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# Calculus, Linear Algebra and Dynamics (CE-)

CE-SCI2

3.0

## Offered by

Civil Engineering

## ECTS

5

### Main purpose

The purpose of the course is to enable the student to understand and apply basic terms within selected topics of mathematical analysis, linear algebra and vector calculations. The student must also obtain an understanding of the principles of plane dynamics of particles and must be capable of using mathematical methods for solving plane dynamics problems.

### Knowledge

The student will get knowledge about:
• Application of integration
• Matrixes and matrix algebra
• Linear equation systems
• Polar coordinates
• Complex numbers
• Ordinary differential equations of the 1st and 2nd order
• Physical quantities and units
• Reference systems
• Kinematics of particles
• Kinetics of particles
• Vehicle dynamics

### Skills

After completing the course, the student will be able to:
• Identify Area, Centroid and Moments of Inertia for a plane region in an x-y coordinate system.
• Identify and solve Linear equations systems.
• Identify Area, Centroid, Moments of Inertia for a plane region and length of a curve in a polar-coordinate system.
• Make simple calculations on complex numbers.
• Describe simple problems and solve Ordinary differential equations of the 1st and 2nd order
• Identify kinematic relations in the description of motion particles in different reference systems.
• Set up and perform serial calculations by using the Law´s of Newton.
• Analyze the motion of a vehicle treated a particle.

### Competences

After completing the course, the student will be able to:
• Identify which parts of the acquired knowledge and skills that’s relevant to a given, simple mathematical or simple real-world particle dynamic problem.
• Model simple real-world problems especially particle dynamics problems.
• Use their acquired skills and knowledge to study more advanced Calculus, Algebra and Dynamics courses on the Engineering programme.
• Use a commercial mathematical software to solve and perform serial technical calculations.

### Teaching methods and study activities

​The expected total workload for the student is 137.5 hours.
The teaching will be lecturing and problem solving in class.
Students will prepare for class by reading sections of textbooks and solving problems initiated by the lecturer.
Homework assignments will be handed out.

### Resources

•Thomas´ Calculus in SI Units;  Maurice D. Weir, Christopher E. Heil& Joel R. Hass, 14. edition
• R. C. Hibbeler: Engineering Mechanics – Dynamics – SI Edition, Prentice Hall. Latest edition.

The teaching is based on the student having a PC with software able to perform operations corresponding to MathCad, and that the student independently acquaints themselves with the use of this.
The teaching is based on the use of MathCad.

### Examination

Prerequisites:
Upload of course assignments in Wiseflow approximately one week before the exam.

Type of exam:
Individual oral examination with internal assessment. 20 min.
Exam is based upon course assignment(s) found by draw and without preparation.

Allowed tools:
None

Re-exams:
Method will be equal to the ordinary exam.

Grading based on the Danish 7-point scale.

Morten Carter

### Valid from

2/1/2022 12:00:00 AM

### Keywords

Calculus and Linear algebra, Particle dynamics