Preface 

ix  
To the Student: Some Preliminary Notation 

xiii  


1  (78) 

Vectors in Two and Three Dimensions 


1  (7) 


8  (10) 


18  (9) 


27  (12) 

Equations for Planes; Distance Problems 


39  (8) 

Some ndimensional Geometry 


47  (14) 


61  (11) 

True/False Exercises for Chapter 1 


72  (1) 

Miscellaneous Exercises for Chapter 1 


73  (6) 

Differentiation in Several Variables 


79  (98) 

Functions of Several Variables; Graphing Surfaces 


79  (14) 


93  (15) 


108  (17) 

Properties; Higherorder Partial Derivatives; Newton's Method 


125  (14) 


139  (14) 

Directional Derivatives and the Gradient 


153  (17) 

True/False Exercises for Chapter 2 


170  (1) 

Miscellaneous Exercises for Chapter 2 


171  (6) 


177  (53) 

Parametrized Curves and Kepler's Laws 


177  (13) 

Arclength and Differential Geometry 


190  (18) 

Vector Fields: An Introduction 


208  (6) 

Gradient, Divergence, Curl, and the Del Operator 


214  (9) 

True/False Exercises for Chapter 3 


223  (1) 

Miscellaneous Exercises for Chapter 3 


223  (7) 

Maxima and Minima in Several Variables 


230  (59) 

Differentials and Taylor's Theorem 


230  (15) 


245  (14) 


259  (14) 

Some Applications of Extrema 


273  (11) 

True/False Exercises for Chapter 4 


284  (1) 

Miscellaneous Exercises for Chapter 4 


285  (4) 


289  (74) 

Introduction: Areas and Volumes 


289  (3) 


292  (17) 

Changing the Order of Integration 


309  (3) 


312  (10) 


322  (21) 

Applications of Integration 


343  (14) 

True/False Exercises for Chapter 5 


357  (1) 

Miscellaneous Exercises for Chapter 5 


358  (5) 


363  (42) 

Scalar and Vector Line Integrals 


363  (18) 


381  (9) 

Conservative Vector Fields 


390  (10) 

True/False Exercises for Chapter 6 


400  (1) 

Miscellaneous Exercises for Chapter 6 


401  (4) 

Surface Integrals and Vector Analysis 


405  (72) 


405  (14) 


419  (20) 

Stokes's and Gauss's Theorems 


439  (18) 

Further Vector Analysis; Maxwell's Equations 


457  (12) 

True/False Exercises for Chapter 7 


469  (1) 

Miscellaneous Exercises for Chapter 7 


470  (7) 

Vector Analysis in Higher Dimensions 


477  (32) 

An Introduction to Differential Forms 


477  (6) 

Manifolds and Integrals of kforms 


483  (15) 

The Generalized Stokes's Theorem 


498  (8) 

True/False Exercises for Chapter 8 


506  (1) 

Miscellaneous Exercises for Chapter 8 


507  (2) 
Suggestions for Further Reading 

509  (2) 
Answers to Selected Exercises 

511  (32) 
Index 

543  