Definition of complex number A Complex number is a pair of real numbers (x;y). Its algebraic form is z=x+i*y, where i is an imaginary…

# Category: Mathematics for Engineering

**Mathematics for Engineers****: Preface**

**Aim of the study element**

To effectively use mathematics for solving engineering problems complex numbers, vectors, integral and differential calculus, matrices and differential equations.

**Learning outcome**

Having successfully completed this element you will be able to:

- Use basic concepts of complex numbers, vectors, integral and differential calculus, matrices and differential equations in application to engineering.
- Resolve engineering problems using mathematical tools.
- Analyse and resolve complex engineering problems, combining basic mathematical concepts.
- Select and use proper mathematical tools for the solution of problems in circuits.

**Covered topics:**

- Complex numbers.
- Derivatives.
- Integral and differential calculus.
- Matrices and operations.

## Complex numbers 2

Let's suggest a function y=f(x) that is defined on the interval (a,b). Choose a point x on the interval (a,b), and another point x+∆x…

## Differentiability, differential of a function and integral

If function y=f(x) has a derivative in the point x: lim∆x→0 ∆y∆x=f' (x) Let's introduce the function: α(x)=∆y∆x-f' (x)=f(x+∆x)-f(x)∆x-f' (x) Function α(x) exists with the…

## Quiz

Solve this quiz and write your answers in comments. Exercise 1. Calculate: a. 5-1i3+i;b. (7+2i)-(3-2i)+(11+i)-(17-3i);c. (2+i)*(5-2i)+(6+13i)*(7-i);d. -13+6i2-i+ (8-i5+2i)2 Exercise 2. Calculate: Re(12-i6+3i), Im(-2i5+i) Exercise 3. Find all…