Differential Calculus

Objectives: To introduce students to Differential Calculus in One Real Variable.

Overview: Why study calculus?

Sets and Functions. Review of Logarithms. Inequalities, Limits: Idea of a limit, definition of a limit, continuity. Derivatives: Definition of a derivative, tangents, product rule, chain rule, quotient rule, higher derivatives, implicit differentiation, Newton's method for roots, the law of the mean, exponential and logarithmic functions. Applications of derivatives: Maxima and minima, monotonic functions and the first derivative test. Curvature of plane curves. Taylor's theorem. Concavity and points of inflection. Symmetry and curve sketching. Applied max-min problems and related rates.

Learning Outcomes:
On successful completion of the module, students should be able to:
-Describe and manipulate functions
-Evaluate limits of basic functions.
-Obtain derivatives of basic functions and combinations of such functions.
-Solve max-min problems.
-Use Newton's method
-Sketch curves of the basic functions and combinations of such functions.
-Use the methods from the course to solve problems.
-State definitions and theorems covered in the course.

Teaching & Learning methods:
36 lecture hours, 7 tutorial hours, 77 private study hours.

Assessment:
Continuous assessment 25%
University scheduled written examination: 75% (90 minutes)

Pre-requisites:
Exposure to sets, functions, algebraic geometry of lines and circles, elementary algebra and trigonometry. Previous exposure to differential calculus is helpful, but not essential. Ordinary Level Leaving Certificate Mathematics C3 (or equivalent) is sufficient.