Introductory Calculus, 5 cr

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.