Module Code - Title:
MA4001
-
ENGINEERING MATHEMATICS 1
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
Rationale and Purpose of the Module:
To develop the student's understanding of and problem solving skills in the areas of Pre-Calculus and Differential Calculus.
Syllabus:
[Series] and tests for convergence. Real valued [functions] of a real variable, [limits, continuity and differentiation from first principles]. Physical and graphical interpretation of derivatives.
[Transcendental functions]: properties of trignometric, exponential, logarithmic and hyperbolic functions and their inverses.
[Vector Algebra]: coordinates, resolution of vectors, dot product and cross product.
[Complex numbers]: Cartesian, polar and exponential forms. The algebra of complex numbers. The nth roots of unity.
[Differential Calculus: properties] of derivatives, product, quotient and chain rules. Derivatives of transcendental functions.
Applications of Differential Calculus to finding [maxima and minima, curve sketching, roots of equations] (Newton's method), [undetermined forms] (L'Hopital's Rule) and [Power Series] (Taylor and Maclaurin Series) of a univariate function.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
Represent a given complex number in the Cartesian and polar forms; perform arithmetic operations with complex numbers.
Given a real-valued function of a real variable, find its derivative from the definition and using tables combined with the product, quotient and chain rules.
Given a real-valued function of a real variable, find its domain, maxima and minima, inflection points, sketch its curve, find the equation of the tangent line to its curve at a given point, evaluate its limit at a given point or at an infinity.
Given a series, evaluate its sum or show that it diverges; given a power series, find its interval of convergence.
Given a real-valued function of a real variable, find its Taylor and Maclaurin series.
Perform arithmetic operations with vectors in 3-space and evaluate their dot products and cross products.
Affective (Attitudes and Values)
N/A
Psychomotor (Physical Skills)
N/A
How the Module will be Taught and what will be the Learning Experiences of the Students:
Normal mathematics lectures. Students will have weekly homework (not for credit), a mid-term exam worth 30% and a final exam worth 70%.
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Adams, R.A. (2006)
Calculus: a complete course
, Pearson Addison Wesley
Other Relevant Texts:
Anton, H. (1988)
Calculus with Analytic Geometry
, Wiley
Atkinson, K. (1993)
Elementary Numerical Analysis
, Wiley
Fraleigh, J.B. (1985)
Calculus of a single variable
, Addison Wesley
Jeffrey, A. (1992)
Essentials of Engineering Mathematics
, Chapman Hall
Stroud, K.A. (1995)
Engineering Mathematics
, Palgrave
Programme(s) in which this Module is Offered:
Semester(s) Module is Offered:
Module Leader:
James.Gleeson@ul.ie