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# Course List

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

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

## Area of Study :

To familiarize students with the basic concepts of MTH 211 and to make them able to develop an understanding of mathematical concepts that provide a foundation for the mathematics encountered in Engineering. The course allows students to work at their own level thereby developing confidence in mathematics and general problem solving. On successful completion of this course the student will be able to: 1. demonstrate a sound understanding of a number of mathematical topics that are essential for studies in Engineering; 2. interpret and solve a range of problems involving mathematical concepts relevant to this course ; 3. Effectively communicate the mathematical concepts and arguments contained in this course.

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

Functions of several variables: limits, continuity and partial derivatives, Chain rule, Tangent planes and normal lines, Extrema and constrained extrema, Ordinary differential equations: equations of first order (separable, homogenous, exact, linear and Bernoulli), Orthogonal trajectories, Equations reducible to first order, High order linear equations, The variation of parameters and operation method, Euler's equation, System of linear differential equations, Series and tests of convergence, Taylor and Maclaurin expansion, Multiple integrals: double integral in Cartesian and Polar coordinates, Triple integrals and Jacobians, Line integral, Green's theorem,

## a. Knowledge and Understanding:

 1- i. Provide a through understanding and working knowledge of mathematics relevant to this course 2- ii. Develop techniques for solving problems that may arise in everyday life

## b. Intellectual Skills:

 1- Think logically 2- Analyze and solve problems 3- Demonstrate knowledge of the theory, concepts, of Functions of several variables , Ordinary differential equations, and vector Analysis at the intellectual level required of this course 4- Organize tasks into a structured form 5- evaluate the evolving state of knowledge in a rapidly developing area 6- • Transfer appropriate knowledge and methods from one topic within the subject to another

## c. Professional and Practical Skills:

 1- Understand. Limits, Continuity, and partial derivatives, Chain rule. Tangent planes and normal lines, Extrema and Constrained Extrema 2- Understand System of linear differential equations. differential Operator method 3- Gain the principle of quality control 4- • Develop skills related to creative thinking, and problem solving 5- Develop a professional attitude and approach to gain conceptual and practical knowledge and understanding Functions of several variables and Ordinary differential equations 6- Understand Multiple integrals: Double integral in Cartesian and Polar coordinates, Triple integrals, Surface integral of scalar functions , Jacobians, Cylindrical and spherical coordinates 7- Understand Scalar and vector fields, Gradient, Divergence, Curl and Directional derivative. Line integral, Green's theorem, Gauss's theorems, Stokes's theorems 8- Understand Ordinary differential equations: Equations of the first order: Separable, Homogenous, nearly Homogenous, Exact, Linear, Bernoulli. Ricatti. And Develop skills related to how to distinguish between them and determine the convenient method 9- Understand higher order linear equations. Equations of the second order. Complementary and particular solutions. Undetermined coefficients, variation of parameters. Euler's equation, Equations reducible to the first order

## d. General and Transferable Skills:

 1- Gain the principle of quality control 2- Develop skills related to creative thinking, and problem solving

## 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 integral in Cartesian and Polar coordinates. Triple integrals, Surface integral of scalar functions. Jacobians, Cylindrical and spherical coordinates 10 6 4
Vector analysis: Scalar and vector fields, Gradient, Divergence, Curl and Directional derivative. Line integral, Green's theorem, Gauss's theorems, Stokes's theorems 10 6 4
First-Exam
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. Complementary and particular solutions. Undetermined coefficients, variation of parameters. Euler's equation, Equations reducible to the first order 10 6 4
Second Exam
System of linear differential equations. Differential Operator method. 10 6 4
Final Exam

## Teaching And Learning Methodologies:

Teaching and learning methods
Lectures
Tutorial
Class discussions and activities
Homework and self-study

## Course Assessment :

Methods of assessment Relative weight % Week No. Assess What

## Books:

Book Author Publisher
Advanced Engineering Mathematics Warren S. Wright, Dennis G. Zill Jones & Bartlett Learning

## Course notes :

Course notes Handouts

## Recommended books :

(1) Larson, R, Edwards, B & Falvo, D 2004, Elementary linear algebra, 5th edn, Houghton Mufflin, Boston, Massachusetts. (2) Stewart, J 2005, Calculus: concepts & contexts, 3rd edn, Thomson/Brooks/Cole, Australia.

## Periodicals :

www.sosmath.com, www.math.hmc.edu

## Web Sites :

www.tutorial.math.lamar.edu, www.web.mit.edu