Mathematics II – Calculus II
Covers Riemann integration, parametric/polar curves, 3D coordinate geometry, multivariable calculus, and optimization methods. Concludes with an in-depth treatment of infinite series.
The course starts with a discussion of integration, integration techniques, and applications of integrals. The topics of discussion include the Riemann Integral and a review of basic integration techniques, such as substitution, integration by parts, partial fraction decomposition, and trigonometric techniques of integration. The course covers applications of definite integrals to simple problems involving area between curves, arc length, volume, projectile motion, work, and center of mass. The course continues with a discussion of parametric curves and polar coordinates. The concepts of calculus are extended to curves related to parametric equations and polar equations. In the course, the geometry of three-space is covered much more extensively than in Mathematics I. Cylindrical and spherical coordinates are introduced. Emphasis is placed on visualization and graphical representation of surfaces in space. This course covers most of the calculus of functions of several variables, including concepts of limits and continuity, partial derivatives, tangent planes, linear approximation, differentials, directional derivatives, and gradients. Substantial focus is on applications of these concepts. The mathematical basis for finding the maximum or minimum of functions of several variables is introduced, and these concepts are applied to optimization problems for functions of several variables. The discussion includes constrained optimization and the method of Lagrange multipliers. The course concludes with a unified discussion of real infinite series. The class meets four hours per week in the second semester.