CALCULUS

After completing this course, students should have developed a clear understanding of the fundamental concepts ofsingle variable calculus and a range of skills allowing them to work effectively with the concepts. The basic concepts are: 

1. Derivatives as rates of change, computed as a limit of ratios.

2. Integrals as an anti-derivative and area under the curve. 

After completing this course, studentsshould demonstrate competency in the following skills: 

• Use both the limit definition and rules of differentiation to differentiate functions. 

• Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity. 

• Apply differentiation to solve applied max/min problems. 

• Apply differentiation to solve related rates problems. 

• Evaluate integrals by using the Fundamental Theorem of Calculus. 

• Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution. 

• Evaluate integrals using advanced techniques of integration, such asinverse substitution, partial fractions and integration by parts. 

• Use L'Hospital's rule to evaluate certain indefinite forms. 

• Determine convergence/divergence of improper integrals and evaluate convergent improper integrals.