TNA003 
Calculus I, 6 ECTS credits.
/Analys I /
For:
ED
ES
KTS
MT


Prel. scheduled
hours: 48
Rec. selfstudy hours: 112


Area of Education: Science
Subject area: Mathematics


Advancement level
(G1, G2, A): G1


Aim:
To give basic proficiency in mathematical concepts, reasoning and relations contained in singlevariable calculus. To provide the skills in calculus and problem solving required for subsequent studies. After a completed course, the student should be able to
 read and interpret mathematical text
 quote and explain definitions of concepts like local extremum, limit, continuity, derivative, antiderivative and integral
 quote, explain and use central theorems such as the first and second fundamental theorem of calculus, the mean value theorems, the intermediate value theorem, the extreme value theorem
 use rules for limits, derivatives, antiderivatives and integrals
 carry out examinations of functions, e.g., using derivatives, limits and the properties of the elementary functions, and by that means draw conclusions concerning the properties of functions
 use standard techniques in order to determine antiderivatives and definite integrals
 make comparisons between sums and integrals
 perform routine calculations with confidence
 carry out inspections of results and partial results, in order to verify that these are correct or reasonable


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Foundadtion course in mathematics
Note: Admission requirements for nonprogramme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.


Organisation:
Lectures and problem classes or classes alone.


Course contents:
Functions of a real variable. Inverse trigonometric functions. Limits and continuity. Derivatives. Rules of differentiation. Properties of differentiable functions. Derivative and monotonicity. Graph sketching, tangents and normals, asymptotes. Local and global extrema. Derivatives of higher order. Convex and concave functions. How to find primitive functions. The Riemann integral. Definition and properties. Connection between the definite integral and primitive function. Methods of integration. Applications of integrals: area, length of curves, volume of solids of revolution, area of surfaces of revolution. Generalised integrals. Estimation of sums. The formulas of Taylor and Maclaurin. The Maclaurin expansion of elementary functions. Applications, e.g. estimation of errors and finding limits. Ordinary differential equations. Equations of the first order: linear and separable equations. Integral equations. Linear equations of higher order with constant coefficients. Applications will be given of mathematical models from various fields. Series.


Course literature:
Forsling, G. and Neymark, N.: Matematisk analys, en variabel. Liber.


Examination: 

Written examination Optional written tests 
6 ECTS 0 ECTS




Course language is Swedish.
Department offering the course: ITN.
Director of Studies: Clas Rydergren
Examiner: Sixten Nilsson
Link to the course homepage at the department

