Applied Engineering Analysis

Chapter 3Vectors and Vector Calculus

Chapter Learning Objectives

• Recap the distinction between scalar and vector quantities in engineering analysis.
• Learn vector calculus and its applications in engineering analysis.
• Learn to manipulate expressions of vectors and vector functions.
• Refresh vector algebra.
• Learn the dot and cross products of vectors and their physical meanings.
• Learn about derivatives, gradient, divergence, and curl in vector calculus.
• Learn to apply vector calculus in engineering analysis.
• Learn to apply vector calculus in rigid body dynamics in rectilinear and plane curvilinear motion along paths and in both rectangular and cylindrical polar coordinate systems.

3.1 Vector and Scalar Quantities

In Section 2.2.3, we introduced functions that represent physical quantities in engineering analyses, and whose values vary with the values of the associated independent variables in space (x, y, z) in a rectangular coordinate system) and time (t). These quantities are called as scalar quantities.

There is another group of physical quantities for which not only the magnitude but also the position and the direction are significant and must be represented.. These are called vector quantities. Thus, a speed of 80 km/h of a moving car is a scalar quantity, but a velocity of 80 km/h implies that the car is traveling in specific direction on the road at this speed, so that it is a vector quantity. Engineering analyses involving vectorial quantities will require the ...