SF1673 Analysis in one variable
KTH Royal Institute of Technology
Basic requirements.
Function, function graph, domain, range. Increasing and decreasing functions, odd and even functions. Inverse functions. The class of elementary functions. Trigonometric functions, exponential and logarithmic functions. Power laws, logarithms. Limits, rules for calculating limits, standard limits. Continuity, theorems on continuous functions. Derivative, rules of differentiation, the mean value theorem, implicit differentiation, applications: rate of change, linear approximation, tangent, extreme value problems, sketching the graph of a function, l'Hôpital's rule. Taylor's formula with error estimates. Linear differential equations with constant coefficients and their applications. The Riemann integral, primitive functions, the fundamental theorem integral calcolus, variable substitution, integration by parts, partial fractions. Riemann sums, geometric and other applications of integrals, improper integrals, estimates and convergence. Paramterization of curves and arc length. Sequences and series, convergence criteria, the Cauchy integral test. Taylor series.
After the course the student should be able to
- use concepts. theorems and methods to solve and present solutions to problems within the parts of one variable calculus described by the course content,
- read and comprehend mathematical text.
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