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# List of Courses  ## Functions of Several Variables and ODE (Math 3)

• Course Code :
MTH 211
• Level :
• Course Hours :
3.00 Hours
• Department :
Department of Petroleum Engineering

## Area of Study :

 Develop the students' knowledge about several variables, multiple integrals, ordinary differential equations, and vector Analysis.  Train students to perform basic mathematical models on electrical engineering applications.

## Functions of Several Variables and ODE (Math 3)

Functions of several variables: Limits, Continuity, partial derivatives, Extrema and Constrained Extrema. Multiple integrals in Cartesian and Polar coordinates. Jacobians, Vector analysis: Scalar and vector fields, Gradient, Divergence, Curl and Directional derivative. Line integral, Green's theorem, Gauss's theorems, and Stoke theorem. Ordinary differential equations of the first and higher orders. Complementary and Particular solutions. Undetermined coefficients, and variation of parameters. Euler's equations and system of linear differential equations. Differential Operator method.

## a. Knowledge and Understanding:

 1- Recognize vector and scalar quantities in calculus. 2- Explain partial derivative for the functions of several variables. 3- Define the line integral for both scalar and vector fields. 4- Identify different types of first and higher order ordinary differential equations.

## b. Intellectual Skills:

 1- Apply theories of Vector analysis to solve engineering problems. 2- Solve the differential equations in engineering problems.

## c. Professional and Practical Skills:

 1- Solve the different types of line integral problems. 2- Apply the system of differential equations to solve Engineering problems.

## d. General and Transferable Skills:

 1- Communicate effectively.

## Course topics and contents:

Topic No. of hours Lecture Tutorial/Practical
Functions of several variables: Limits, Continuity, and partial derivatives, Chain rule. Tangent planes and normal lines, Extrema and Constrained Extrema. 10 6 4
Multiple integrals: Double integrals in Cartesian and Polar coordinates, Jacobians, Cylindrical and spherical coordinates 10 6 4
Vector analysis: Scalar and vector fields, Surface integrals of scalar and vector functions, gradient, divergence, curl, directional derivative, Line integrals. 10 6 4
Line integrals, Green's theorem, Gauss's theorem, Stoker's theorem and triple integrals in Cartesian and Polar coordinates. 10 6 4
Ordinary differential equations: Equations of the first order: Separable, Homogenous, nearly Homogenous, Exact, Linear, Bernoulli. Ricatti. 10 6 4
Higher order linear equations. Equations of the second order. Equations reducible to the first order. Complementary, and particular solutions. 10 6 4
Methods of Undetermined coefficients, and variation of parameters. Euler's equation 10 6 4
System of linear differential equations. Differential Operator method. 5 3 2

## Teaching And Learning Methodologies:

Teaching and learning methods
Interactive Lecture
Discussion
Problem-based Learning
Report

## Course Assessment :

Methods of assessment Relative weight % Week No. Assess What
Assignment 5.00
Final Exam 40.00
Lab.Computer 5.00
Mid- Exam I 15.00
Mid- Exam II 25.00
Quizzes 10.00

## Books:

Book Author Publisher

# List of Courses 