Calculus

Course Objectives

  • Calculus is the mathematical study of continuous change. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves). Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.
  • 2.5-hour sessions, 13 weeks.
  • Text: Thomas Calculus.

Syllabus Week Topic

1st Functions

2nd Limits and Continuity

3rd Derivatives

4th Applications of Derivatives

5th Integrals

6th Applications of Definite Integrals

7th Integrals and Transcendental Functions

8th Techniques of Integration

9th First-Order Differential Equations

10th Infinite Sequences and Series

11th Parametric Equation and Polar Coordinates

12th Vectors and the Geometry of Space

13th Vector-Valued Functions and Motion in Space