## MAT 225: Calculus with Analytic Geometry II

3 credits | Prerequisites: MAT 104

### Course rationale

This course is a continuation of the study of single variable calculus which was started in MAT 104. Calculus is an indispensable subject for mathematicians, engineers, and scientists.

### Course content

Applications of differentiation, related rates, concavity, curve sketching, techniques of integration, applications of integration, volume of solids, arc length and surface area of revolution, improper integrals, polar coordinates, area and arc length in polar coordinates, vectors in plane and space, algebra of vectors, applications in plane and space geometry, conic sections, standard forms, reduction of second degree equations to standard forms, pairs of straight lines, identification of conics, equations of conics in polar coordinates, infinite series, convergence of series, power series, Maclaurin and Taylor series.

### Course objectives

- To learn applications of differentiation.
- To learn applications of integration.
- To learn the various integration techniques.
- To learn about improper integrals.
- To learn about polar coordinates, vectors and conic sections.
- To learn about infinite series and their convergence.
- To learn about Maclaurin and Taylor series.

### References

*Calculus*by Anton, Bivens and Davis, 10th edition.*Calculus*by James Stewart, 8th edition.