Calculus II: Further Study of Motion and Change

Catalog description

Calculus is the mathematical gift that keeps on giving—thank you, Newton and company! In this course, students will expand their knowledge of limits, derivatives, and integrals with concepts and techniques that will enable them to solve many important problems in mathematics and the sciences. By the end of the course, students will be able to judge whether answers provided by engine services such as WolframAlpha or ChatGPT are correct. Topics will include differentiation review, integration review, integration with non-polynomial functions, applications of integration (finding area, volume, length, center of mass, moment of inertia, probability), advanced techniques for integration (substitution, integration-by-parts, partial fractions), infinite sequences, infinite series, convergent and divergent sums, power series, differential equations and modeling dynamical systems, and, time permitting, parametric equations of a curve and polar coordinates. Students will work on a conference project related to the mathematical topics covered in class and are free to choose technical, historical, crafty, computational, or creative projects. At least one semester of high school or college calculus recommended with extensive experience with limits and derivatives of elementary functions, including a basic understanding of integrals as Riemann sums. Multivariable Mathematics: Linear Algebra, Vector Calculus, and Differential Equations