Mathematical methods 3

Differentiation

Limits and continuity. Directional derivative and the gradient. Tangent planes and tangent lines. Linear approximation and differentiability. The chain rule. Parametric curves in the plane and in space. Curvature and torsion.

Integration

Double integrals and iterated integration using cartesian and polar coordinates. Triple integrals and iterated integration using cartesian, cylinder- and spherical coordinates. Integration on curves and surfaces in space, curve length, surface area, volume and centroids.

Vector analysis

Static vector fields. Divergence,curl, gradient fields and potentials. Conservative and curl free vector fields. Work/circulation and flux. Green theorem, Stokes' theorem and Gauss' Theorem. Applications of vector analysis in fluid mechanics and/or electro-magnetism (Maxwell's equations).

Knowledge:

The candidate knows concepts, theorem, and methods from calculus in several variables related to differentiation, integration, and vector analysis for static vector fields.

Skills:

The candidate can

• use mathematical language to formulate problems in mathematics and science related to calculus in several variables.
• apply methods from multivariable calculus to find analytic solutions to mathematical and engineering problems.
• use mathematical software to visualise and solve relevant problems in calculus in several variables.

General competencies

The candidate can

• use mathematical language to communicate about problems in engineering.
• translate between a mathematical language and a language suitable for use with mathematical software

Recorded lectures and digital exercises.

Digitale øvingstimer.

There are no lectures in this course.

This course is intended for those accepted to engineering programs in 2023 or earlier. Other students should take IMAx3011 or IMAx3012.