This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…

Two heuristic and three rigorous arguments are given for the fact that functions of the form Ce[kx], with C an arbitrary constant, are the only solutions of the equation dy/dx=ky where k is constant. Various of the proofs in this self-contained note could find classroom use in a first-year calculus course, an introductory course on differential…