| Description |
xii, 274 pages : illustrations ; 24 cm. |
| Series |
Demystified series |
|
McGraw-Hill "Demystified" series.
|
| Note |
Includes index. |
| Contents |
Preface -- Acknowledgments -- 1: Functions Of Multiple Variables -- Functions -- Three dimensions -- Introduction to graphing -- Graphing level curves -- Putting it all together -- Functions of three variables -- Parameterized curves -- Quiz -- 2: Fundamentals Of Advanced Calculus -- Limits of functions of multiple variables -- Continuity -- Quiz -- 3: Derivatives -- Partial derivatives -- Composition and the chain rule -- Second partials -- Quiz -- 4: Integration -- Integrals over rectangular domains -- Integrals over nonrectangular domains -- Computing volume with triple integrals -- Quiz -- 5: Cylindrical And Spherical Coordinates -- Cylindrical coordinates -- Graphing cylindrical equations -- Spherical coordinates -- Graphing spherical equations -- Quiz -- 6: Parameterizations -- Parameterized surfaces -- Importance of the domain -- This stuff can be hard! -- Parameterized areas and volumes -- Quiz -- 7: Vectors And Gradients -- Introduction to vectors -- Dot products -- Gradient vectors and directional derivatives -- Maxima, minima, and saddles -- Application: optimization problems -- LaGrange multipliers -- Determinants -- Cross product -- Quiz -- 8: Calculus With Parameterizations -- Differentiating parameterizations -- Arc length -- Line integrals -- Surface area -- Surface integrals -- Volume -- Change of variables -- Quiz -- 9: Vector Fields And Derivatives -- Definition -- Gradients, revisited -- Divergence -- Curl -- Quiz -- 10: Integrating Vector Fields -- Line integrals -- Surface integrals -- Quiz -- 11: Integration Theorems -- Path independence -- Green's theorem on rectangular domains -- Green's theorem over more general domains -- Stokes' theorem -- Geometric interpretation of curl -- Gauss' theorem -- Geometric interpretation of divergence -- Quiz -- Final Exam -- Answers To Problems -- Index. |
| Summary |
Synopsis: 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 concepts, geometric interpretations of vector operations such as div, grad, and curl, coverage of key integration theorems including Green's, Stokes', and Gauss', quizzes at the end of each chapter to reinforce learning, and a 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! |
| Subject |
Calculus.
|
| ISBN |
9780071481212 paperback |
|
0071481214 paperback |
|
