MA0035, Single-variable calculus, 10.0 Hp
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Syllabus

Finalized by: PN-O, 2025-12-12
Valid from : Autumn semester 2026 (2026-08-31)

Level

First cycle (G1N)

Subject

Mathematics/Applied Mathematics

Grading Scale

The grade requirements within the course grading system are set out in specific criteria. These criteria must be available by the course start at the latest.

Course language

Swedish

Entry Requirements

Objectives

The course provides an introduction to mathematical analysis in one variable and contributes to establishing the mathematical foundation necessary for further studies.

The focus is on differential calculus, integral calculus, and elementary differential equations.

After completing the course, the student shall be able to:

• explain the concepts of limit, continuity, and derivative;

• recall a number of standard limits and use them in limit calculations;

• apply the rules of differentiation to compute derivatives and determine extrema;

• explain the concepts of integral and antiderivative;

• compute integrals using substitution, integration by parts, and integration rules for rational functions;

• use integrals to calculate** areas**, volumes, and arc lengths;

• explain and apply the basic concepts of infinite series;

• compute Taylor expansions of elementary functions;

• solve first-order linear differential equations using an integrating factor, as well as separable differential equations;

• solve simple second-order linear differential equations;

• explain the definition and basic properties of the Laplace transform;

• translate problems from relevant application areas into suitable mathematical form and present the solutions clearly.

Content

Subject-related content

Limits and continuity: concepts and computational rules.
Derivatives: concept, differentiation rules, chain rule, and the Mean Value Theorem.
Extrema and optimization problems. Curve sketching. Applications of differential calculus.

Indefinite and definite integrals, antiderivatives, the Fundamental Theorem of Calculus.
Integration methods: substitution, integration by parts, and integration of rational functions.
Applications of integrals: area, volume, and arc length.

Series: definitions, geometric series, the integral test.
Power series. Taylor expansions and applications.

Ordinary differential equations (ODEs): the concept of solution, existence and uniqueness.
Linear ODEs with constant coefficients. Solvable types of ODEs: separable equations and equations solvable by an integrating factor.

Laplace transform: definition and standard formulas.
Solution of initial value problems for linear ODEs.

Real-world examples and applications.

Teaching formats

The course uses lectures and problem-solving sessions to support and enhance student learning.

The course emphasizes the following general competences: Critical thinking; Problem-solving; Scientific methods.

Examination Formats and Requirements for Passing the Course

Approved written exam.

Responsible Department/Equivalent

Department of Energy and Technology

Supplementary information

Included in program

• Bioresource Systems Engineering