Courses

After completing this course, you will be able to:

Limits and Continuity :

• Calculate and evaluate limits and represent these concepts graphically, algebraically, numerically and in words.
• Apply knowledge of limits and continuity to analyze and solve real-world problems.
• Determine when the use of technology is appropriate for solving problems related to limits and continuity, and how to apply the technology.

Derivatives and Differentiation :

• Explain the definition of derivative and how it is related to tangent lines and rates of change, and to compute derivatives from the limit definition.
• Compute derivatives using all of the standard rules, displaying, in particular, a strong mastery of the Chain Rule.
• Compute derivatives of trigonometric functions and compute closely related trigonometric limits.
• Explain the concept of an implicitly defined function, and use the technique of implicit differentiation to differentiate functions that are defined implicitly.
• Model and solve related rates problems.

Applications of the Derivative :

• Solve problems related to rates of change.
• Identify and describe properties of functions and their graphs.
• Apply the properties of functions and their graphs to real life problem situations.

Integration :

• Calculate anti-derivatives by using some basic rules.
• Evaluate anti-derivatives using the substitution technique.
• Define the definite integral.
• Evaluate a few definite integrals using the definition as a limit of Riemann sums.
• State the Fundamental Theorem of Calculus.
• Apply the Fundamental Theorem of Calculus to evaluate definite integral.