Vector Calculus 6th edition

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Jerrold E. Marsden and Anthony Tromba
Publisher: W. H. Freeman

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  • Chapter 1: The Geometry of Euclidean Space
    • 1.1: Vectors in Two- and Three-Dimensional Space (16)
    • 1.2: The Inner Product, Length, and Distance (16)
    • 1.3: Matrices, Determinants, and the Cross Product (19)
    • 1.4: Cylindrical and Spherical Coordinates (6)
    • 1.5: n-Dimensional Euclidean Space (4)
    • 1: Review Exercises (1)

  • Chapter 2: Differentiation
    • 2.1: The Geometry of Real-Valued Functions (13)
    • 2.2: Limits and Continuity (8)
    • 2.3: Differentiation (15)
    • 2.4: Introduction to Paths and Curves (12)
    • 2.5: Properties of the Derivative (10)
    • 2.6: Gradients and Directional Derivatives (12)
    • 2: Review Exercises

  • Chapter 3: Higher-Order Derivatives: Maxima and Minima
    • 3.1: Iterated Partial Derivatives (12)
    • 3.2: Taylor's Theorem (5)
    • 3.3: Extrema of Real-Valued Functions (15)
    • 3.4: Constrained Extrema and Lagrange Multipliers (13)
    • 3.5: The Implicit Function Theorem (Optional)
    • 3: Review Exercises (3)

  • Chapter 4: Vector-Valued Functions
    • 4.1: Acceleration and Newton's Second Law (11)
    • 4.2: Arc Length (6)
    • 4.3: Vector Fields (4)
    • 4.4: Divergence and Curl (7)
    • 4: Review Exercises

  • Chapter 5: Double and Triple Integrals
    • 5.1: Introduction (6)
    • 5.2: The Double Integral Over a Rectangle (12)
    • 5.3: The Double Integral Over More General Regions (12)
    • 5.4: Changing the Order of Integration (6)
    • 5.5: The Triple Integral (11)
    • 5: Review Exercises

  • Chapter 6: The Change of Variables Formula and Applications of Integration
    • 6.1: The Geometry of Maps from ℝ2 to ℝ2 (2)
    • 6.2: The Change of Variables Theorem (8)
    • 6.3: Applications (3)
    • 6.4: Improper Integrals (Optional)
    • 6: Review Exercises (2)

  • Chapter 7: Integrals Over Paths and Surfaces
    • 7.1: The Path Integral (6)
    • 7.2: Line Integrals (5)
    • 7.3: Parametrized Surfaces (4)
    • 7.4: Area of a Surface (6)
    • 7.5: Integrals of Scalar Functions Over Surfaces (5)
    • 7.6: Surface Integrals of Vector Fields (6)
    • 7.7: Applications to Differential Geometry, Physics, and Forms of Life
    • 7: Review Exercises

  • Chapter 8: The Integral Theorems of Vector Analysis
    • 8.1: Green's Theorem (6)
    • 8.2: Stokes' Theorem (5)
    • 8.3: Conservative Fields (4)
    • 8.4: Gauss' Theorem (6)
    • 8.5: Differential Forms
    • 8: Review Exercises


Vector Calculus, 6th edition, by Jerrold E. Marsden and Anthony Tromba helps students gain an intuitive and solid understanding of calculus. The book's careful account is a contemporary balance between theory, application, and historical development, providing its readers with an insight into how mathematics progresses and is in turn influenced by the natural world. The WebAssign component for this title offers students immediate feedback on randomized questions straight from the textbook as well as access to an eBook.

Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

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Group Quantity Questions
Chapter 1: The Geometry of Euclidean Space
1.R 1 030
1.1 16 001 003 004 005 007 009 011 013 016 017 021 022 024 025 027 028
1.2 16 001 003 004 007 008 009 012 013 015 016 019 020 023 026 029 037
1.3 19 002 003 004 005 006 008 011 012 013 015 016c 021 022 027 029 031 032 034 035
1.4 6 003 004 005 008 010 014
1.5 4 001 009 010 011
Chapter 2: Differentiation
2.1 13 002 003 005 007 012 013 020 025 027 028 030 031 033
2.2 8 001 003 006 009 012 014 015 025ab
2.3 15 001 003 005 007 008 010 011 012 013 016a 016b 016c 019 021 026
2.4 12 001 003 004 005 007 009 011 013 017 019 023 024
2.5 10 003 009 010 013 016 019c 033 034 035 036
2.6 12 001 003 004 005 007 008 009 011 013 017 022 030
Chapter 3: Higher-Order Derivatives: Maxima and Minima
3.R 3 022a 022b 022c
3.1 12 001 003 006 007a 007b 009 011 014a 014b 019 021a 025
3.2 5 001 004 007 009 010
3.3 15 001 002 003 004 007 009 012 017 019 028 031 039 042 043 044
3.4 13 001 003 005 007 012 013 015 016 017 018 019 020 021
Chapter 4: Vector-Valued Functions
4.1 11 001 003 005 006 007 008 011 013 015 017 023
4.2 6 001 003 005 006 010 013
4.3 4 009 010 016 017
4.4 7 001 002 009 013 017 018 023
Chapter 5: Double and Triple Integrals
5.1 6 001 003 006 009 013 015
5.2 12 001b 001c 002a 002b 002c 002d 003 005 006 007 008 011
5.3 12 001 003 004a 004b 004c 004d 004e 004f 009 010 013 017
5.4 6 001 003 004c 005 007 009
5.5 11 001 003 005 011 013 016 018 019 022 023 024
Chapter 6: The Change of Variables Formula and Applications of Integration
6.R 2 005 006
6.1 2 001 002
6.2 8 003 011 013 015 025 030a 030b 034
6.3 3 002 004 012
Chapter 7: Integrals Over Paths and Surfaces
7.1 6 001 005 006 011 023 024
7.2 5 003 004 005 017 018
7.3 4 001 007 008 010
7.4 6 001 006 007 015 017 025
7.5 5 001 004 007 011 019
7.6 6 001 004 007 011 013 014
Chapter 8: The Integral Theorems of Vector Analysis
8.1 6 001 004 007 011 013 015
8.2 5 001 005 007 015 031
8.3 4 001 007 013 018
8.4 6 001 005 006 009 011 012
Total 323