Calculus, one variable

Aim

That you as a student will learn to feel confident with the mathematical expressions, reasoning and relations from Single Variable Calculus and that it will teach you calculating and problem solving skills needed for your further studies. After a completed course you should be able to:

• Read and interpret mathematical texts
• Explain definitions and expressions like local extremes, limits, continuity, derivatives, primitive functions and integrals
• Explain and use central theorems like The Fundamental Theorem of Calculus, Mean-Value Theorems, The Intermediate-Value Theorem and The Max-Min Theorem.
• Use mathematical laws for limits of functions and derivatives.
• Perform investigations of functions using derivatives, limits and the properties of basic functions and from this draw conclusions regarding the properties of the functions

Content

Preparatory course: Equations and systems of equations. Geometric and arithmetic sums. Inequalities. Binomial theorem. Exponential functions and logarithms. Polynomials. Trigonometry and trigonometric functions.

Calculus: Real and complex numbers. Functions of a real variable. Elementary functions. Sequences, limits. Derivatives and continuity. Rules for differentiation. Properties of continuous functions. Study of functions. Teaching and working methods Teaching is done in lectures and problem classes. Examination KTR2Written test0 creditsU, 3, 4, 5KTR1Written test0 creditsU, 3, 4, 5TEN1Written examination6 creditsU, 3, 4, 5Passed written test 1 and written test 2 gives a bonus on the written examination (TEN1). The right to count the bonuses from the tests is 12 months from the date of writing. Grades for examination modules are decided in accordance with the assessment criteria presented at the start of the course. Grades Four-grade scale, LiU, U, 3, 4, 5 Other information Supplentary courses: Mathematics, second course. About teaching and examination languageThe teaching language is presented in the Overview tab for each course. The examination language relates to the teaching language as follows: If teaching language is “Swedish”, the course as a whole could be given in Swedish, or partly in English. Examination language is Swedish, but parts of the examination can be in English.If teaching language is “English”, the course as a whole is taught in English. Examination language is English.If teaching language is “Swedish/English”, the course as a whole will be taught in English if students without prior knowledge of the Swedish language participate. Examination language is Swedish or English depending on teaching language.OtherThe course is conducted in such a way that there are equal opportunities with regard to sex, transgender identity or expression, ethnicity, religion or other belief, disability, sexual orientation and age.The planning and implementation of a course should correspond to the course syllabus. The course evaluation should therefore be conducted with the course syllabus as a starting point. The course is campus-based at the location specified for the course, unless otherwise stated under “Teaching and working methods”. Please note, in a campus-based course occasional remote sessions could be included. Department Matematiska institutionen Course literature BooksForsling, Göran och Neymark Mats, (2011) Matematisk analys, en variabel. Liber