Calculus

This course consists of two parts:

1. Part 1: Functions of multiple variables

2. Part 2: Differential equations

In Part 1, we extend the student's knowledge of calculus applied to functions depending on one variable to functions depending on two or more variables.

We focus on the operations of differentiation and integration applied to such functions.

In addition, the student's "mathematical toolbox" will be expanded with techniques for working with vectors, taking derivatives and performing integration.

Topics in Part 1 are among others

• Vectors, inner product, cross product;

• Equations of lines and planes;

• Inverse trigonometric functions;

• Differentiation and Integration techniques;

• Functions of multiple variables;

• Partial and directional derivative;

• Extreme values of functions;

• Multiple integrals;

• Coordinate systems.

In Part 2, we focus on differential equations. These are needed during the modeling of physical phenomena in the study of the earth and climate.

We focus on solving some specific types of differential equations.

Topics in Part 2 are among others

• Complex numbers;

• Direction field;

• First and second order differential equations;

• Taylor polynomials.