Worldwide Multivariable Calculus 1st edition

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David B. Massey
Publisher: Worldwide Center of Mathematics

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  • Chapter 1: Multivariable Spaces and Functions
    • 1.1: Euclidean Space (60)
    • 1.2: ℜn as a Vector Space (153)
    • 1.3: Dot Product, Angles, & Projection (104)
    • 1.4: Lines, Planes, and Hyperplanes (158)
    • 1.5: The Cross Product (100)
    • 1.6: Functions of a Single Variable (177)
    • 1.7: Multivariable Functions (56)
    • 1.8: Graphing Surfaces (115)

  • Chapter 2: Multivariable Derivatives
    • 2.1: Partial Derivatives (38)
    • 2.2: The Total Derivative (17)
    • 2.3: Linear Approximation, Tangent Planes, and the Differential (29)
    • 2.4: Differentiation Rules (32)
    • 2.5: The Directional Derivative (16)
    • 2.6: Change of Coordinates (19)
    • 2.7: Level Sets & Gradient Vectors (57)
    • 2.8: Parameterizing Surfaces (52)
    • 2.9: Local Extrema (48)
    • 2.10: Optimization (10)
    • 2.11: Lagrange Multipliers (17)
    • 2.12: Implicit Differentiation
    • 2.13: Multivariable Taylor Polynomials & Series

  • Chapter 3: Multivariable Integrals
    • 3.1: Iterated Integrals (1)
    • 3.2: Integration in ℜ2 (56)
    • 3.3: Polar Coordinates (33)
    • 3.4: Integration in ℜ3 and ℜn (44)
    • 3.5: Volume (28)
    • 3.6: Cylindrical and Spherical Coordinates (41)
    • 3.7: Average Value (7)
    • 3.8: Density and Mass
    • 3.9: Centers of Mass (7)
    • 3.10: Moments of Inertia (6)
    • 3.11: Surfaces and Area (15)

  • Chapter 4: Integration and Vector Fields
    • 4.1: Vector Fields (30)
    • 4.2: Line Integrals (16)
    • 4.3: Conservative Vector Fields (54)
    • 4.4: Green's Theorem (17)
    • 4.5: Flux Through a Surface (25)
    • 4.6: The Divergence Theorem (8)
    • 4.7: Stokes' Theorem (14)

Appropriate for a Calculus III or Multivariable Calculus class, this book reexamines both differential and integral calculus from the perspective of functions with more than one variable. Sections are divided into Basics, More Depth, and +Linear Algebra where appropriate to give more depth than what might typically be covered in class. The third book in the Worldwide Calculus series, this book takes a unique approach in its combination of down-to-earth, conversational text mixed with completely rigorous definitions, statements of theorems, and proofs. Dr. David Massey, the author, is an award-winning and world-renowned research mathematician, who has been teaching college students for over 30 years. Available for low cost in PDF format, the digital version of the book contains a host of new features right in the text, including:

  • Full-length video lectures at the beginning of each section
  • Step-by-step video solutions to select problems at the end of each section
  • Applicable sections of the text linked to individual questions
  • Hyperlinked cross-references for easy navigation
  • Animated and interactive graphs

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Group Quantity Questions
Chapter 1: Multivariable Spaces and Functions
1.1 60 501a.XP 501b.XP 501c.XP 501d.XP 501e.XP 502a.XP 502b.XP 502c.XP 502d.XP 502e.XP 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP 505d.XP 505e.XP 506a.XP 506b.XP 506c.XP 506d.XP 507a.XP 507b.XP 507c.XP 507d.XP 507e.XP 507f.XP 508a.XP 508b.XP 508c.XP 508d.XP 508e.XP 509a.XP 509b.XP 509c.XP 510a.XP 510b.XP 510c.XP 510d.XP 510e.XP 511a.XP 511b.XP 511c.XP 511d.XP 511e.XP 512a.XP 512b.XP 512c.XP 512d.XP 512e.XP 513a.XP 513b.XP 513c.XP 514a.XP 514b.XP 514c.XP
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1.3 104 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 504d.XP 505a.XP 505b.XP 505c.XP 505d.XP 506a.XP 506b.XP 506c.XP 506d.XP 507a.XP 507b.XP 507c.XP 508a.XP 508b.XP 508c.XP 508d.XP 509a.XP 509b.XP 509c.XP 509d.XP 510a.XP 510b.XP 510c.XP 511a.XP 511b.XP 511c.XP 511d.XP 512a.XP 512b.XP 512c.XP 512d.XP 512e.XP 512f.XP.Tut 512g.XP.Tut 513a.XP 513b.XP 513c.XP 514a.XP 514b.XP 514c.XP 515a.XP 515b.XP 515c.XP 516a.XP 516b.XP 516c.XP 516d.XP 517a.XP 517b.XP 517c.XP 518a.XP 518b.XP 518c.XP 519a.XP 519b.XP 519c.XP 520a.XP 520b.XP 520c.XP 520d.XP 521a.XP 521b.XP 521c.XP 521d.XP 522a.XP 522b.XP 522c.XP 522d.XP 523a.XP 523b.XP 523c.XP 523d.XP 524a.XP 524b.XP 524c.XP 525a.XP 525b.XP 525c.XP 526a.XP 526b.XP 526c.XP 527a.XP 527b.XP 527c.XP 527d.XP 528a.XP 528b.XP 528c.XP 529a.XP 529b.XP 529c.XP 529d.XP
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1.5 100 501I.XP 501a.XP 501b.XP 501c.XP 501d.XP 501e.XP 501f.XP 501g.XP 501h.XP 501j.XP 501k.XP 502a.XP 502b.XP 502c.XP 502d.XP 502e.XP 503a.XP 503b.XP 503c.XP 503d.XP 503e.XP 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP 505d.XP 506a.XP 506b.XP 506c.XP 507a.XP 507b.XP 507c.XP 507d.XP 508a.XP 508b.XP 508c.XP 509a.XP 509b.XP 509c.XP 510a.XP 510b.XP 510c.XP 510d.XP 510e.XP.Tut 511a.XP 511b.XP 511c.XP 512a.XP 512b.XP 512c.XP 512d.XP.Tut 513a.XP 513b.XP 513c.XP 513d.XP 514a.XP 514b.XP 514c.XP 515a.XP 515b.XP 515c.XP 516a.XP 516b.XP 516c.XP 517a.XP 517b.XP 517c.XP 518a.XP 518b.XP 518c.XP 519a.XP 519b.XP 519c.XP 520a.XP 520b.XP 520c.XP 521a.XP 521b.XP 521c.XP 522a.XP 522b.XP 522c.XP 523a.XP 523b.XP 523c.XP 524a.XP 524b.XP 524c.XP 524d.XP 525a.XP 525b.XP 525c.XP 526a.XP 526b.XP 526c.XP 527a.XP 527b.XP 527c.XP
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1.7 56 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 503d.XP 504a.XP 504b.XP 504c.XP 504d.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 506c.XP 506d.XP 506e.XP 506f.XP 507a.XP 507b.XP 507c.XP 507d.XP 507e.XP 507f.XP 508a.XP 508b.XP 508c.XP 508d.XP 508e.XP 508f.XP 509a.XP 509b.XP 509c.XP 509d.XP 509e.XP 509f.XP 509g.XP.Tut 510a.XP 510b.XP 510c.XP 511a.XP 511b.XP 511c.XP 511d.XP 512a.XP 512b.XP 512c.XP 513a.XP 513b.XP 513c.XP 513d.XP.Tut
1.8 115 501a.XP 501b.XP 501c.XP 501d.XP 501e.XP 502a.XP 502b.XP 502c.XP 502d.XP 502e.XP 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 504d.XP 504e.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 506c.XP 507a.XP 507b.XP 507c.XP 508a.XP 508b.XP 508c.XP 508d.XP 509a.XP 509b.XP 509c.XP 510a.XP 510b.XP 511a.XP 511b.XP 511c.XP 511d.XP.Tut 512a.XP 512b.XP 512c.XP 512d.XP 513a.XP 513b.XP 513c.XP 514a.XP 514b.XP 514c.XP 515a.XP 515b.XP 515c.XP 515d.XP 516a.XP 516b.XP 516c.XP 517a.XP 517b.XP 517c.XP 517d.XP 518a.XP 518b.XP 518c.XP 519a.XP 519b.XP 519c.XP 519d.XP 520a.XP 520b.XP 520c.XP 520d.XP 521a.XP 521b.XP 521c.XP 521d.XP 522a.XP 522b.XP 522c.XP 523a.XP 523b.XP 523c.XP 524a.XP 524b.XP 524c.XP 524d.XP 524e.XP 524f.XP 525a.XP 525b.XP 525c.XP 525d.XP 525e.XP 525f.XP 525g.XP 526a.XP 526b.XP 526c.XP 526d.XP 526e.XP 527a.XP 527b.XP 527c.XP 527d.XP 527e.XP 528a.XP 528b.XP 528c.XP 528d.XP 528e.XP 529a.XP 529b.XP 529c.XP 529d.XP 529e.XP
Chapter 2: Multivariable Derivatives
2.1 38 501a.XP 501b.XP 501c.XP 502b.XP 502c.XP 502d.XP 502f.XP 503a.XP 503c.XP 503d.XP 503e.XP 503g.XP.Tut 504a.XP 504b.XP 504c.XP 504d.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 506c.XP 507a.XP 507b.XP 507c.XP 507d.XP.Tut 508a.XP 508b.XP 508c.XP 509a.XP 509b.XP 509c.XP 510a.XP 510b.XP 510c.XP 511a.XP 511b.XP 511c.XP
2.2 17 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 506a.XP 506b.XP 506c.XP
2.3 29 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 503d.XP.Tut 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 506c.XP 507a.XP 507b.XP 507c.XP 508a.XP 508b.XP 508c.XP 509a.XP 509b.XP 509c.XP 509d.XP.Tut
2.4 32 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 502d.XP 502e.XP 502f.XP.Tut 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 504d.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 506c.XP 506d.XP 507a.XP 507b.XP 507c.XP 507d.XP 507e.XP 507f.XP.Tut 508a.XP 508b.XP 508c.XP
2.5 16 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP 505d.XP
2.6 19 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP 505d.XP.Tut 506a.XP 506b.XP 506c.XP
2.7 57 501a.XP 501b.XP 501c.XP 501d.XP 501e.XP.Tut 502a.XP 502b.XP 502c.XP 502d.XP 502e.XP 502f.XP 502g.XP 503a.XP 503b.XP 503c.XP 503d.XP 503e.XP 504a.XP 504b.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 506c.XP 506d.XP.Tut 507a.XP 507b.XP 507c.XP 508a.XP 508b.XP 508c.XP 508d.XP.Tut 509a.XP 509b.XP 509c.XP 510a.XP 510b.XP 510c.XP 511a.XP 511b.XP 511c.XP 512a.XP 512b.XP 512c.XP 512d.XP 513a.XP 513b.XP 513c.XP 514a.XP 514b.XP 514c.XP 514d.XP 515a.XP 515b.XP 515c.XP 515d.XP
2.8 52 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 506c.XP 507a.XP 507b.XP 507c.XP 508a.XP 508b.XP 508c.XP 509a.XP 509b.XP 509c.XP 510a.XP 510b.XP 510c.XP 511a.XP 511b.XP 511c.XP 512a.XP 512b.XP 512c.XP 513a.XP 513b.XP 513c.XP 514a.XP 514b.XP 514c.XP 515a.XP 515b.XP 515c.XP 516a.XP 516b.XP 516c.XP 517a.XP 517b.XP 517c.XP 518a.XP.Tut
2.9 48 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 502d.XP 502e.XP 502f.XP 502g.XP 503a.XP 503b.XP 503c.XP 503d.XP 504a.XP 504b.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 506c.XP 507a.XP 507b.XP 507c.XP 508a.XP 508b.XP 508c.XP 509a.XP 509b.XP 509c.XP 509d.XP.Tut 510a.XP 510b.XP 510c.XP 511a.XP 511b.XP 511c.XP 512a.XP 512b.XP 512c.XP 512d.XP 513a.XP 513b.XP 513c.XP 514a.XP 514b.XP 514c.XP
2.10 10 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 502d.XP.Tut 503a.XP 503b.XP 503c.XP
2.11 17 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 503d.XP.Tut 503e.XP.Tut 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP
Chapter 3: Multivariable Integrals
3.1 1 501a.XP.Tut
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3.7 7 501a.XP 501b.XP 501c.XP 501d.XP 502a.XP 502b.XP 502c.XP
3.9 7 501a.XP 501b.XP 501c.XP 501d.XP 502a.XP 502b.XP 502c.XP
3.10 6 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP
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Chapter 4: Integration and Vector Fields
4.1 30 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 506c.XP 507a.XP 507b.XP 507c.XP 508a.XP 508b.XP 508c.XP 509a.XP 509b.XP 509c.XP 510a.XP 510b.XP 510c.XP
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4.3 54 501a.XP 501b.XP 501c.XP 502a.XP.Tut 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP 506a.XP.Tut 507a.XP 507b.XP 507c.XP 508a.XP 508b.XP 508c.XP 509a.XP 509b.XP 509c.XP 510d.XP 510e.XP 510f.XP 511a.XP 511b.XP 511c.XP 512a.XP 512b.XP 512c.XP 513a.XP 513b.XP 513c.XP 514a.XP 514b.XP 514c.XP 515a.XP 515b.XP 515c.XP 516a.XP 516b.XP 516c.XP 517a.XP 517b.XP 517c.XP 517d.XP.Tut 518a.XP 518b.XP 518c.XP 519a.XP 519b.XP 519c.XP
4.4 17 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 502d.XP 503a.XP 503b.XP 503c.XP 503d.XP 504a.XP 504b.XP 504c.XP 504d.XP 504e.XP.Tut 505a.XP.Tut
4.5 25 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 504a.XP 504b.XP 504c.XP 505a.XP 505b.XP 505c.XP 506a.XP 506b.XP 507a.XP.Tut 508a.XP.Tut 509a.XP 509b.XP 509c.XP 510a.XP 510b.XP 510c.XP
4.6 8 501a.XP 501b.XP 501c.XP 502a.XP.Tut 503a.XP 503b.XP 503c.XP 504a.XP.Tut
4.7 14 501a.XP 501b.XP 501c.XP 502a.XP 502b.XP 502c.XP 503a.XP 503b.XP 503c.XP 504a.XP.Tut 505a.XP 505b.XP 505c.XP 506a.XP.Tut
Total 1660