Foundation Course in Mathematics

Aim

The course aims to give students a positive start to their engineering university studies, they will experience a "social class" and also rehearse and develop their mathematical ability for future studies in Calculus I, Calculus II and applications in other courses. Some new mathematical concepts are introduced. An important goal is to develop learning by using different types of work and various forms of examination. This will contribute to improving students

• skills in writing, reading and speaking mathematical language, being able to present solutions of mathematical problems with clear thinking - both written with mathematical symbols, and in oral
• capacity for logical reasoning
• conceptualization and experience to perform the solution controls
• ability to reflect on their learning and giving familiarity with working in a group and where one should see the group as a resource where good cooperation encouraged
• able to demonstrate a basic ability to both write, read and speak the mathematical language
• able to show good algebraic numerate with real and complex numbers
• able to use the basic concepts of function theory, as defined quantity, value, quantity and inverse function
• elementary functions properties and use this in problem solving
• able to set up and solve equations and inequalities containing absolute values ​​
• able to perform calculations using trigonometric functions Course content Real numbers Factors, polynomial Equations and inequalities, containing rational expressions and absolute values ​​ Higher degree polynomial equations with real coefficients Functions and graphs Straight lines , quadratic functions, exponential and power functions and associated inverses Trigonometry and trigonometric functions Complex numbers and complex plane Euler's formula and the formula Moivres Polynomials of a complex variable and complex polynomial equations The emphasis of the course is handling of algebraic expressions and properties of elementary functions. Solution of data must contain a clear logical way. Teaching and working methods The course consists of lectures, seminars and mentoring of teachers. Also mathematics mentors from higher grades are available for support. Sometimes class is divided into groups of about 4 students - in order to develop the oral mathematical language. Much of the work done in groupings. course is taken during the period HT0 and HT1. Examination TEN2Written examination6 creditsU, 3, 4, 5KTR6Written Test0 creditsU, GKTR5Written Test0 creditsU, GKTR4Written Test0 creditsU, GThe three approved KTR1-3 give the final grade 3. Written examination is required for higher grades. 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 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 Institutionen för teknik och naturvetenskap Course literature BooksForsling-Neymark, Matematisk analys, en variabel Senaste Lieber AB ISBN: 9147051884CompendiaGöran Forsling, Övningar i analys i en variabelPeter Holgersson, Matematisk Grundkurs

Content

• Real numbers
• Factors, polynomial
• Equations and inequalities, containing rational expressions and absolute values ​​
• Higher degree polynomial equations with real coefficients
• Functions and graphs
• Straight lines , quadratic functions, exponential and power functions and associated inverses
• Trigonometry and trigonometric functions
• Complex numbers and complex plane
• Euler's formula and the formula Moivres
• Polynomials of a complex variable and complex polynomial equations