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University Calculus 1st edition

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Joel Hass, Maurice Weir and George Thomas
Publisher: Addison Wesley

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Table of Contents

  • Chapter 1: Functions
    • 1.1: Functions and Their Graphs (8)
    • 1.2: Combining Functions; Shifting and Scaling Graphs (11)
    • 1.3: Trigonometric Functions (10)
    • 1.4: Exponential Functions
    • 1.5: Inverse Functions and Logarithms
    • 1.6: Graphing with Calculators and Computers

  • Chapter 2: Limits and Continuity
    • 2.1: Rates of Change and Tangents to Curves
    • 2.2: Limit of a Function and Limit Laws (11)
    • 2.3: The Precise Definition of a Limit (7)
    • 2.4: One-Sided Limits and Limits at Infinity (13)
    • 2.5: Infinite Limits and Vertical Asymptotes (7)
    • 2.6: Continuity (10)
    • 2.7: Tangents and Derivatives at a Point (6)
    • 2: Questions to Guide Your Review
    • 2: Practice Exercises
    • 2: Additional and Advanced Exercises

  • Chapter 3: Differentiation
    • 3.1: The Derivative as a Function (7)
    • 3.2: Differentiation Rules for Polynomials, Exponentials, Products and Quotients (8)
    • 3.3: The Derivative as a Rate of Change (5)
    • 3.4: Derivatives of Trigonometric Functions (7)
    • 3.5: The Chain Rule and Parametric Equations (10)
    • 3.6: Implicit Differentiation (2)
    • 3.7: Derivatives of Inverse Functions and Logarithms
    • 3.8: Inverse Trigonometric Functions
    • 3.9: Related Rates (4)
    • 3.10: Linearization and Differentials (5)
    • 3.11: Hyperbolic Functions (5)
    • 3: Questions to Guide Your Review
    • 3: Practice Exercises
    • 3: Additional and Advanced Exercises

  • Chapter 4: Applications of Derivatives
    • 4.1: Extreme Values of Functions (8)
    • 4.2: The Mean Value Theorem (5)
    • 4.3: Monotonic Functions and the First Derivative Test (9)
    • 4.4: Concavity and Curve Sketching (7)
    • 4.5: Applied Optimization (8)
    • 4.6: Indeterminate Forms and L'Hopital's Rule (1)
    • 4.7: Newton's Method (3)
    • 4.8: Antiderivatives (9)
    • 4: Questions to Guide Your Review
    • 4: Practice Exercises
    • 4: Additional and Advanced Exercises

  • Chapter 5: Integration
    • 5.1: Estimating with Finite Sums (7)
    • 5.2: Sigma Notation and Limits of Finite Sums (8)
    • 5.3: The Definite Integral (11)
    • 5.4: The Fundamental Theorem of Calculus (8)
    • 5.5: Indefinite Integrals and the Substitution Rule (9)
    • 5.6: Substitution and Area Between Curves (10)
    • 5.7: The Logarithm Defined as an Integral
    • 5: Questions to Guide Your Review
    • 5: Practice Exercises
    • 5: Additional and Advanced Exercises

  • Chapter 6: Applications of Definite Integrals
    • 6.1: Volumes by Slicing and Rotation About an Axis (5)
    • 6.2: Volumes by Cylindrical Shells (8)
    • 6.3: Lengths of Plane Curves (6)
    • 6.4: Areas of Surfaces of Revolution (9)
    • 6.5: Exponential Change and Separable Differential Equations
    • 6.6: Work (9)
    • 6.7: Moments and Centers of Mass (5)
    • 6: Questions to Guide Your Review
    • 6: Practice Exercises
    • 6: Additional and Advanced Exercises

  • Chapter 7: Techniques of Integration
    • 7.1: Integration by Parts (7)
    • 7.2: Trigonometric Integrals (6)
    • 7.3: Trigonometric Substitutions (6)
    • 7.4: Integration of Rational Functions by Partial Fractions (7)
    • 7.5: Integral Tables and Computer Algebra Systems (3)
    • 7.6: Numerical Integration
    • 7.7: Improper Integrals (7)
    • 7: Questions to Guide Your Review
    • 7: Practice Exercises
    • 7: Additional and Advanced Exercises

  • Chapter 8: Infinite Sequences and Series
    • 8.1: Sequences (10)
    • 8.2: Infinite Series (9)
    • 8.3: The Integral Test (5)
    • 8.4: Comparison Tests (4)
    • 8.5: The Ration and Root Tests (5)
    • 8.6: Alternating Series, Absolute and Conditional Convergence (5)
    • 8.7: Power Series (6)
    • 8.8: Taylor Maclaurin Series (6)
    • 8.9: Convergence of Taylor Series (5)
    • 8.10: The Binomial Series (3)
    • 8: Questions to Guide Your Review
    • 8: Practice Exercises
    • 8: Additional and Advanced Exercises

  • Chapter 9: Polar Coordinates and Conics
    • 9.1: Polar Coordinates (6)
    • 9.2: Graphing in Polar Coordinates
    • 9.3: Areas and Lengths in Polar Coordinates (6)
    • 9.4: Conic Sections (14)
    • 9.5: Conics in Polar Coordinates (4)
    • 9.6: Conics and Parametric Equations; The Cycloid (3)
    • 9: Questions to Guide Your Review
    • 9: Practice Exercises
    • 9: Additional and Advanced Exercises

  • Chapter 10: Vectors and the Geometry of Space
    • 10.1: Three-Dimensional Coordinate Systems (12)
    • 10.2: Vectors (9)
    • 10.3: The Dot Product (6)
    • 10.4: The Cross Product (10)
    • 10.5: Lines and Planes in Space (10)
    • 10.6: Cylinders and Quadric Surfaces (12)
    • 10: Questions to Guide Your Review
    • 10: Practice Exercises
    • 10: Additional and Advanced Exercises

  • Chapter 11: Vector-Valued Functions and Motion in Space
    • 11.1: Vector Functions and Their Derivatives (5)
    • 11.2: Integrals of Vector Functions (3)
    • 11.3: Arc Length in Space (6)
    • 11.4: Curvature of a Curve (4)
    • 11.5: Tangential and Normal Components of Acceleration (4)
    • 11.6: Velocity and Acceleration in Polar Coordinates
    • 11: Questions to Guide Your Review
    • 11: Practice Exercises
    • 11: Additional and Advanced Exercises

  • Chapter 12: Partial Derivatives
    • 12.1: Functions of Several Variables (7)
    • 12.2: Limits and Continuity in Higher Dimensions (11)
    • 12.3: Partial Derivatives (11)
    • 12.4: The Chain Rule (8)
    • 12.5: Directional Derivatives and Gradient Vectors (6)
    • 12.6: Tangent Planes and Differentials (8)
    • 12.7: Extreme Values and Saddle Points (8)
    • 12.8: Lagrange Multipliers (6)
    • 12.9: Taylor's Formula for Two Variables (3)
    • 12: Questions to Guide Your Review
    • 12: Practice Exercises
    • 12: Additional and Advanced Exercises

  • Chapter 13: Multiple Integrals
    • 13.1: Double and Iterated Integrals over Rectangles (2)
    • 13.2: Double Integrals over General Regions (7)
    • 13.3: Area by Double Integration (2)
    • 13.4: Double Integrals in Polar Form (6)
    • 13.5: Triple Integrals in Rectangular Coordinates (8)
    • 13.6: Moments and Centers of Mass (4)
    • 13.7: Triple Integrals in Cylilndrical and Spherical Coordinates (12)
    • 13.8: Substitutions in Multiple Integrals (3)
    • 13: Questions to Guide Your Review
    • 13: Practice Exercises
    • 13: Additional and Advanced Exercises

  • Chapter 14: Integration in Vector Fields
    • 14.1: Line Integrals (2)
    • 14.2: Vector Fields, Work, Circulation, and Flux (3)
    • 14.3: Path Independence, Potential Functions, and Conservative Fields (2)
    • 14.4: Green's Theorem in the Plane (3)
    • 14.5: Surfaces and Area
    • 14.6: Surface Integrals and Flux
    • 14.7: Stokes' Theorem
    • 14.8: The Divergence Theorem and a Unified Theory
    • 14: Questions to Guide Your Review
    • 14: Practice Exercises
    • 14: Additional and Advanced Exercises

  • Chapter 15: First-Order Difrerential Equations (online)
    • 15.1: Solutions, Slope Fields, and Picard's Theorem
    • 15.2: First-Order Linear Equations
    • 15.3: Applications
    • 15.4: Euler's Method
    • 15.5: Graphical Solutions of Autonomous Equations
    • 15.6: Systems of Equations and Phase Planes
    • 15: Questions to Guide Your Review
    • 15: Practice Exercises
    • 15: Additional and Advanced Exercises

  • Chapter 16: Second-Order Differential Equations (online)
    • 16.1: Second-Order Linear Equations
    • 16.2: Nonhomogeneous Linear Equations
    • 16.3: Applications
    • 16.4: Euler Equations
    • 16.5: Power Series Solutions
    • 16: Questions to Guide Your Review
    • 16: Practice Exercises
    • 16: Additional and Advanced Exercises

  • Chapter A: Appendices
    • A.1: Real Numbers and the Real Line
    • A.2: Mathematical Induction
    • A.3: Lines, Circles, and Parabolas (1)
    • A.4: Trigonometry Formulas
    • A.5: Proofs of Limit Theorems
    • A.6: Commonly Occurring Limits
    • A.7: Theory of the Real Numbers
    • A.8: The Distributive Law for Vector Cross Products
    • A.9: The Mixed Derivative Theorem and the Increment Theorem

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Group Quantity Questions
Chapter A: Appendices
A.3 1 042
Chapter 1: Functions
1.1 8 002 004 010 012 016 024 056 061
1.2 11 002 004 006 012 014 018 020 022 028 056 060
1.3 10 002 004 008 010 014 020 040 044 066 068
Chapter 2: Limits and Continuity
2.2 11 004 006 010 010.alt 012 016 024 030 034 062 068
2.3 7 016 020 024 030 032 052 056
2.4 13 002 002.alt 004 004.alt 014 016 022 026 034 038 052 070 074
2.5 7 002 004 008 010 018 022 044
2.6 10 006 008 014 018 022 030 032 052 058 058.alt
2.7 6 012 016 028 030 034 034.alt
Chapter 3: Differentiation
3.1 7 002 004 006 008 012 016 024
3.2 8 002 004 010 014 022 038 040 059
3.3 5 008 010 024 026 028
3.4 7 006 012 020 024 044 054 056
3.5 10 006 008 032 034 050 062 064 068 078 112
3.6 2 010 020
3.9 4 002 008 016 020
3.10 5 020 026 046 056 064
3.11 5 002 004 014 026 036
Chapter 4: Applications of Derivatives
4.1 8 002 002.alt 006 006.alt 018 026 042 056
4.2 5 002 024 024.alt 028 058
4.3 9 002 004 008 014 018 036 038 056 056.alt
4.4 7 002 004 072 074 076 082 082.alt
4.5 8 004 008 010 012 018 022 032 044
4.6 1 060
4.7 3 004 012 014
4.8 9 002 004 014 026 030 070 090 118 120
Chapter 5: Integration
5.1 7 002 012 014 015 016 019 020
5.2 8 002 004 008 012 014 018 020 022
5.3 11 002 004 008 012 014 016 018 030 034 052 064
5.4 8 002 006 008 014 020 042 052 070
5.5 9 002 004 005 006 008 020 037 060 064
5.6 10 002 004 006 018 020 022 048 066 086 092
Chapter 6: Applications of Definite Integrals
6.1 5 004 006 011 014 016
6.2 8 008 010 012 016 018 022 028 030
6.3 6 002 004 006 012 028 030
6.4 9 010 012 014 016 018 022 026 034 040
6.6 9 002 003 004 005 006 008 010 018 022
6.7 5 004 008 016 028 030
Chapter 7: Techniques of Integration
7.1 7 004 006 010 012 022 030 034
7.2 6 006 008 014 018 026 032
7.3 6 004 008 016 034 040 042
7.4 7 002 008 012 016 024 030 034
7.5 3 028 032 036
7.7 7 008 022 024 044 048 054 060
Chapter 8: Infinite Sequences and Series
8.1 10 006 014 018 024 032 042 052 076 098 102
8.2 9 006 008 016 020 030 036 052 056 070
8.3 5 002 008 010 014 024
8.4 4 006 010 020 026
8.5 5 006 010 024 030 042
8.6 5 006 008 018 022 051
8.7 6 006 014 024 034 040 042
8.8 6 002 006 010 020 022 024
8.9 5 004 006 012 020 036
8.10 3 002 008 012
Chapter 9: Polar Coordinates and Conics
9.1 6 024 026 032 044 050 052
9.3 6 002 006 010 012 018 020
9.4 14 001 002 003 004 005 006 007 008 040 042 046 052 056 060
9.5 4 030 048 050 060
9.6 3 014 016 018
Chapter 10: Vectors and the Geometry of Space
10.1 12 008 010 016 020 022 036 038 040 042 044 048 050
10.2 9 004 008 012 018 024 026 036 038 046
10.3 6 002 004 008 010 012 014
10.4 10 004 007 008 016 018 024 028 036 038 040
10.5 10 004 006 022 024 028 034 038 048 056 068
10.6 12 001 002 003 004 005 006 007 008 009 010 011 012
Chapter 11: Vector-Valued Functions and Motion in Space
11.1 5 002 006 012 016 018
11.2 3 016 018 020
11.3 6 004 006 010 012 014 016
11.4 4 002 010 019 022
11.5 4 004 012 014 016
Chapter 12: Partial Derivatives
12.1 7 002 004 006 008 010 012 030
12.2 11 004 006 008 016 018 022 028 032 044 052 054
12.3 11 002 004 006 008 016 024 026 030 044 054 058
12.4 8 004 008 009 026 030 036 040 048
12.5 6 004 006 010 014 018 022
12.6 8 004 012 016 020 028 028.alt 038 048
12.7 8 004 010 016 020 032 040 042 046
12.8 6 008 010 020 022 026 032
12.9 3 002 004 010
Chapter 13: Multiple Integrals
13.1 2 021 022
13.2 7 010 012 014 026 036 038 040
13.3 2 016 018
13.4 6 002 004 008 018 024 027
13.5 8 006 008 010 016 024 026 038 042
13.6 4 004 008 012 022
13.7 12 002 004 006 008 010 022 024 028 050 056 058 062
13.8 3 002 004 008
Chapter 14: Integration in Vector Fields
14.1 2 010 020
14.2 3 010 023 026
14.3 2 008 030
14.4 3 006 008 018
Chapter 15: First-Order Difrerential Equations (online)
15 0  
Chapter 16: Second-Order Differential Equations (online)
16 0  
Total 612  
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