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# Mathematical Methods 1

This is the study programme for 2019/2020. It is subject to change.

Complex numbers. Introduction to basic topics in real analysis and their applications : limits, continuity, differentiation, integration and differential equations.

### Learning outcome

After completing this course the student will be able to:
• Compute with complex numbers on Cartesian and exponential form, and use de Moivre's theorem.
• Use the limit concept to define continuity, differentiability and integration.
• Differentiate all elementary functions, and use the derivative of a function to describe its properties, in particular, to determine its extremal values.
• Use Leibniz notation to solve problems on related rates.
• Compute antiderivatives by using substitution, partial integration, partial fraction decomposition and inverse trigonometric substitutions.
• Compute areas, lengths and volumes by integration.
• Apply and solve first order linear and separable differential equations, and second order linear differential equations with constant coefficients.

### Contents

Complex numbers. Introduction to basic topics in real analysis and their applications : limits, continuity, differentiation, integration and differential equations.

None.

### Exam

Weight Duration Marks Aid
Written exam1/15 hoursA - FCompilation of mathematical formulae (Rottmann).
Specified printed and hand-written means are allowed. Definite, basic calculator allowed.

### Coursework requirements

Tre obligatoriske innleveringer
Three mandatory assignments have to be approved before the student is allowed to take the exam.

### Course teacher(s)

Course coordinator
Sigbjørn Hervik
Tutor
Course teacher
Sigbjørn Hervik

### Method of work

6 hours lectures, 2 hours exercises. Three compulsory assigned exercises. Mandatory work demands (such as hand in assignments, lab- assignments, projects, etc) must be approved by subject teacher three weeks ahead of examination date.

### Overlapping courses

Course Reduction (SP)
Mathematical analysis for economists (ØK0025_1) 3
Mathematical methods 1 (TE0549_1) 9
Mathematical methods 1 (TE0549_A) 9
Mathematical analysis for economists (BØK135_1) 5
Mathematical analysis for economists (BØK135_2) 5
Mathematical analysis for economy and social science (BØK135_3) 5
Mathematical methods 1 (ÅMA100_1) 10
Mathematical methods 2 (TE0561_1) 5

### Open to

Mathematics - One Year Foundation Programme at the Faculty of Science and Technology.

Bachelor studies at the Faculty of Science and Technology.

Master studies at the Faculty of Science and Technology.

### Course assessment

Form and/or discussion

### Literature

Text book : Adams & Essex: Calculus. (Pearson). Detailed description of syllabus will be given at the semester start.

This is the study programme for 2019/2020. It is subject to change.

Sist oppdatert: 14.11.2019