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Essential Calculus: Early Transcendental Functions 1st edition

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Ron Larson, Robert P. Hostetler, Bruce H. Edwards
Publisher: Brooks/Cole

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Table of Contents

  • Chapter 1: Limits and Their Properties
    • 1.1: Linear Models and Rates of Change (5)
    • 1.2: Functions and Their Graphs (3)
    • 1.3: Inverse Functions (17)
    • 1.4: Exponential and Logarithmic Functions (2)
    • 1.5: Finding Limits Graphically and Numerically (5)
    • 1.6: Evaluating Limits Analytically (4)
    • 1.7: Continuity and One-Sided Limits (10)
    • 1.8: Infinite Limits (4)

  • Chapter 2: Differentiation
    • 2.1: The Derivative and the Tangent Line Problem (8)
    • 2.2: Basic Differentiation Rules and Rates of Change (7)
    • 2.3: Product and Quotient Rules and Higher-Order Derivatives (6)
    • 2.4: The Chain Rule (5)
    • 2.5: Implicit Differentiation (9)
    • 2.6: Derivatives of Inverse Functions (6)
    • 2.7: Related Rates (5)
    • 2.8: Newton's Method (2)

  • Chapter 3: Applications of Differentiation
    • 3.1: Extrema on an Interval (4)
    • 3.2: Rolle's Theorem and the Mean Value Theorem (5)
    • 3.3: Increasing and Decreasing Functions and the First Derivative Test (8)
    • 3.4: Concavity and the Second Derivative Test (3)
    • 3.5: Limits at Infinity (9)
    • 3.6: Optimization Problems (10)
    • 3.7: Differentials (1)

  • Chapter 4: Integration
    • 4.1: Antiderivatives and Indefinite Integration (6)
    • 4.2: Area (7)
    • 4.3: Riemann Sums and Definite Integrals (5)
    • 4.4: The Fundamental Theorem of Calculus (9)
    • 4.5: Integration by Substitution (9)
    • 4.6: Numerical Integration (2)
    • 4.7: The natural Logarithmic Function: Integration (9)
    • 4.8: Inverse Trigonometric Functions: Integration (6)
    • 4.9: Hyperbolic Functions (8)

  • Chapter 5: Applications of Integration
    • 5.1: Area of a Region Between Two Curves (10)
    • 5.2: Volume: The Disk Method (6)
    • 5.3: Volume: The Shell Method (6)
    • 5.4: Arc Length and Surfaces of Revolution (7)
    • 5.5: Applications in Physics and Engineering (9)
    • 5.6: Differential Equations: Growth and Decay (8)

  • Chapter 6: Integration Techniques, L'Hopital's Rule, and Improper Integrals
    • 6.1: Integration by Parts (7)
    • 6.2: Trigonometric Integrals (6)
    • 6.3: Trigonometric Substitution (10)
    • 6.4: Partial Fractions (2)
    • 6.5: Integration by Tables and Other Integration Techniques (2)
    • 6.6: Indeterminate Forms and L'Hopital's Rule (3)
    • 6.7: Improper Integrals (11)

  • Chapter 7: Infinite Series
    • 7.1: Sequences (9)
    • 7.2: Series and Convergence (12)
    • 7.3: The Integral and Comparison Tests (5)
    • 7.4: Other Convergence Tests (16)
    • 7.5: Taylor Polynomials and Approximations (7)
    • 7.6: Power Series (7)
    • 7.7: Representation of Functions by Power Series (7)
    • 7.8: Taylor and Maclaurin Series (7)

  • Chapter 8: Conics, Parametric Equations, and Polar Coordinates
    • 8.1: Plane Curves and Parametric Equations (3)
    • 8.2: Parametric Equations and Calculus (11)
    • 8.3: Polar Coordinates and Polar Graphs (4)
    • 8.4: Area and Arc Length in Polar Coordinates (6)
    • 8.5: Polar Equations and Conics and Kepler's Laws (4)

  • Chapter 9: Vectors and the Geometry of Space
    • 9.1: Vectors in the Plane (10)
    • 9.2: Space Coordinates and Vectors in Space (10)
    • 9.3: The Dot Product of Two Vectors (8)
    • 9.4: The Cross Product of Two Vectors in Space (7)
    • 9.5: Lines and Planes in Space (13)
    • 9.6: Surfaces in Space (3)
    • 9.7: Cylindrical and Spherical Coordinates (8)

  • Chapter 10: Vector-Valued Functions
    • 10.1: Vector-Valued Functions (4)
    • 10.2: differentiation and Integration of Vector-Valued Functions (9)
    • 10.3: Velocity and Acceleration (6)
    • 10.4: Tangent Vectors and Normal Vectors (5)
    • 10.5: Arc Length and Curvature (8)

  • Chapter 11: Functions of Several Variables
    • 11.1: Introduction to Functions of Several Variables (4)
    • 11.2: Limits and Continuity (6)
    • 11.3: Partial Derivatives (13)
    • 11.4: Differentials and the Chain Rule (14)
    • 11.5: Directional Derivatives and Gradients (6)
    • 11.6: Tangent Planes and Normal Lines (5)
    • 11.7: Extrema of Functions of Two Variables (10)
    • 11.8: Lagrange Multipliers (5)

  • Chapter 12: Multiple Integration
    • 12.1: Iterated Integrals and Area in the Plane (8)
    • 12.2: Double Integrals and Volume (7)
    • 12.3: Change of Variables: Polar Coordinates (8)
    • 12.4: Center of Mass and Moments of Inertia (4)
    • 12.5: Surface Area (3)
    • 12.6: Triple Integrals and Applications (6)
    • 12.7: Triple Integrals in Cylindrical and Spherical Coordinates (8)
    • 12.8: Change of Variables: Jacobians (5)

  • Chapter 13: Vector Analysis
    • 13.1: Vector Fields (5)
    • 13.2: Line Integrals (7)
    • 13.3: conservative Vector Fields and Independence of Path (5)
    • 13.4: Green's Theorem (3)
    • 13.5: Parametric Surfaces (6)
    • 13.6: Surface Integrals (5)
    • 13.7: Divergence Theorem (3)
    • 13.8: Stokes's Theorem (3)

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Group Quantity Questions
Chapter 1: Limits and Their Properties
1.1 5 002 008 022 038 048
1.2 3 012 016 022
1.3 17 010 012 016 018 030 038 043 044 058 067 068 074 082 084 094 106 112
1.4 2 012 048
1.5 5 010 018 020 028 032
1.6 4 018 032 056 058
1.7 10 008 010 012 026 028 036 040 042 052 086
1.8 4 020 026 037 046
Chapter 2: Differentiation
2.1 8 008 012 018 028 042 054 060 068
2.2 7 014 036 054 080 082 088 096
2.3 6 002 012 014 026 038 076
2.4 5 010 018 040 046 080
2.5 9 002 006 012 026 028 036 052 082 090
2.6 6 016 022 024 027 028 040
2.7 5 002 006 014 022 030
2.8 2 018 030
Chapter 3: Applications of Differentiation
3.1 4 002 006 010 032
3.2 5 004 008 012 032 048
3.3 8 004 012 026 036 050 072 084 088
3.4 3 012 016 056
3.5 9 010 014 018 024 028 042 090 092 096
3.6 10 004 010 012 016 018 020 022 036 044 050
3.7 1 022
Chapter 4: Integration
4.1 6 006 022 054 056 062 064
4.2 7 002 010 026 028 040 056 066
4.3 5 006 020 024 032 040
4.4 9 016 020 028 032 040 048 062 082 090
4.5 9 002 008 012 018 024 026 034 082 101
4.6 2 024 031
4.7 9 002 008 012 018 020 022 040 046 068
4.8 6 008 014 018 032 042 050
4.9 8 004 014 020 038 048 056 066 076
Chapter 5: Applications of Integration
5.1 10 010 014 024 036 052 056 058 068 072 074
5.2 6 008 014 016 026 027 042
5.3 6 002 010 014 022 028 042
5.4 7 004 010 022 028 032 058 060
5.5 9 002 003 010 016 022 034 044 058 064
5.6 8 002 008 014 018 034 036 038 042
Chapter 6: Integration Techniques, L'Hopital's Rule, and Improper Integrals
6.1 7 002 016 020 032 036 042 064
6.2 6 004 008 030 036 042 070
6.3 10 004 006 010 014 016 026 036 040 050 058
6.4 2 012 036
6.5 2 004 034
6.6 3 004 008 064
6.7 11 004 006 014 024 030 038 048 054 060 064 070
Chapter 7: Infinite Series
7.1 9 008 010 013 016 022 036 044 052 065
7.2 12 002 006 016 032 036 046 052 056 078 092 100 108
7.3 5 002 012 024 093 094
7.4 16 004 006 014 016 032 034 042 044 050 058 066 074 078 079 098 118
7.5 7 008 016 020 024 032 042 048
7.6 7 010 020 028 030 032 040 068
7.7 7 002 004 010 014 016 024 056
7.8 7 002 010 018 024 034 054 066
Chapter 8: Conics, Parametric Equations, and Polar Coordinates
8.1 3 032 034 056
8.2 11 002 006 016 024 036 042 052 060 066 080 082
8.3 4 020 028 048 054
8.4 6 006 012 018 028 034 053
8.5 4 008 018 026 054
Chapter 9: Vectors and the Geometry of Space
9.1 10 022 026 030 034 036 044 046 056 060 074
9.2 10 010 018 020 028 030 034 048 054 060 078
9.3 8 006 008 010 014 022 032 042 044
9.4 7 002 008 012 022 028 034 035
9.5 13 018 022 026 038 044 048 052 056 074 088 092 094 108
9.6 3 032 044 046
9.7 8 004 010 022 028 030 035 038 048
Chapter 10: Vector-Valued Functions
10.1 4 006 034 044 058
10.2 9 010 016 018 024 028 036 044 050 054
10.3 6 010 016 020 026 032 046
10.4 5 018 024 026 030 058
10.5 8 008 012 022 026 030 036 040 060
Chapter 11: Functions of Several Variables
11.1 4 006 016 046 079
11.2 6 007 012 026 040 046 058
11.3 13 008 018 028 030 034 038 046 050 052 060 066 094 098
11.4 14 004 014 018 030 034 036 040 044 048 054 060 078 090 094
11.5 6 010 016 022 028 044 048
11.6 5 010 012 016 024 036
11.7 10 032 034 047 048 054 064 066 068 072 077
11.8 5 008 010 012 024 029
Chapter 12: Multiple Integration
12.1 8 002 010 016 022 024 032 052 066
12.2 7 002 010 012 020 026 036 044
12.3 8 002 006 014 018 026 030 036 042
12.4 4 004 010 018 020
12.5 3 006 010 018
12.6 6 006 010 016 022 036 048
12.7 8 004 005 008 014 016 022 024 026
12.8 5 002 012 016 018 030
Chapter 13: Vector Analysis
13.1 5 012 020 030 036 040
13.2 7 006 010 012 014 020 028 054
13.3 5 004 008 010 014 028
13.4 3 008 014 016
13.5 6 002 020 028 032 038 050
13.6 5 002 012 014 020 034
13.7 3 006 016 018
13.8 3 004 014 020
Total 624  
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