MATH& 254 Calculus IV • 5 Cr.
Extends the concepts of calculus to vector-valued functions and functions of several variables. Partial derivatives are included. Fulfills the quantitative or symbolic reasoning course requirement at BC. Prerequisite: Placement by assessment or MATH& 152 or higher, with a C or better. Preferred: MATH& 153.
After completing this class, students should be able to:
- Visualize, plot and interpret points, lines, vectors, curves, and surfaces in 3D.
- Translate among rectangular, cylindrical and spherical coordinate systems and state some advantages and disadvantages of each system.
- Perform basic vector operations and apply these operations.
- Interpret the fundamental ideas of rates of change and accumulation for curves in higher dimensions: tangent vectors, arc length, curvature.
- Interpret the fundamental ideas of rates of change and accumulation for surfaces in higher dimensions: directional derivatives, tangent planes, max/min applications, volumes, and surface areas