The pedagogy of the course is “problem-based learning”. There
will be introductory and summing up lectures and students will work
in small groups with projects, problem solving, computer
simulations and case studies.
To provide the students with basic knowledge in fundamental tools
to solve engineering problems and to construct and analyze
mathematical models, as well as to provide a foundation for further
studies in modern engineering mathematics. The use of graphing
calculators supports both of these aspects.
Læringsmål:
En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:
Apply differentiation and integration to solve engineering
problems
Use power series to approximate functions with
polynomials.
Use polar coordinates and parametric equations to solve
geometrical problems.
Use vectors and vector-values functions to solve space motion
problems.
Find lengths, areas, volumes and centers of mass of geometrical
entities.
Use the algebraic and geometric representations of complex
numbers and the complex exponential function.
Solve linear first order and second order differential
equations.
Apply the Laplace Transform to solve linear differential
equations.
Use graphing calculators for the solution and the graphical
illustration of mathematical problems.
Apply the topics of the lectures to practical problems through
project work in groups.
Learn new topics in engineering mathematics through guided
assignments.
Kursusindhold:
Applications of derivatives to optimization problems. Applications
of definite integrals to lengths, areas, volumes, moments and
centers of mass. Infinite sequences and series, including Taylor
series. Parametric equations and polar coordinates. Vectors and the
geometry of space. Vector-valued functions and motion in space.
Complex numbers. First and second order differential equations. The
Laplace Transform. Examples of applications in the engineering
sciences.
Litteraturhenvisninger:
- Thomas' Calculus, Global Edition, 12th Edition, by George B.
Thomas, Maurice D. Weir, and Joel Hass. ISBN-13: 978-0-321-64363-6,
Pearson 2010.
- Lecture notes on CampusNet.
Bemærkninger:
This course is an integrated part of the study program in
Mechanical Engineering. It is, however, a general methodological
course aimed at all engineering students, regardless of
specialization.
