# HF1000 Mathematics 2 7.5 credits

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus HF1000 (Autumn 2007–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Complex numbers: The complex plane. Modulus and argument. Polar, rectangular and exponential form. Euler´s and de Moivre´s theorems. Binomial equations. Algebraic equations.
• Taylor’s formula
• Differential equations: Separable differential equations. First order differential equations.
• Linear differential equations with constant coefficients. Applications.
• Transforms:
• Heaviside function. Dirac function.
• Laplace transforms.
• Z-transform.
• Fourier transforms.
• Fourier series.
• Applications on continuous and discrete dynamical systems. Stability.

### Intended learning outcomes

• After completing this course, students should be able to:
Solve problems which involve complex numbers
• Solve first order differential equation.
• Solve second order linear differential equation with constant coefficient.
• Apply differential equations to different technical fields
Use Laplace an Fourier transforms to solve differential and integral equations
• Use  the Z-transform  to solve difference equations
• Use suitable software for symbolic as well as numerical solving mathematical   problems and applications mentioned above.

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

No information inserted

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

Part 1:   Modern Engineering Mathematics, 4th Edition, Glyn James
Alternatives for part 1: Matematik för ingenjörer, S Rodhe, H Sollervall
Part 2: Transformteori för ingenjörer; författare: H. Sollervall, B Styf

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• LAB1 - Assignments, 1,5 hp, betygsskala: P, F
• TEN1 - Defferential Equations, 3,0 hp, betygsskala: A, B, C, D, E, FX, F
• TEN2 - Transforms, 3,0 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Other requirements for final grade

• LAB1 - Assignments, 1.5 credits, grade scale: P, F
• TEN1 - Defferential Equations, 3.0 credits, grade scale: A, B, C, D, E, FX, F
• TEN2 - Transforms, 3.0 credits, grade scale: A, B, C, D, E, FX, F

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web HF1000

### Offered by

CBH/Biomedical Engineering and Health Systems

### Main field of study

Mathematics, Technology

First cycle