Course

Published

(Updated )

Tampere University

Introductory Calculus

From

5 cr

Registration open
Face-to-faceOnline
Basic studies
Core content
  • Set union, intersection, difference and complement. Introduction of the logic and proofs needed in mathematical analysis.
  • Definition of a function. Monotonicity of a function. Inverse function and combined function. Properties of basic functions. Hyperbolic functions and their inverses.
  • Complex numbers and their basic properties (sum, difference, product, quotient, conjugate and modulus), presenting and calculating complex numbers both in coordinate form and polar form, complex roots.
  • Limit and continuity of a fuction. One-sided and inproper limits, l'Hopital's rule.
  • Derivative as limit of difference quotient. Derivating basic functions, products and quotients, chain rule. Studying the values and extrema of a function based on derivatives..
  • Basics of integral calculus.
  • Partial derivatives and gradient of a multivariable function.
Complementary knowledge
  • Preimage, injection, surjection, bijection.
  • Roots of real valued polynomials, factorisation.
  • Intermediate value theorem. Continuity of inverse function. 
  • Derivative of inverse function. 
  • Applications, for example linear approximations.
Specialist knowledge
  • Mean value theorem.

Contains

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Additional information and registration

Price and registration period

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Additional information:

Fields

Engineering and technology

Scope

5 cr

Code

MATH.APP.111

Organiser

Tampere University

Tampere University

Contact details

avoin.tau@tuni.fi

Belongs to themes:

Renewal of working life and competence