Fundamentals of Engineering Mathematics, 5 cr

Core content

• Set union, intersection, difference and complement. Existence and universal quatifications. Direct and indirect proof, proof by induction.
• 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'Hospital'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.

Complementary knowledge

• Preimage, injection, surjection, bijection.
  
• Roots of real valued polynomials, factorisation.
• Sandwich principle. Intermediate value theorem, continuity of inverse fuction. 
• Derivative of inverse function, linear approksimations. 
• Applications of integral, like area and volume.

Specialist knowledge

• Mean value theorem.