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Calculus: Single and Multivariable 4th edition

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Deborah Hughes-Hallett, Andrew M. Gleason, and William G. McCallum
Publisher: John Wiley & Sons

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Table of Contents

  • Chapter 1: A Library of Functions
    • 1.1: Functions and Change (15)
    • 1.2: Exponential Functions (18)
    • 1.3: New Functions From Old (14)
    • 1.4: Logarithmic Functions (22)
    • 1.5: Trigonometric Functions (20)
    • 1.6: Powers, Polynomials, and Rational Functions (13)
    • 1.7: Introduction to Continuity (6)
    • 1.8: Limits (18)

  • Chapter 2: Key Concept: The Derivative
    • 2.1: How do we Measure Speed? (13)
    • 2.2: The Derivative at a Point (18)
    • 2.3: The Derivative Function (15)
    • 2.4: Interpretations of the Derivative (9)
    • 2.5: The Second Derivative (11)
    • 2.6: Differentiability (8)

  • Chapter 3: Short-Cuts to Differentiation
    • 3.1: Powers and Polynomials (19)
    • 3.2: The Exponential Function (14)
    • 3.3: The Product and Quotient Rules (15)
    • 3.4: The Chain Rule (13)
    • 3.5: The Trigonometric Functions (10)
    • 3.6: The Chain Rule and Inverse Functions (14)
    • 3.7: Implicit Functions (10)
    • 3.8: Hyperbolic Functions
    • 3.9: Linear Approximation and the Derivative (7)
    • 3.10: Theorems about Differentiable Functions

  • Chapter 4: Using the Derivative
    • 4.1: Using First and Second Derivatives (11)
    • 4.2: Families of Curves (7)
    • 4.3: Optimization (16)
    • 4.4: Applications to Marginality (7)
    • 4.5: Optimization and Modeling (17)
    • 4.6: Rates and Related Rates (7)
    • 4.7: L'Hopital's Rule, Growth, and Dominance
    • 4.8: Parametric Equations

  • Chapter 5: Key Concept: The Definite Integral
    • 5.1: How do we Measure Distance Traveled? (9)
    • 5.2: The Definite Integral (13)
    • 5.3: The Fundamental Theorem and Interpretations (14)
    • 5.4: Theorems about Definite Integrals (18)

  • Chapter 6: Constructing Antiderivatives
    • 6.1: Antiderivatives Graphically and Numerically (14)
    • 6.2: Constructing Antiderivatives Analytically (25)
    • 6.3: Differential Equations
    • 6.4: Second Fundamental Theorem of Calculus (10)
    • 6.5: The Equations of Motion

  • Chapter 7: Integration
    • 7.1: Integration by Substitution (28)
    • 7.2: Integration by Parts (23)
    • 7.3: Tables of Integrals (1)
    • 7.4: Algebraic Identities and Trigonometric Substitutions
    • 7.5: Approximating Definite Integrals (14)
    • 7.6: Approximation Errors and Simpson's Rule (1)
    • 7.7: Improper Integrals (19)

  • Chapter 8: Using the Definite Integral
    • 8.1: Areas and Volumes (17)
    • 8.2: Applications to Geometry (21)
    • 8.3: Area and Arc Length in Polar Coordinates (4)
    • 8.4: Density and Center of Mass (3)
    • 8.5: Applications to Physics (14)
    • 8.6: Applications to Economics (8)
    • 8.7: Distribution Functions
    • 8.8: Probability, Mean, and Median

  • Chapter 9: Sequences and Series
    • 9.1: Sequences (7)
    • 9.2: Geometric Series (21)
    • 9.3: Convergence of Series (7)
    • 9.4: Tests for Convergence (14)
    • 9.5: Power Series and Interval of Convergence (12)
    • 9: Review Problems (1)

  • Chapter 10: Approximating Functions Using Series
    • 10.1: Taylor Polynomials (17)
    • 10.2: Taylor Series (15)
    • 10.3: Finding and Using Taylor Series (7)
    • 10.4: The Error in Taylor Polynomial Approximations
    • 10.5: Fourier Series

  • Chapter 11: Differential Equations
    • 11.1: What is a Differential Equation? (3)
    • 11.2: Slope Fields (5)
    • 11.3: Euler's Method (5)
    • 11.4: Separation of Variables (26)
    • 11.5: Growth and Decay (17)
    • 11.6: Applications and Modeling (11)
    • 11.7: Models of Population Growth (8)
    • 11.8: Systems of Differential Growth
    • 11.9: Analyzing the Phase Plane
    • 11.10: Second-Order Differential Equations: Oscillations
    • 11.11: Linear Second-Order Differential Equations
    • 11: Review Problems (5)

  • Chapter 12: Functions of Several Variables
    • 12.1: Functions of Two Variables (4)
    • 12.2: Graphs of Functions of Two Variables (3)
    • 12.3: Contour Diagrams (4)
    • 12.4: Linear Functions (6)
    • 12.5: Functions of Three Variables
    • 12.6: Limits and Continuity

  • Chapter 13: A Fundamental Tool: Vectors
    • 13.1: Displacement Vectors (21)
    • 13.2: Vectors in General (18)
    • 13.3: The Dot Product (17)
    • 13.4: The Cross Product (3)
    • 13: Review Problems (3)

  • Chapter 14: Differentiating Functions of Several Variables
    • 14.1: The Partial Derivative (1)
    • 14.2: Computing Partial Derivatives Algebraically (4)
    • 14.3: Local Linearity and the Differential (2)
    • 14.4: Gradients and Directional Derivatives in the Plane (5)
    • 14.5: Gradients and Directional Derivatives in Space (4)
    • 14.6: The Chain Rule (4)
    • 14.7: Second-Order Partial Derivatives (4)
    • 14.8: Differentiability

  • Chapter 15: Optimization: Local and Global Extrema
    • 15.1: Local Extrema (2)
    • 15.2: Optimization (4)
    • 15.3: Constrained Optimization: Lagrange Multipliers (4)

  • Chapter 16: Integrating Functions of Several Variables
    • 16.1: The Definite Integral of a Function of Two Variables
    • 16.2: Iterated Integrals (8)
    • 16.3: Triple Integrals (3)
    • 16.4: Double Integrals in Polar Coordinates (3)
    • 16.5: Integrals in Cylindrical and Spherical Coordinates (5)
    • 16.6: Applications of Integration to Probability
    • 16.7: Change of Variables in a Multiple Integral

  • Chapter 17: Parameterization and Vector Fields
    • 17.1: Parameterized Curves (9)
    • 17.2: Motion, Velocity, and Acceleration (4)
    • 17.3: Vector Fields
    • 17.4: The Flow of a Vector Field
    • 17.5: Parameterized Surfaces

  • Chapter 18: Line Integrals
    • 18.1: The Idea of a Line Integral (4)
    • 18.2: Computing Line Integrals Over Parameterized Curves (2)
    • 18.3: Gradient Fields and Path-Independent Fields (4)
    • 18.4: Path-Dependent Vector Fields and Green's Theorem (3)

  • Chapter 19: Flux Integrals
    • 19.1: The Idea of a Flux Integral (3)
    • 19.2: Flux Integrals for Graphs, Cylinders, and Spheres
    • 19.3: Flux Integrals Over Parameterized Surfaces

  • Chapter 20: Calculus of Vector Fields
    • 20.1: The Divergence of a Vector Field (2)
    • 20.2: The Divergence Theorem (2)
    • 20.3: The Curl of a Vector Field (3)
    • 20.4: Stokes' Theorem (2)
    • 20.5: The Three Fundamental Theorems

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Group Quantity Questions
Chapter 1: A Library of Functions
1.1 15 006 011 012 013 015 016 020 022 023 029 030 033 034 035 038
1.2 18 003 004 006 011 012 014 018 019 023 024 028 029 034 035 036 037 038 039
1.3 14 015 016 018 026 028 030 038 039 040 044 049 050 051 052
1.4 22 002 004 006 010 013 014 015 017 023 025 026 027 029 031 032 033 034 035 036 037 039 040
1.5 20 001 002 004 006 008 010 012 013 014 018 020 021 028 030 035 037 038 040 041 044
1.6 13 001 003 004 005 006 007 009 014 016 017 018 021 029
1.7 6 002 004 006 008 017 019
1.8 18 001 002 008 010 014 017 018 019 020 021 029 030 032 034 036 038 039 046
Chapter 2: Key Concept: The Derivative
2.1 13 002 003 004 005 006 007 008 009 010 014 015 017 018
2.2 18 001 002 003 007 010 011 012 013 015 016 020 024 025 028 033 034 039 040
2.3 15 002 004 006 008 010 012 014 016 021 022 033 035 037 038 042
2.4 9 002 004 006 007 008 010 014 015 021
2.5 11 001 002 003 007 009 011 012 013 014 021 022
2.6 8 001 002 004 005 006 007 008 015
Chapter 3: Short-Cuts to Differentiation
3.1 19 002 008 010 016 020 024 027 028 035 042 047 053 054 057 058 059 062 063 064
3.2 14 002 004 011 012 013 016 020 023 026 036 037 038 041 042
3.3 15 004 006 007 011 012 014 018 022 026 040 044 045 050 051 055
3.4 13 005 006 011 012 029 032 035 041 048 068 078 080 082
3.5 10 004 008 010 016 018 022 026 035 045 046
3.6 14 002 004 006 010 012 020 043 052 053 054 055 056 058 059
3.7 10 002 006 008 010 012 019 022 023 028 030
3.9 7 002 004 006 008 012 022 024
Chapter 4: Using the Derivative
4.1 11 004 005 006 007 018 019 027 036 038 040 044
4.2 7 006 010 011 012 013 014 022
4.3 16 002 005 006 013 014 015 017 018 019 020 021 022 023 024 030 032
4.4 7 002 004 006 015 017 021 022
4.5 17 004 011 012 016 017 018 019 020 021 022 023 025 027 028 032 033 034
4.6 7 002 004 006 008 010 020 022
Chapter 5: Key Concept: The Definite Integral
5.1 9 001 002 006 007 015 016 022 025 026
5.2 13 001 002 003 008 009 012 018 020 020.alt 025 027 028 029
5.3 14 002 006 009 010 011 013 015 016 017 022 030 033 034 036
5.4 18 002 008 009 015 016 017 018 019 022 030 031 034 035 036 037 038 040 042
Chapter 6: Constructing Antiderivatives
6.1 14 001 004 005 008 009 010 011 013 014 015 017 018 019 023
6.2 25 001 003 005 010 015 016 020 021 028 032 039 040 047 050 052 058 062 063 064 066 070 072 077 086 087
6.4 10 004 006 008 012 016 018 019 022 035 036
Chapter 7: Integration
7.1 28 002 003 006 010 016 018 020 021 022 023 024 027 031 032 035 037 045 050 054 055 056 060 063 075 080 083 087 088
7.2 23 002 007 008 009 012 013 015 017 018 019 022 027 031 033 038 039 040 042 048 052 053 054 056
7.3 1 047
7.5 14 001 002 003 004 006 007 009 010 012 015 016 017 018 023
7.6 1 005.alt
7.7 19 001 003 004 005 006 007 008 010 011 012 019 023 026 030 033 034 035 036 044
Chapter 8: Using the Definite Integral
8.1 17 002 02 003 004 007 008 010 012 013 014 015 017 019 020 024 026 028
8.2 21 001 004 005 006 007 010 011 012 012.alt 015 016 017 019 021 022 023 024 033 034 035 037
8.3 4 004 008 016 018
8.4 3 009 012 013
8.5 14 002 003 005 006 008 009 014 015 016 023 024 025 026 031
8.6 8 001 004 006 007 010 011 013 015
Chapter 9: Sequences and Series
R 1 061
9.1 7 006 008 016 017 026 042 043
9.2 21 001 002 003 004 005 006 007 008 009 010 011 012 018 019 020 021 024 025 026 028 031
9.3 7 001 002 003 011 016 017 018
9.4 14 001 002 004 005 006 007 011 012 015 021 024 042 044 046
9.5 12 001-4 005 008 009 012 014 016 017 020 022 024 025
Chapter 10: Approximating Functions Using Series
10.1 17 001 002 003 004 005 006 011 012 014 017 018 019 020 022 023 026 036
10.2 15 005 006 007 009 010 013 014 017 020 023 024 026 031 033 035
10.3 7 001 006 008 012 013 026 029
Chapter 11: Differential Equations
R 5 001 014 019 032 033
11.1 3 001 006 016
11.2 5 003 004 005 008 010
11.3 5 001 004 005 006 009
11.4 26 002 003 004 005 006 008 010 016 018 019 020 021 024 026 027 028 030 030.alt 036 036.alt 039 041 041.alt 044 044.alt 046
11.5 17 001 002 003 004 005 008 010 011 012 012.alt 013 014 019 020 021 021.alt 022
11.6 11 002 003 003.alt 004 007 009 013 014 016 019 024
11.7 8 001 002 003 006 008 009 010 013
Chapter 12: Functions of Several Variables
12.1 4 002 006 007 029
12.2 3 002 011 014
12.3 4 017 020 022 024
12.4 6 002 004 005 012 013 017
Chapter 13: A Fundamental Tool: Vectors
R 3 004 008 026
13.1 21 003 004 005 006 008 011 012 014 015 016 018 021 022 023 025 026 027 028 029 030 034
13.2 18 001 002 003 004 005 006 007 008 009 012 013 014 015 016 018 020 021 023
13.3 17 002 004 007 009 010 016 017 018 022 025 026 030 032 033 034 035 036
13.4 3 004 016 020
Chapter 14: Differentiating Functions of Several Variables
14.1 1 002
14.2 4 001 003 019 028
14.3 2 003 018
14.4 5 022 025 033 054 067
14.5 4 008 011 014 022
14.6 4 001 004 010 020
14.7 4 001 008 027 035
Chapter 15: Optimization: Local and Global Extrema
15.1 2 008 014
15.2 4 018 019 021 023
15.3 4 003 005 010 015
Chapter 16: Integrating Functions of Several Variables
16.2 8 001 002 007 020 022 041 042 044
16.3 3 003 019 047
16.4 3 003 013 018
16.5 5 002-3 004-5 020 022-23 028
Chapter 17: Parameterization and Vector Fields
17.1 9 003 010 014 018 021 035 038 039 048
17.2 4 001 003 005 011
Chapter 18: Line Integrals
18.1 4 006 010 015 031
18.2 2 014 016
18.3 4 011 012 022 027
18.4 3 001 011 017
Chapter 19: Flux Integrals
19.1 3 006 009 025
Chapter 20: Calculus of Vector Fields
20.1 2 002 007
20.2 2 015 018
20.3 3 007 008 022
20.4 2 004 023
Total 974  
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