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How Will Virtual Reality Change Vector Calculus?
One goal of this book is to address this question, via exploring many of the topics
of three-dimensional calculus using the power of virtual reality a la VRML. Until
recently, all of multivariable/vector calculus was taught algebraically. Now
many courses utilize computers via computer algebra systems and graphing
tools to visually investigate the geometry of curves and surfaces in 3-space.
Virtual Reality/VRML holds many possibilities for extending the visual investigation
experience. The incorporation of CAS's forced many changes in the curriculum
for 3D calculus over the last five years; we ask: how will VR change it in the next five years?
- Special Notes about Using the VRML Plugin Live3D
Part I: Calculus, VR, and Three Dimensions
- Chapter 1 - Intuition via VR in 3D
- §1.1 - Plotting Points and Vectors
- §1.2 - Geometric Relationships in 3D
- §1.3 - Geometric Measurements in 3D
- §1.4 - Basic Constructions: Lines and Planes
- §1.5 - Other Coordinate Systems
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- Chapter 2 - Surfaces in 3D Via VR
- §2.1 - Making
VR Surfaces using a Computer Algebra System
- §2.2 - Library of Surfaces in VR
- §2.3 - Extrema of Surfaces
- §2.4 - Slicing a Surface
- §2.5 - Level Curves of a Surface
- §2.6 - Intersections of Surfaces
- §2.7 - Orientation
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- Chapter 3 - Curves in 3D Via VR
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 §3.1 - Library of Parametric Curves
- §3.2 - Points Moving Along a Curve
- §3.3 - Tangents, Normals, and Binormals
- §3.4 - Twisting and Torsion
- §3.5 - Projections of Curves
- §3.6 - Curves as Intersections of Surfaces
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- Chapter 4 - Differentiation in 3D
- §4.1 - Partial Derivatives
- §4.2 - Tangent Planes
- §4.3 - Directional Derivatives
- §4.4 - Gradients and Derivative Fields
- §4.5 - Lagrange Multipliers Revisited
- §4.6 - Curvature of a Surface
- §4.7 - Second Derivatives
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- Chapter 5 - Vector Fields
- §5.1 - 2D and 3D Vector Fields
- §5.2 - Behaviors of Vector Fields
- §5.3 - Curl, Divergence, and Dual Vector Fields
- §5.4 - Differentiation of Vector Fields
- §5.5 - Integration Along Vector Fields
- §5.6 - Fundamental Theorem of Vector Calculus
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- Chapter 6 - Multiple Integration
- §6.1 - Volumes
- §6.2 - Visualizing Multiple Integrals
- §6.3 - Volume Elements
- §6.4 - Change of Variables
- §6.5 - Jacobians
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Part II: Applications via Calculus and VR
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- Chapter 8 - Applications to Physics
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- Chapter 8 - Applications to Engineering
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- Chapter 9 - More Applications to Physics
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- Chapter 10 - More Applications to Engineering
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Authors: Robert R. Curtis, San Joaquin
Delta College • Bill Davis, The
Ohio State University •
• Lee Wayand,
The Ohio State University •
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