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# Calculus

IT-CAL1

1.0

ICT Engineering

## ECTS

5

### Prerequisites

Mathematics equivalent to the admission requirements for the Software Engineering Programme.

### Main purpose

​In the course, the students attain knowledge about and practical experience in applying the methods and tools of calculus. Most importantly, the course will enable the student to apply differential and integral calculus in solving a wide range of problems.

### Knowledge

After having successfully completed the course, the student will have gained knowledge about the theory, techniques and tools of calculus, in particular knowledge about:
- Functions
- Limits and continuity
- Derivatives
- Integrals
- Infinite series and sequences
- Partial derivatives
- Multiple integrals
- Differential equations

### Skills

Upon completion of this course, students will be able to:
- Define and interpret functions, including calculating limits of functions and the concept of continuity
- Calculate and interpret ordinary and partial derivates of real functions.
- Calculate and interpret definite and indefinite integrals of real functions.
- Perform calculations pertaining to infinite series and sequences.
- Solve differential equations.

### Competences

Upon completion of this course, the goal is that the students have acquired the competences to:
- Make informed choices about the use of differential and integral calculus.
- Apply the tools of calculus to real-world problems.
Communicate and discuss the theory, tools and techniques of calculus.

### Teaching methods and study activities

​The mode of teaching will be classroom based and will involve lectures by the teacher and exercise solutions presented in class by the students. The students are expected to work on exercises in between classes. The total work-load for the student is expected be around 125 hours, including preparing for the exam.

### Resources

Hass, Heil & Weir: Thomas' Calculus, 14th ed. in SI units., Pearson.

### Examination

Exam prerequisites:
The student must hand in all mandatory assignments to qualify for the exam.

Exam type:
The course is evaluated based on an oral examination, which will take 20 minutes including everything.

A selection of approximately 10 of the exercises of the course will form the basis for the exam. These exercises will be selected in the last teaching session.

During the exam, the student will present one of these exercises, which will be chosen randomly. There is no preparation time. The exam will then evolve into a general discussion of the course curriculum

Tools allowed:
The student is allowed to bring their notes to the oral exam, but these must be placed on the table during the examination. During the presentation, the student is allowed to consult their notes if they need to, but excessive use of the notes will count negatively towards the grade. During the discussion that follows the presentation, the student is not allowed to consult their notes.

Re-exam:
Please note that re-examinations may take a different form than the ordinary exams.

​Grading based on the Danish 7-point scale.

The grade will reflect an overall assessment of the mandatory assignments (10 %) and the oral examination (90 %). To earn an overall passing grade, the oral examination must be passed.

### Responsible

Frederik Thorning Bjørn

### Valid from

2/1/2023 12:00:00 AM

### Keywords

Functions. Limits. Derivatives. Integrals. Infinite series. Differential equations.