Print Syllabus

Syllabus

MA0035 Single-variable calculus, 10.0 Credits

Envariabelanalys

Subjects

Mathematics/Applied Mathematics

Education cycle

Bachelor’s level

Advanced study in the main field

First cycle, has only upper-secondary level entry requirements
Bachelor’s level (G1N)

Grading scale

Language

Swedish

Prior knowledge

- General entry requirements for courses or study programmes that begin in the first cycle and that are intended for new entrants to higher education
- Mathematics 4 or Mathematics E

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.

Grading form

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.

Formats and requirements for examination

Approved written exam.

• If a student has failed an examination, the examiner has the right to issue supplementary assignments. This applies if it is possible and there are grounds to do so.

• The examiner can provide an adapted assessment to students entitled to study support for students with disabilities following a decision by the university. Examiners may also issue an adapted examination or provide an alternative way for the students to take the exam.

• If this syllabus is withdrawn, SLU may introduce transitional provisions for examining students admitted based on this syllabus and who have not yet passed the course.

• For the assessment of an independent project (degree project), the examiner may also allow a student to add supplemental information after the deadline for submission. Read more in the Education Planning and Administration Handbook.

Other information

• The right to participate in teaching and/or supervision only applies for the course instance the student was admitted to and registered on.

• If there are special reasons, students are entitled to participate in components with compulsory attendance when the course is given again. Read more in the Education Planning and Administration Handbook.

Responsible department

Department of Energy and Technology