Differential Equations

About this course

The objective that is pursued with this subject is that the student knows the basic techniques of the integral calculus in several variables, vector calculus, ordinary differential equations and their applications.

Expected learning outcomes

Understanding of the basic concepts of integral calculus in several variables.
Knowledge of the main techniques of integration of functions of several variables.
Knowledge of the main results of the vector calculus and applications.
Acquisition of the basic knowledge for the resolution of equations and linear differential systems.
Understanding of the importance of integral calculus, vector calculus and differential equations for the study of the physical world.
Application of the knowledge of integral calculus, vector calculus and differential equations.
Acquisition of the necessary capacity to use these knowledge in the manual and computer resolution of questions, exercises and problems.

Indicative Syllabus

Ordinary differential equations. Solution concept. Existence and uniqueness theorems for initial condition problems. Methods for solving first-order ordinary differential equations: in separable variables, reducible to separable, homoxeneous, linear variables and reducible to linear variables. Exact differential equations. Integrating factors. Differential equation dunha family dun parameter of plane curves. Orthogonal trajectories. Linear differential equations of order 2 and of higher order. You are starting problems. Fundamental sets. Parameter variation method. Method two indeterminate coefficients. Order reduction. Euler’s equation. Linear differential formulation systems.

Teaching / Learning Methodology

lectures 92 hours
Problem solving 46 hours
Lab 9 hours
Exam 3 hours

Recommended Reading

TBA