Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil's current areas of research include redundant representations, operator theory, and applied harmonic analysis. In his spare time, Heil pursues his hobby of astronomy.

Maurice D. Weir holds a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He is a Professor Emeritus of the Department of Applied Mathematics at the Naval Postgraduate School in Monterey, California. Weir enjoys teaching Mathematical Modeling and Differential Equations. His current areas of research include modeling and simulation as well as mathematics education. Weir has been awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He has coauthored eight books, including the University Calculus series and Thomas’ Calculus.

Przemyslaw Bogacki is an Associate Professor of Mathematics and Statistics and a University Professor at Old Dominion University. He received his PhD in 1990 from Southern Methodist University. He is the author of a text on linear algebra, to appear in 2019. He is actively involved in applications of technology in collegiate mathematics. His areas of research include computer aided geometric design and numerical solution of initial value problems for ordinary differential equations.

1.      Infinite Sequences and Series

1.1    Sequences

1.2    Infinite Series

1.3    The Integral Test

1.4    Comparison Tests

1.5    Absolute Convergence; The Ratio and Root Tests

1.6    Alternating Series and Conditional Convergence

1.7    Power Series

1.8    Taylor and Maclaurin Series

1.9    Convergence of Taylor Series

1.10  Applications of Taylor Series

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises 

2.      Parametric Equations and Polar Coordinates

2.1    Parametrizations of Plane Curves

2.2    Calculus with Parametric Curves

2.3    Polar Coordinates

2.4    Graphing Polar Coordinate Equations 

2.5    Areas and Lengths in Polar Coordinates

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

3.     Vectors and the Geometry of Space

3.1    Three-Dimensional Coordinate Systems

3.2    Vectors

3.3    The Dot Product

3.4    The Cross Product

3.5    Lines and Planes in Space

3.6    Cylinders and Quadric Surfaces

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

4.     Vector-Valued Functions and Motion in Space

4.1 Curves in Space and Their Tangents

4.2    Integrals of Vector Functions; Projectile Motion

4.3    Arc Length in Space

4.4    Curvature and Normal Vectors of a Curve  

4.5    Tangential and Normal Components of Acceleration

4.6    Velocity and Acceleration in Polar Coordinates

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

5.     Partial Derivatives        

5.1    Functions of Several Variables

5.2    Limits and Continuity in Higher Dimensions

5.3    Partial Derivatives 

5.4    The Chain Rule

5.5    Directional Derivatives and Gradient Vectors

5.6    Tangent Planes and Differentials

5.7    Extreme Values and Saddle Points

5.8 Lagrange Multiplier

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

6.     Multiple Integrals

6.1    Double and Iterated Integrals over Rectangles

6.2    Double Integrals over General Regions

6.3    Area by Double Integration

6.4    Double Integrals in Polar Form

6.5    Triple Integrals in Rectangular Coordinates

6.6    Applications

6.7    Triple Integrals in Cylindrical and Spherical Coordinates

6.8    Substitutions in Multiple Integrals

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

7.     Integrals and Vector Fields

7.1    Line Integrals of Scalar Functions

7.2    Vector Fields and Line Integrals: Work, Circulation, and Flux

7.3    Path Independence, Conservative Fields, and Potential Functions

7.4    Green’s Theorem in the Plane

7.5    Surfaces and Area

7.6    Surface Integrals

7.7    Stokes’ Theorem

7.8    The Divergence Theorem and a Unified Theory

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

Appendix

A.1 Real Numbers and the Real Line

A.2 Mathematical Induction AP-6

A.3 Lines and Circles AP-10

A.4 Conic Sections AP-16

A.5 Proofs of Limit Theorems

A.6 Commonly Occurring Limits

A.7 Theory of the Real Numbers

A.8 Complex Numbers

A.9 The Distributive Law for Vector Cross Products

A.10 The Mixed Derivative Theorem and the increment Theorem

Additional Topics (online at  bit.ly/2IDDl8w )

B.1   Relative Rates of Growth  

B.2   Probability 

B.3   Conics in Polar Coordinates  

B.4   Taylor’s Formula for Two Variables 

B.5   Partial Derivatives with Constrained Variables          

Odd Answers

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