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University Calculus

ISBN: 9780321350145 | 0321350146
Edition: 1st
Format: Hardcover
Publisher: Addison Wesley
Pub. Date: 1/1/2007

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SummaryTable of Contents
This streamlined version of Thomas Calculus provides a faster-paced, precise and accurate presentation of calculus for a college-level calculus course. University Calculus covers both single variable and multivariable calculus and is appropriate for a three semester or four quarter course. University Calculus is the ideal choice for professors who want a faster-paced text with a more conceptually balanced exposition. It is a blend of intuition and rigor. Transcendental functions are introduced early, and are continually revisited in more depth ... MORE
Prefacexi
Functions
1(54)
Functions and Their Graphs
1(13)
... MORE
Combining Functions; Shifting and Scaling Graphs
14(8)
Trigonometric Functions
22(8)
Exponential Functions
30(6)
Inverse Functions and Logarithms
36(14)
Graphing with Calculators and Computers
50(5)
Limits and Continuity
55(70)
Rates of Change and Tangents to Curves
55(7)
Limit of a Function and Limit Laws
62(12)
The Precise Definition of a Limit
74(10)
One-Sided Limits and Limits at Infinity
84(13)
Infinite Limits and Vertical Asymptotes
97(6)
Continuity
103(12)
Tangents and Derivatives at a Point
115(10)
Questions to Guide Your Review
119(1)
Practice Exercises
120(2)
Additional and Advanced Exercises
122(3)
Differentiation
125(112)
The Derivative as a Function
125(9)
Differentiation Rules for Polynomials, Exponentials, Products, and Quotients
134(12)
The Derivative as a Rate of Change
146(11)
Derivatives of Trigonometric Functions
157(7)
The Chain Rule and Parametric Equations
164(13)
Implicit Differentiation
177(6)
Derivatives of Inverse Functions and Logarithms
183(11)
Inverse Trigonometric Functions
194(7)
Related Rates
201(8)
Linearization and Differentials
209(12)
Hyperbolic Functions
221(16)
Questions to Guide Your Review
227(1)
Practice Exercises
228(6)
Additional and Advanced Exercises
234(3)
Applications of Derivatives
237(78)
Extreme Values of Functions
237(8)
The Mean Value Theorem
245(9)
Monotonic Functions and the First Derivative Test
254(6)
Concavity and Curve Sketching
260(11)
Applied Optimization
271(12)
Indeterminate Forms and L'Hopital's Rule
283(8)
Newton's Method
291(5)
Antiderivatives
296(19)
Questions to Guide Your Review
306(1)
Practice Exercises
307(4)
Additional and Advanced Exercises
311(4)
Integration
315(76)
Estimating with Finite Sums
315(10)
Sigma Notation and Limits of Finite Sums
325(7)
The Definite Integral
332(13)
The Fundamental Theorem of Calculus
345(9)
Indefinite Integrals and the Substitution Rule
354(6)
Substitution and Area Between Curves
360(10)
The Logarithm Defined as an Integral
370(21)
Questions to Guide Your Review
381(1)
Practice Exercises
382(4)
Additional and Advanced Exercises
386(5)
Applications of Definite Integrals
391(57)
Volumes by Slicing and Rotation About an Axis
391(10)
Volumes by Cylindrical Shells
401(7)
Lengths of Plane Curves
408(7)
Areas of Surfaces of Revolution
415(6)
Exponential Change and Separable Differential Equations
421(9)
Work
430(7)
Moments and Centers of Mass
437(11)
Questions to Guide Your Review
444(1)
Practice Exercises
444(2)
Additional and Advanced Exercises
446(2)
Techniques of Integration
448(54)
Integration by Parts
448(7)
Trigonometric Integrals
455(6)
Trigonometric Substitutions
461(3)
Integration of Rational Functions by Partial Fractions
464(7)
Integral Tables and Computer Algebra Systems
471(6)
Numerical Integration
477(10)
Improper Integrals
487(15)
Questions to Guide Your Review
497(1)
Practice Exercises
497(3)
Additional and Advanced Exercises
500(2)
Infinite Sequences and Series
502(75)
Sequences
502(13)
Infinite Series
515(8)
The Integral Test
523(6)
Comparison Tests
529(4)
The Ratio and Root Tests
533(4)
Alternating Series, Absolute and Conditional Convergence
537(6)
Power Series
543(10)
Taylor and Maclaurin Series
553(6)
Convergence of Taylor Series
559(10)
The Binomial Series
569(8)
Questions to Guide Your Review
572(1)
Practice Exercises
573(2)
Additional and Advanced Exercises
575(2)
Polar Coordinates and Conics
577(37)
Polar Coordinates
577(5)
Graphing in Polar Coordinates
582(4)
Areas and Lengths in Polar Coordinates
586(4)
Conic Sections
590(9)
Conics in Polar Coordinates
599(7)
Conics and Parametric Equations; The Cycloid
606(8)
Questions to Guide Your Review
610(1)
Practice Exercises
610(2)
Additional and Advanced Exercises
612(2)
Vectors and the Geometry of Space
614(49)
Three-Dimensional Coordinate Systems
614(5)
Vectors
619(9)
The Dot Product
628(8)
The Cross Product
636(6)
Lines and Planes in Space
642(10)
Cylinders and Quadric Surfaces
652(11)
Questions to Guide Your Review
657(1)
Practice Exercises
658(2)
Additional and Advanced Exercises
660(3)
Vector-Valued Functions and Motion in Space
663(39)
Vector Functions and Their Derivatives
663(9)
Integrals of Vector Functions
672(6)
Are Length in Space
678(5)
Curvature of a Curve
683(6)
Tangential and Normal Components of Acceleration
689(5)
Velocity and Acceleration in Polar Coordinates
694(8)
Questions to Guide Your Review
698(1)
Practice Exercises
698(2)
Additional and Advanced Exercises
700(2)
Partial Derivatives
702(83)
Functions of Several Variables
702(9)
Limits and Continuity in Higher Dimensions
711(8)
Partial Derivatives
719(12)
The Chain Rule
731(8)
Directional Derivatives and Gradient Vectors
739(8)
Tangent Planes and Differentials
747(9)
Extreme Values and Saddle Points
756(9)
Lagrange Multipliers
765(10)
Taylor's Formula for Two Variables
775(10)
Questions to Guide Your Review
779(1)
Practice Exercises
780(3)
Additional and Advanced Exercises
783(2)
Multiple Integrals
785(66)
Double and Iterated Integrals over Rectangles
785(5)
Double Integrals over General Regions
790(9)
Area by Double Integration
799(3)
Double Integrals in Polar Form
802(5)
Triple Integrals in Rectangular Coordinates
807(9)
Moments and Centers of Mass
816(9)
Triple Integrals in Cylindrical and Spherical Coordinates
825(12)
Substitutions in Multiple Integrals
837(14)
Questions to Guide Your Review
846(1)
Practice Exercises
846(2)
Additional and Advanced Exercises
848(3)
Integration in Vector Fields
851(1)
Line Integrals
851(5)
Vector Fields, Work, Circulation, and Flux
856(11)
Path Independence, Potential Functions, and Conservative Fields
867(10)
Green's Theorem in the Plane
877(10)
Surfaces and Area
887(9)
Surface Integrals and Flux
896(9)
Stokes' Theorem
905(9)
The Divergence Theorem and a Unified Theory
914(11)
Questions to Guide Your Review
925(1)
Practice Exercises
925(3)
Additional and Advanced Exercises
928
First-Order Differential Equations (online)
Solutions, Slope Fields, and Picard's Theorem
First-Order Linear Equations
Applications
Euler's Method
Graphical Solutions of Autonomous Equations
Systems of Equations and Phase Planes
Second-Order Differential Equations (online)
Second-Order Linear Equations
Nonhomogeneous Linear Equations
Applications
Euler Equations
Power Series Solutions
Appendices
1(1)
A.1 Real Numbers and the Real Line
1(6)
A.2 Mathematical Induction
7(3)
A.3 Lines, Circles, and Parabolas
10(9)
A.4 Trigonometry Formulas
19(2)
A.5 Proofs of Limit Theorems
21(4)
A.6 Commonly Occurring Limits
25(1)
A.7 Theory of the Real Numbers
26(3)
A.8 The Distributive Law for Vector Cross Products
29(1)
A.9 The Mixed Derivative Theorem and the Increment Theorem
30
Answers1(1)
Index1(1)
A Brief Table of Integrals1(1)
Credits1

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