The paper examines the features of visual thinking, the authors note the importance of visual examples in modern engineering education. The article describes a methodological approach to presenting the course, based on visual theorem proofs. An example is considered the course “Theory of multivariable function” Visual examples were created at the Department of Computational Mathematics and Mathematical Physics of the Bauman Moscow State Technical University. The proposed methodological approach to the development of the course “Theory of multivariable function” allows you to use the elements of the created course in various variations for disciplines using the concept of functions of many variables, depending on the direction of training (specialty).