# HF1905 Mathematical Analysis 5.0 credits

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Headings with content from the Course syllabus HF1905 (Autumn 2021–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Concepts of function, limits and continuity.

• Elementary functions.

• Differentiation rules.
• Taylor's formula
• Application to curve sketching, rates, and extremum problems.

• L'Hospital's rule.

• Definite and indefinite integration. Techniques of integration.

• Basic integration techniques and applications.

• Functions of several variables. Partial derivatives. Maxima and minima.

• Double integrals in Cartesian and polar coordinates and applications: area, volume and moments of inertia.

• Differential equations:  First order ordinary differential equations. Separable differential equations. Linear first-order  differential equations.

• Linear higher-order differential equations. Linear differential equations with constant coefficients. Applications.

### Intended learning outcomes

After completing the course students should for a passing grade be able to:

• Define and interpret the fundamental concepts of linear algebra and calculus : vector, dot product, cross product, triple product, line, plane, matrix, determinant, limit, continuity, derivative, integral.

• Do calculations with complex numbers  in polar, rectangular and exponential form.

• Solve and geometrically interpret systems of linear equations.

• Use vector algebra to evaluate projections, distance, areas and volumes.

• Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.

• Apply differentiation to solve applied max/min problems for functions of one variable.

• Use L'Hospital's rule to evaluate certain indefinite forms.

• Evaluate integrals using techniques of integration, such as substitution, and integration by parts.

• Use the methods of integration to evaluate areas and volumes.

• Solve first order differential equation.

•  Solve second order linear differential equation with constant coefficient.

•  Apply differential equations to different technical fields. Understand and apply the procedures for integrating rational functions.

• Calculate partial derivatives.

• Apply partial derivatives for finding extreme values for functions of two variables.

• Calculate and apply double integrals for computing areas, volumes and moments of inertia.

• Use suitable software for symbolic as well as numerical solving mathematical   problems and applications mentioned above.

• Derive important relations in mathematical analysis.

• Generalize and adapt the methods to use in somewhat new contexts.

• Solve problems that require synthesis of material and ideas from all over the course.

• Solve more advanced problems in, for example, integrals and applications.

### Course disposition

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## Literature and preparations

### Specific prerequisites

Basic and specific requirements for bachelor's program in engineering.

### Recommended prerequisites

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### Equipment

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### Literature

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## 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

• TEN1 - Examination, 5.0 credits, grading scale: 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.

### Opportunity to complete the requirements via supplementary examination

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

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### 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 HF1905

### Offered by

ABE/Constructional Engineering and Design

Technology

First cycle