Module Code - Title:
MB5022
-
CALCULUS 2
Year Last Offered:
2026/7
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
MB5021
Rationale and Purpose of the Module:
The purpose of this module is to provide post-primary mathematics teachers with mathematics content knowledge required by the Teaching Council for accreditation.
The module builds on and extends the concepts and skills introduced in Calculus 1 that provide the necessary knowledge, skills and understanding for teaching the Mathematics syllabus to the highest level in post-primary education.
Syllabus:
The following topics are covered: mean value theorem and its application to increasing and decreasing functions; concepts of maximum and minimum; convexity; use of derivatives to study functions behaviour; optimisation word problems; definite and indefinite integral, areas between curves; the logarithmic function as an integral, the exponential function, and their properties; the fundamental theorem of differential and integral calculus; convergence/divergence of infinite series; consideration of how these topics could be taught in a second level classroom.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
On successful completion of this module, students will be able to:
1. Demonstrate an understanding of the concepts introduced in the course,
2. Apply the material learned to solving unseen problems (detect maxima/minima, monotonicity and use these to sketch graphs of functions, optimise and integrate various classes of functions, manipulate expressions involving the exponential and natural logarithm function),
3. Explain the connection between differential and integral calculus using the Fundamental Theorem of Calculus,
4. Understand the reasoning behind any methods used,
5. Recognise, read and correctly use standard mathematical notation,
6. Provide examples in order to illustrate certain specified properties,
7. Identify connections between mathematical concepts and opportunities to explore related connections within the school mathematics curriculum.
Affective (Attitudes and Values)
On successful completion of this module, students will be able to:
1. Appreciate the relevance of the concepts covered in this module for teaching mathematics in post-primary schools.
Psychomotor (Physical Skills)
N/A
How the Module will be Taught and what will be the Learning Experiences of the Students:
Blended learning approach: online lectures with interactive exercises; online and face to face tutorials.
Based on the course team's published research on designing blended professional development programmes for out-of-field teachers of mathematics.
Develops knowledgeable graduates with high levels of mathematical competence needed for Teaching Council recognition as a fully-qualified teacher of post-primary mathematics.
Prime Texts:
Stewart, J. (2012)
Calculus, 7th Edition
, Brooks/Cole,Pacific Grover, California
Other Relevant Texts:
Adams, R.A. (2006)
Calculus: A Complete Course, 6th Edition
, Prentice Hall, Canada.
Programme(s) in which this Module is Offered:
PROFESSIONAL DIPLOMA IN MATHEMATICS FOR TEACHING
Semester(s) Module is Offered:
Autumn
Module Leader:
niamh.omeara@ul.ie