This is an introductory course to Calculus. The course aims at introducing the learner to the concepts of limits and derivatives and their uses. The main resource (Book) for the course are lecture notes by Paul Dawkins. See the course web page where you can download a pdf copy of the notes. He also has lots of questions on the course together with their solutions. These should provide good practice.
In this course we will cover
Vector Algebra: Scalars and vectors; types of vectors; addition and subtraction; multiplication and division by a scalar; position vector of point of division, scalar (or dot) product; vector (or cross) product scalar triple product; vector triple product; vector product of vectors; reciprocal vector triads; applications of vector algebra.
Vector Calculus: Differential vector calculus; applications of differential geometry and mechanics; Integral calculus; Riemann, line, vector line, double, surface and volume. Gradient of a scalar function;Divergence of a vector; curl of a vector. Stoke’s and Green’s theorems: orthogonal curvilinear coordinates.
The purpose of this course is to introduce the students to the concepts of indefinite and definite integrals and their applications.