DIFFERENTIAL EQUATIONS DOMAIN MATHEMATICS 1 Introduction to Differential

DIFFERENTIAL EQUATIONS DOMAIN: MATHEMATICS 1

Introduction to Differential Equations Differential equations are very important in engineering mathematics. A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders. It provides the medium for the interaction between mathematics and various branches of science and engineering. Most common differential equations are radioactive decay, chemical reactions, Newton’s law of cooling, series RL, RC and RLC circuits, simple harmonic motions, etc. 2

LEARNING OBJECTIVES 1. Define Exact DE and solve problems on it. (R) 2. Find the solution of reducible Exact DE(A) 3. Calculate the solution of reducible linear DE(A) 4. Identify appropriate method to solve DE occurring in electrical engg. (AN) LEARNING OUTCOMES At the end of this lesson Learner should be able to 1. develop the skill to identify the order of differential equations and to solve Exact differential equations. 2. identify and solve reducible to Exact differential equations. 3. develop the skill to identify the type of Exact differential equations solve reducible linear differential equations. 4. identify the differential equation appearing in engineering field and to solve it using appropriate method 3

Differential Equations of First Order & First Degree (10 marks) 4

TYPES OF DIFFERENTIAL EQUATIONS (1) Exact differential equations (2) Non-Exact differential equations reducible to exact form (3) Linear differential equations (4) Non-Linear differential equations reducible to linear form 5

Exact Differential Equation (4 marks) 6

Solution of Exact Differential Equation 7

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Non exact differential equations reducible to exact form (6 marks) 9

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