MAT 136 - Calculus II

This second part of the introductory Calculus sequence focuses on integral calculus beginning with the Fundamental Theorem of Calculus, the connection between two seemingly unrelated problems: measuring changing quantities and finding areas of curved shapes. Students will develop a deep understanding of the integral, and use it to: unpack equations involving derivatives; to make sense of infinite sums; to write complicated functions as ‘infinite polynomials’; and to compute areas, volumes, and totals in applied problems. This course will further develop students’ abilities to translate between algebraic, graphical, numerical, and verbal descriptions of mathematics in a variety of applied contexts.  The following concepts will be studied: Integration, basic techniques of integration (substitution and by parts), improper integrals, using computer algebra systems (CAS) for integration, Taylor polynomials and Taylor series, ratio test for power series, radius of convergence of power series, first-order differential equations and systems of differential equations: modelling, separable DEs, and using CAS to study and find solutions.