this book. And If It's on the GRE Math Subject Test, It's In This Book We don't try to teach you everything there is to know about math--only what you'll need to know to score higher on the GRE Math Test. There's a big difference. InCracking the GRE Math, we'll teach you how to think like the test-makers and *Improve your score by focusing on the material most likely to appear on the test *Test your knowledge with review questions for each math topic covered *Practice your test-taking skills on a comprehensive sample test

Preface	p. XVII
Precalculus	p. 1
Introduction	p. 1
Functions	p. 1
Composition of Functions	p. 2
Inverse Functions	p. 3
Graphs in the x-y Plane	p. 5
Analytic Geometry	p. 7
Lines	p. 7
Parabolas	p. 7
Circles	p. 9
Ellipses	p. 10
Hyperbolas	p. 11
Polynomial Equations	p. 13
The Division Algorithm, Remainder Theorem, and Factor Theorem	p. 13
The Fundamental Theorem of Algebra and Roots of Polynomial Equations	p. 14
The Root Location Theorem	p. 14
The Rational Roots Theorem	p. 14
The Conjugate Radical Roots Theorem	p. 14
The Complex Conjugate Roots Theorem	p. 15
Sum and Product of the Roots	p. 15
Logarithms	p. 16
Trigonometry	p. 18
Trig Functions of Acute Angles	p. 18
Trig Functions of Arbitrary Angles	p. 19
Trig Functions of Real Numbers	p. 19
Trig Identities and Formulas	p. 20
Periodicity of the Trig Functions	p. 22
Graphs of the Trig Functions	p. 23
The Inverse Trig Functions	p. 24
Chapter 1 Review Questions	p. 26
Calculus I	p. 31
Introduction	p. 31
Limits of Sequences	p. 31
Limits of Functions	p. 34
Limits of Functions as x [right arrow] [plus or minus] [infinity]	p. 36
Continuous Functions	p. 37
Theorems Concerning Continuous Functions	p. 39
The Derivative	p. 41
Linear Approximations using Differentials	p. 45
Implicit Differentiation	p. 46
Higher-Order Derivatives	p. 46
Curve Sketching	p. 47
Theorems Concerning Differentiable Functions	p. 49
Max/Min Problems	p. 50
Related Rates	p. 52
Indefinite Integration (Antidifferentiation)	p. 54
Techniques of Integration	p. 54
Integration by Substitution	p. 54
Integration by Parts	p. 56
Trig Substitutions	p. 57
The Method of Partial Fractions	p. 58
Definite Integration	p. 59
The Fundamental Theorem of Calculus	p. 61
The Average Value of a Function	p. 63
Finding the Area Between Two Curves	p. 64
Polar Coordinates	p. 66
Volumes of Solids of Revolution	p. 68
Arc Length	p. 70
The Natural Exponential and Logarithm Functions	p. 71
L'Hopital's Rule	p. 74
Improper Integrals	p. 76
Infinite Series	p. 79
Alternating Series	p. 83
Power Series	p. 83
Functions Defined by Power Series	p. 85
Taylor Series	p. 86
Taylor Rolynomials	p. 88
Review Questions	p. 90
Calculus II	p. 101
Introduction	p. 101
Analytic Geometry of R[superscript 3]	p. 101
The Dot Product	p. 103
The Cross Product	p. 105
The Triple Scalar Product	p. 106
Lines in 3-Space	p. 108
Planes in 3-Space	p. 109
Cylinders	p. 111
Surfaces of Revolution	p. 113
Level Curves and Level Surfaces	p. 115
Cylindrical Coordinates	p. 117
Spherical Coordinates	p. 117
Partial Derivatives	p. 118
Geometric Interpretation of f[subscript x] and f[subscript y]	p. 119
Higher-Order Partial Derivatives	p. 120
The Tangent Plane to a Surface	p. 122
Linear Approximations	p. 123
The Chain Rule for Partial Derivatives	p. 124
Directional Derivatives and The Gradient	p. 128
Max/Min Problems	p. 130
Max/Min Problems with a Constraint	p. 133
The Lagrange Multiplier Method	p. 134
Line Integrals	p. 135
Line Integrals with Respect to Arc Length	p. 136
The Line Integral of a Vector Field	p. 139
The fundamental Theorem of Calculus for Line Integrals	p. 143
Double Integrals	p. 146
Double Integrals in Polar Coordinates	p. 150
Green's Theorem	p. 152
Path Independence and Gradient Fields	p. 154
Chapter 3 Review Questions	p. 157
Differential Equations	p. 165
Introduction	p. 165
Separable Equations	p. 167
Homogeneous Equations	p. 168
Exact Equations	p. 168
Non-exact Equations and Integrating Factors	p. 170
First-Order Linear Equations	p. 171
Higher-Order Linear Equations with Constant Coefficients	p. 173
Chapter 4 Review Questions	p. 176
Linear Algebra	p. 181
Introduction	p. 181
Solutions of Linear Systems	p. 181
Matrices and Matrix Algebra	p. 183
Matrix Operations	p. 183
Identity Matrices and Inverses	p. 186
Gaussian Elimination	p. 188
Solving Matrix Equations Using A[superscript -1]	p. 193
Vector Spaces	p. 195
The Nullspace	p. 196
Linear Combinations	p. 196
The Rank, Column Space, and Row Space of a Matrix	p. 198
Other Vector Spaces	p. 200
Determinants	p. 200
Laplace Expansions	p. 204
The Adjugate Matrix	p. 205
Cramer's Rule	p. 206
Linear Transformations	p. 207
Standard Matrix Representative	p. 208
The Rank Plus Nullity Theorem	p. 208
A Note on Inverses and Composition	p. 209
Eigenvalues and Eigenvectors	p. 209
Eigenspaces	p. 211
The Cayley-Hamilton Theorem	p. 212
Chapter 5 Review Questions	p. 214
Number Theory and Abstract Algebra	p. 219
Introduction	p. 219
Number Theory	p. 220
Divisibility	p. 220
The Division Algorithm	p. 221
Primes	p. 221
The Greatest Common Divisor and the Least Common Multiple	p. 221
The Euclidean Algorithm	p. 222
The Diophantine Equation ax + by = c	p. 223
Congruences	p. 225
The Congruence Equation ax [identical with] b (mod n)	p. 226
Abstract Algebra	p. 227
Binary Structures and the Definition of a Group	p. 227
Examples of Groups	p. 228
Cyclic Groups	p. 231
Subgroups	p. 232
Cyclic Subgroups	p. 233
Generators and Relations	p. 234
Some Theorems Concerning Subgroups	p. 234
The Concept of Isomorphism	p. 235
The Classification of Finite Abelian Groups	p. 237
Group Homomorphisms	p. 241
Rings	p. 245
Ring Homomorphisms	p. 248
Integral Domains	p. 252
Fields	p. 253
Chapter 6 Review Questions	p. 256
Additional Topics	p. 261
Introduction	p. 261
Set Theory	p. 261
Subsets and Complements	p. 262
Union and Intersection	p. 262
Cartesian Products	p. 263
Intervals of the Real Line	p. 263
Venn Diagrams	p. 265
Cardinality	p. 266
Combinatorics	p. 268
Permutations and Combinations	p. 269
With Repetitions Allowed	p. 270
The Pigeonhole Principle	p. 272
Probability and Statistics	p. 272
Probability Spaces	p. 274
Bernoulli Trials	p. 276
Random Variables	p. 278
Expectation, Variance, and Standard Deviation	p. 279
The Normal Distribution	p. 281
The Normal Approximation to the Binomial Distribution	p. 283
Point-Set Topology	p. 284
Introduction	p. 284
The Subspace Topology	p. 285
The Interior, Exterior, Boundary, Limit Points, and Closure of a Set	p. 285
Basis for a Topology	p. 287
The Product Topology	p. 288
Connectedness	p. 289
Compactness	p. 289
Metric Spaces	p. 290
Continuous Functions	p. 291
Open Maps and Homeomorphisms	p. 293
Real Analysis	p. 294
The Completeness of the Real Numbers	p. 294
Lebesgue Measure	p. 295
Lebesgue Measurable Functions	p. 296
Lebesgue Integrable Functions	p. 297
Complex Variables	p. 299
Introduction	p. 299
The Polar Form	p. 300
The Exponential Form	p. 301
Complex Roots	p. 301
Complex Logarithms	p. 303
Complex Powers	p. 303
The Trigonometric Functions	p. 304
The Hyperbolic Functions	p. 305
The Derivative of a Function of a Complex Variable	p. 306
The Cauchy--Riemann Equations	p. 307
Analytic Functions	p. 309
Complex Line Integrals	p. 310
Theorems Concerning Analytic Functions	p. 311
Taylor Series for Functions of a Complex Variable	p. 312
Singularities, Poles, and Laurent Series	p. 312
The Residue Theorem	p. 315
Solutions To the Chapter Review Questions	p. 319
The Princeton Review GRE Mathematics Diagnostic Exam	p. 383
Answers and Explanations To the Diagnostic Exam	p. 415
About the Author	p. 439
Table of Contents provided by Syndetics. All Rights Reserved.

Amazon no longer offers textbook rentals. We do!

Cracking the GRE Math

Cracking the GRE Math

9780375753992

0375753990

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Cracking the GRE Math

Cracking the GRE Math

9780375753992

0375753990

Summary

Table of Contents

Supplemental Materials

Write a Review

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