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Calculus: Single and Multivariable 5th 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 (19)
    • 1.2: Exponential Functions (21)
    • 1.3: New Functions From Old (21)
    • 1.4: Logarithmic Functions (28)
    • 1.5: Trigonometric Functions (23)
    • 1.6: Powers, Polynomials, and Rational Functions (17)
    • 1.7: Introduction to Continuity (9)
    • 1.8: Limits (17)

  • Chapter 2: Key Concept: The Derivative
    • 2.1: How do we Measure Speed? (9)
    • 2.2: The Derivative at a Point (14)
    • 2.3: The Derivative Function (12)
    • 2.4: Interpretations of the Derivative (8)
    • 2.5: The Second Derivative (8)
    • 2.6: Differentiability (8)

  • Chapter 3: Short-Cuts to Differentiation
    • 3.1: Powers and Polynomials (13)
    • 3.2: The Exponential Function (9)
    • 3.3: The Product and Quotient Rules (13)
    • 3.4: The Chain Rule (15)
    • 3.5: The Trigonometric Functions (13)
    • 3.6: The Chain Rule and Inverse Functions (14)
    • 3.7: Implicit Functions (11)
    • 3.8: Hyperbolic Functions (6)
    • 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 (13)
    • 4.2: Families of Curves (11)
    • 4.3: Families of Functions (10)
    • 4.4: Optimization, Geometry, and Modeling (16)
    • 4.5: Applications to Marginality (4)
    • 4.6: Rates and Related Rates (8)
    • 4.7: L'Hopital's Rule, Growth, and Dominance (8)
    • 4.8: Parametric Equations (9)

  • Chapter 5: Key Concept: The Definite Integral
    • 5.1: How do we Measure Distance Traveled? (7)
    • 5.2: The Definite Integral (13)
    • 5.3: The Fundamental Theorem and Interpretations (12)
    • 5.4: Theorems about Definite Integrals (10)

  • Chapter 6: Constructing Antiderivatives
    • 6.1: Antiderivatives Graphically and Numerically (11)
    • 6.2: Constructing Antiderivatives Analytically (21)
    • 6.3: Differential Equations (6)
    • 6.4: Second Fundamental Theorem of Calculus (9)
    • 6.5: The Equations of Motion (3)

  • Chapter 7: Integration
    • 7.1: Integration by Substitution (28)
    • 7.2: Integration by Parts (14)
    • 7.3: Tables of Integrals (10)
    • 7.4: Algebraic Identities and Trigonometric Substitutions (3)
    • 7.5: Approximating Definite Integrals (8)
    • 7.6: Approximation Errors and Simpson's Rule (3)
    • 7.7: Improper Integrals (16)
    • 7.8: Comparison of Improper Integrals (6)

  • Chapter 8: Using the Definite Integral
    • 8.1: Areas and Volumes (9)
    • 8.2: Applications to Geometry (14)
    • 8.3: Area and Arc Length in Polar Coordinates (9)
    • 8.4: Density and Center of Mass (6)
    • 8.5: Applications to Physics (12)
    • 8.6: Applications to Economics (6)
    • 8.7: Distribution Functions (6)
    • 8.8: Probability, Mean, and Median (4)

  • Chapter 9: Sequences and Series
    • 9.1: Sequences (8)
    • 9.2: Geometric Series (12)
    • 9.3: Convergence of Series (10)
    • 9.4: Tests for Convergence (13)
    • 9.5: Power Series and Interval of Convergence (12)

  • Chapter 10: Approximating Functions Using Series
    • 10.1: Taylor Polynomials (9)
    • 10.2: Taylor Series (10)
    • 10.3: Finding and Using Taylor Series (8)
    • 10.4: The Error in Taylor Polynomial Approximations (4)
    • 10.5: Fourier Series (5)

  • Chapter 11: Differential Equations
    • 11.1: What is a Differential Equation? (4)
    • 11.2: Slope Fields (4)
    • 11.3: Euler's Method (2)
    • 11.4: Separation of Variables (10)
    • 11.5: Growth and Decay (10)
    • 11.6: Applications and Modeling (8)
    • 11.7: The Logistic Model (5)
    • 11.8: Systems of Differential Growth (7)
    • 11.9: Analyzing the Phase Plane (3)
    • 11.10: Second-Order Differential Equations: Oscillations (6)
    • 11.11: Linear Second-Order Differential Equations (10)

  • Chapter 12: Functions of Several Variables
    • 12.1: Functions of Two Variables (11)
    • 12.2: Graphs of Functions of Two Variables (7)
    • 12.3: Contour Diagrams (9)
    • 12.4: Linear Functions (4)
    • 12.5: Functions of Three Variables (4)
    • 12.6: Limits and Continuity (6)

  • Chapter 13: A Fundamental Tool: Vectors
    • 13.1: Displacement Vectors (10)
    • 13.2: Vectors in General (11)
    • 13.3: The Dot Product (17)
    • 13.4: The Cross Product (5)

  • Chapter 14: Differentiating Functions of Several Variables
    • 14.1: The Partial Derivative (6)
    • 14.2: Computing Partial Derivatives Algebraically (9)
    • 14.3: Local Linearity and the Differential (7)
    • 14.4: Gradients and Directional Derivatives in the Plane (15)
    • 14.5: Gradients and Directional Derivatives in Space (12)
    • 14.6: The Chain Rule (9)
    • 14.7: Second-Order Partial Derivatives (7)
    • 14.8: Differentiability (7)

  • Chapter 15: Optimization: Local and Global Extrema
    • 15.1: Local Extrema (8)
    • 15.2: Optimization (8)
    • 15.3: Constrained Optimization: Lagrange Multipliers (6)

  • Chapter 16: Integrating Functions of Several Variables
    • 16.1: The Definite Integral of a Function of Two Variables (7)
    • 16.2: Iterated Integrals (12)
    • 16.3: Triple Integrals (9)
    • 16.4: Double Integrals in Polar Coordinates (8)
    • 16.5: Integrals in Cylindrical and Spherical Coordinates (10)
    • 16.6: Applications of Integration to Probability (5)
    • 16.7: Change of Variables in a Multiple Integral (6)

  • Chapter 17: Parameterization and Vector Fields
    • 17.1: Parameterized Curves (11)
    • 17.2: Motion, Velocity, and Acceleration (9)
    • 17.3: Vector Fields (5)
    • 17.4: The Flow of a Vector Field (3)
    • 17.5: Parameterized Surfaces (10)

  • Chapter 18: Line Integrals
    • 18.1: The Idea of a Line Integral (7)
    • 18.2: Computing Line Integrals Over Parameterized Curves (6)
    • 18.3: Gradient Fields and Path-Independent Fields (9)
    • 18.4: Path-Dependent Vector Fields and Green's Theorem (6)

  • Chapter 19: Flux Integrals
    • 19.1: The Idea of a Flux Integral (9)
    • 19.2: Flux Integrals for Graphs, Cylinders, and Spheres (6)
    • 19.3: Flux Integrals Over Parameterized Surfaces (4)

  • Chapter 20: Calculus of Vector Fields
    • 20.1: The Divergence of a Vector Field (6)
    • 20.2: The Divergence Theorem (6)
    • 20.3: The Curl of a Vector Field (6)
    • 20.4: Stokes' Theorem (7)
    • 20.5: The Three Fundamental Theorems (5)

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Group Quantity Questions
Chapter 1: A Library of Functions
1.1 19 006 013 016 017 018 019 022 023 025 026 027 030 031 032 033 036 037 041 045
1.2 21 005 006 007.alt 008 009 010 011 013 015 016 017 018 023 024 025 027 028 032 033 035 036
1.3 21 002 011 013 014 016 019 020 024 028 031 033 036 041 042 043 044 046 055 056 060 061
1.4 28 002 003 004 006 010 013 014 015 016 017 024 026 027 028 030 031 032 033 035 037 040 041 042 043 044 045 047 049
1.5 23 001 002 004 006 008 010 012 013 014 016 019 020 027 029 030 031 034 037 041 042 043 046 049
1.6 17 001 002 003 004 006 007 009 011 012 013 015 016 017 018 020 024 026
1.7 9 002 004 006 008 016 020 022 023 029
1.8 17 001 003 010 011 012 013 027 029 035 036 040 042 043 045 047 048 055
Chapter 2: Key Concept: The Derivative
R 1 016
2.1 9 001 010 011 012 013 014 025 026 027
2.2 15 001 002 011 012 016 017 022 023 024 025 028 033 034 044 045
2.3 12 002 004 012 014 024 025 037 038 040 041 048 049
2.4 8 003 005 007 008 009 014 018 028
2.5 8 001 002 003 009 011 022 029 030
2.6 7 001 002 003 004 005 012 014
Chapter 3: Short-Cuts to Differentiation
3.1 13 002 013 019 026 027 030 039 042 050 058 059 060 064
3.2 9 002 013 016 023 026 038 039 040 044
3.3 13 004 011 012 018 022 026 030 031 043 046 048 051 053
3.4 15 003 004 010 013 023 029 030 033 039 049 055 061 071 077 083
3.5 13 004 008 010 011 013 014 016 022 026 027 033 039 045
3.6 14 002 010 011 015 020 030 043 045 052 054 055 056 058 059
3.7 11 002 006 008 009 012 019 022 023 026 028 030
3.8 6 002 005 007 010 011 015
3.9 7 003 005 007 010 016 021 023
Chapter 4: Using the Derivative
4.1 13 005 007 012 013 019 020 021 037 041 046 048 051 052
4.2 11 002 008 010 012 014 015 025 026 027 028 035
4.3 10 003 004 012 014 018 019 036 038 041 042
4.4 16 (1) 001 002 004 010 011 012 013 032 033 034 035 036 038 042 046 047 048
4.5 4 004 005 016 017
4.6 8 (1) 004 006 012 013 017 021 032 033 045
4.7 8 002 010 011 012 025 026 040 041
4.8 9 005 006 014 016 023 039 040 044 045
Chapter 5: Key Concept: The Definite Integral
5.1 7 002 003 008 015 016 025 026
5.2 13 002 003 004 007 009 015 016 017 024 026 029 030 031
5.3 12 002 003 006 007 008 010 020 021 032 037 038 039
5.4 10 002 008 009 022 023 024 025 039 045 046
Chapter 6: Constructing Antiderivatives
6.1 11 001 002 005 006 012 013 014 016 017 022 023
6.2 21 001 003 014 015 016 027 028 039 041 043 046 048 053 055 056 057 064 067 071 072 074
6.3 6 002 003 004 006 007 012
6.4 9 004 011 014 017 027 028 045 046 047
6.5 3 001 003 004
Chapter 7: Integration
7.1 28 002 007 012 018 020 021 022 023 024 025 026 034 039 042 047 052 054 056 057 058 064 065 075 089 090 102 109 110
7.2 14 003 009 010 013 014 018 019 020 039 046 047 049 060 061
7.3 10 (1) 002 009 011 012 013 030 031 034 036 037 039
7.4 3 (1) 012 014 046 048
7.5 8 001 002 003 004 007 009 014 015
7.6 3 001 005 006
7.7 16 001 003 004 005 006 012 013 021 025 028 029 040 041 042 043 050
7.8 6 001 006 008 020 024 025
Chapter 8: Using the Definite Integral
8.1 9 002 003 007 012 013 014 018 019 028
8.2 14 001 005 006 014 015 019 030 031 032 033 038 042 046 047
8.3 9 004 008 012 016 017 018 024 030 036
8.4 6 012 013 019 021 024 028
8.5 12 002 003 005 006 015 016 017 018 019 025 026 027
8.6 6 001 004 006 007 010 013
8.7 6 008 009 010 011 013 018
8.8 4 004 005 006 010
Chapter 9: Sequences and Series
R 1 070
9.1 8 002 005 008 018 019 024 025 051
9.2 12 001 002 003 004 005 006 009 014 017 025 026 027
9.3 10 004 005 006 007 024 026 027 028 033 037
9.4 13 001 002 008 009 010 012 019 028 029 030 035 056 064
9.5 12 001 002 003 004 005 008 009 017 018 022 038 041
Chapter 10: Approximating Functions Using Series
R 1 037
10.1 9 (1) 001 002 005 006 013 014 021 022 024 029
10.2 10 005 006 010 014 018 024 025 030 034 037
10.3 8 001 004 005 012 014 019 024 027
10.4 4 (1) 005 008 010 014 016
10.5 5 (2) 002 004 005 008 013 015 018
Chapter 11: Differential Equations
R 6 005 018 023 037 039 041
11.1 4 002 008 015 021
11.2 4 005 007 008 013
11.3 2 001 006
11.4 10 002 004 010 018 021 026 028 036 039 045
11.5 10 001 002 003 004 005 012 015 016 018 024
11.6 8 002 003 004 013 015 018 023 026
11.7 5 013 015 023 024 027
11.8 7 003 005 008 009 013 018 020
11.9 3 001 010 012
11.10 6 006 009 011 013 018 022
11.11 10 006 010 011 019 023 026 030 031 032 034
Chapter 12: Functions of Several Variables
R 1 017
12.1 11 001 004 005 010 011 014 019 023 024 029 030
12.2 7 002 003 006 010 011 017 023
12.3 9 006 010 016 017 021 022 024 026 027
12.4 4 004 009 013 022
12.5 4 001 008 010 028
12.6 6 004 005 010 017 018 021
Chapter 13: A Fundamental Tool: Vectors
R 9 004 011 015 021 035 037 038 040 042
13.1 10 004 009 010 017 019 024 026 030 031 042
13.2 11 001 002 003 004 005 006 007 013 014 020 024
13.3 17 002 003 004 007 009 010 029 030 031 033 039 040 041 045 046 050 051
13.4 5 002 004 011 020 028
Chapter 14: Differentiating Functions of Several Variables
14.1 6 002 009 011 012 013 022
14.2 9 002 004 007 011 020 021 028 029 033
14.3 7 003 004 014 015 018 028 030
14.4 15 008 012 016 019 026 028 030 032 051 062 063 065 068 074 078
14.5 12 009 011 013 022 023 024 030 041 042 051 053 054
14.6 9 001 010 011 012 018 019 023 024 025
14.7 7 001 006 024 028 041 042 044
14.8 7 002 005 007 008 016 019 020
Chapter 15: Optimization: Local and Global Extrema
15.1 8 006 007 013 014 017 019 021 026
15.2 8 004 010 012 016 017 018 020 026
15.3 6 005 010 018 021 024 027
Chapter 16: Integrating Functions of Several Variables
R 1 052
16.1 7 004 005 010 011 015 016 022
16.2 12 005 006 017 019 023 027 028 029 038 043 049 052
16.3 9 003 004 025 035 045 046 049 050 056
16.4 8 003 004 014 016 017 024 027 028
16.5 10 008 014 015 018 031 033 034 052 056 063
16.6 5 005 010 013 015 020
16.7 6 004 005 007 010 023 025
Chapter 17: Parameterization and Vector Fields
17.1 11 (1) 009 014 019 026 027 028 038 040 040 047 058 065
17.2 9 001 005 010 020 021 024 032 035 044
17.3 5 006 008 011 016 037
17.4 3 005 006 018
17.5 10 002 003 004 011 012 017 020 028 029 036
Chapter 18: Line Integrals
18.1 7 002 007 008 014 032 033 034
18.2 6 009 011 016 018 019 033
18.3 9 004 010 011 022 029 030 033 036 038
18.4 6 002 003 010 016 020 021
Chapter 19: Flux Integrals
19.1 9 003 011 015 019 023 028 036 048 049
19.2 6 008 014 016 019 020 029
19.3 4 003 005 006 010
Chapter 20: Calculus of Vector Fields
20.1 6 003 004 009 010 016 017
20.2 6 (1) 002 005 006 015 016 033 040
20.3 6 003 006 012 013 021 023
20.4 7 004 005 007 016 018 021 024
20.5 5 001 002 008 009 011
Total 1170 (10)  
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