# Calculus, Linear Algebra and Dynamics (BY-)

## Code

BY-SCI2

## Version

4.0

## Offered by

Bygningsingeniør

## ECTS

5### Prerequisites

### Main purpose

### Knowledge

- 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

- 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

- 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.

### Topics

### Teaching methods and study activities

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
- Downloads from the intra net.
- 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.

### Evaluation

### Examination

Exam prerequisites:

None

Type of exam:

Individual oral exam, 20 minutes.

The exam is on the basis of course assignments found by lot and without preparation.

The course assignments are selected by the examiner and communicated to the students no later than the last day of teaching on VIA's intranet.

Course assignments must be uploaded in WISEflow approx. 1 week before the exam.

If the student does not upload the course assignments in WISEflow, the student is offered to solve the course assignments during the examination.

Internal assessment.

Allowed tools:

None

Re-exams:

Equal to the ordinary exam.

### Grading criteria

### Additional information

See Appendix 1 - CE SCI 2 ; BY SCI 2 ( uploaded on intranet )

### Responsible

Morten Carter (mc)

### Valid from

01-08-2023 00:00:00

### Course type

Compulsory for Civil Engineering

2. semester

### Keywords

Calculus and Linear algebra, Particle dynamics