Advanced calculus demystified: a self-teaching guide

David Bachman0071481214, 9780071481212, 9780071511094

Your INTEGRAL tool for mastering ADVANCED CALCULUS

Interested in going further in calculus but don’t where to begin? No problem! With Advanced Calculus Demystified, there’s no limit to how much you will learn.

Beginning with an overview of functions of multiple variables and their graphs, this book covers the fundamentals, without spending too much time on rigorous proofs. Then you will move through more complex topics including partial derivatives, multiple integrals, parameterizations, vectors, and gradients, so you’ll be able to solve difficult problems with ease. And, you can test yourself at the end of every chapter for calculated proof that you’re mastering this subject, which is the gateway to many exciting areas of mathematics, science, and engineering.

This fast and easy guide offers:
Numerous detailed examples to illustrate basic conceptsGeometric interpretations of vector operations such as div, grad, and curlCoverage of key integration theorems including Green’s, Stokes’, and Gauss’Quizzes at the end of each chapter to reinforce learningA time-saving approach to performing better on an exam or at work
Simple enough for a beginner, but challenging enough for a more advanced student, Advanced Calculus Demystified is one book you won’t want to function without!

 

---

Table of contents :
Contents……Page 9
Preface……Page 13
Acknowledgments……Page 15
1.1 Functions……Page 17
1.2 Three Dimensions……Page 18
1.3 Introduction to Graphing……Page 20
1.4 Graphing Level Curves……Page 22
1.5 Putting It All Together……Page 25
1.6 Functions of Three Variables……Page 27
1.7 Parameterized Curves……Page 28
Quiz……Page 31
2.1 Limits of Functions of Multiple Variables……Page 33
2.2 Continuity……Page 37
Quiz……Page 38
3.1 Partial Derivatives……Page 39
3.2 Composition and the Chain Rule……Page 42
3.3 Second Partials……Page 47
Quiz……Page 48
4.1 Integrals over Rectangular Domains……Page 49
4.2 Integrals over Nonrectangular Domains……Page 54
4.3 Computing Volume with Triple Integrals……Page 60
Quiz……Page 63
5.1 Cylindrical Coordinates……Page 65
5.2 Graphing Cylindrical Equations……Page 67
5.3 Spherical Coordinates……Page 69
5.4 Graphing Spherical Equations……Page 71
Quiz……Page 74
6.1 Parameterized Surfaces……Page 75
6.2 The Importance of the Domain……Page 78
6.3 This Stuff Can Be Hard!……Page 79
6.4 Parameterized Areas and Volumes……Page 81
Quiz……Page 84
7.1 Introduction to Vectors……Page 85
7.2 Dot Products……Page 88
7.3 Gradient Vectors and Directional Derivatives……Page 91
7.4 Maxima, Minima, and Saddles……Page 94
7.5 Application: Optimization Problems……Page 99
7.6 LaGrange Multipliers……Page 100
7.7 Determinants……Page 104
7.8 The Cross Product……Page 107
Quiz……Page 110
8.1 Differentiating Parameterizations……Page 111
8.2 Arc Length……Page 116
8.3 Line Integrals……Page 118
8.4 Surface Area……Page 120
8.5 Surface Integrals……Page 129
8.6 Volume……Page 131
8.7 Change of Variables……Page 134
Quiz……Page 139
9.1 Definition……Page 141
9.2 Gradients, Revisited……Page 143
9.3 Divergence……Page 144
9.4 Curl……Page 145
Quiz……Page 147
10.1 Line Integrals……Page 149
10.2 Surface Integrals……Page 155
Quiz……Page 159
11.1 Path Independence……Page 161
11.2 Green’s Theorem on Rectangular Domains……Page 165
11.3 Green’s Theorem over More General Domains……Page 172
11.4 Stokes’ Theorem……Page 176
11.5 Geometric Interpretation of Curl……Page 180
11.6 Gauss’ Theorem……Page 182
11.7 Geometric Interpretation of Divergence……Page 187
Quiz……Page 189
Final Exam……Page 191
Answers to Problems……Page 193
C……Page 281
E……Page 282
F……Page 283
I……Page 284
M……Page 285
P……Page 286
R……Page 287
S……Page 288
V……Page 289
X……Page 290