20406 Differential and Integral Calculus I 1

Credits: 6 intermediate credits in Mathematics

Prerequisites: none

The course is based on a translation (by Naomi Shaked-Monderer) of chapters 1-11 of Calculus with Analytic Geometry (5th ed.), by H. Anton and A. Herr (John Wiley & Sons, 1995).

The course presents differential and integral calculus of single variable functions. It emphasizes techniques and applications and in many cases omits rigorous proofs. Accordingly, it is suitable for students of Natural Sciences, Life Sciences, Economics, Management and Engineering but not for those majoring in Mathematics or Computer Science (or taking any dual-disciplinary degree that includes Mathematics). The Open University offers two alternative calculus courses � Infinitesimal Calculus I (20106) and Calculus for Students of Economics and Management (10142). Students should carefully choose from among these, the course appropriate to their needs.

To complement the background material and for review purposes, the textbook includes a short appendix on set theory and a comprehensive appendix on trigonometry. Other background topics are reviewed in the first chapter of the text. Nonetheless, students are advised to refresh their high school Mathematics background (on the 4- or 5-point level) by reviewing material in traditional texts, or by taking the Mathematics Refresher Workshop for Social Science Students (95001).

Topics: Coordinates, graphs, lines; Functions and limits; Differentiation; Applications of differentiation; Integration; Applications of the definite integral; Logarithmic and exponential functions; Inverse trigonometric and hyperbolic functions; Techniques of integration; Improper integrals; L�Hopital�s rule; First order differential equations; Infinite series.

1There is some overlap in the content of this and other courses. For details, see Overlapping Courses.