Upon successful completion of the course, the student will be able to
Explain and apply key concepts related to sequences and series of numbers and functions.
Explain and apply key concepts related to parametric curves and elementary real valued functions of two variables.
Analyze the graphs of functions of two variables and optimize such functions over given a set of constrains.
Know characteristic features of parametric curves and movements in the plane and in the space.
Find iterated anti-derivatives and apply these.
Course contents
Sequences and series of reals numbers and functions, power series. Convergence and divergence. Differentiation and anti-differentiation of power series. Analysis of non-elementary functions by means of power series. Parametric curves and movements in the plane and space, velocity, acceleration, curvature, and torque. Functions of two variables, partial differentiation, gradient, level curves, tangent plane, optimization with and without constraints. Lagrange’s method. Double- and triple integral. Applications.
Teaching methods
Lectures, group work, mandatory hand-ins, and peer review. Estimated workload of the course is 267 hours.
Examination requirements
Approved mandatory hand-ins. See Canvas for more information.
Assessment methods and criteria
5-hours written exam under supervision. The exam is graded.
Evaluation
The faculty member in charge of the module confers with the student rep which form of evaluation will be organized, and whether midterm or post hoc. Cfr the University regulations on quality assurance, chapter 4.1.