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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 Petroleum Engineering

## Area of Study :

Functions of several variables: Limits, Continuity and partial derivatives, Tangent planes and normal lines, Chain rule, Extrema and Constrained Extrema, Taylor and Maclaurin expansion. Vector analysis: Scalar and vector fields, Gradient, Divergence, Curl and Directional derivative. Multiple integrals: Double integral in Cartesian and Polar coordinates, Triple integrals, Jacobians, Line integral, Green's theorem, Gauss's theorems, Stokes's theorems. Ordinary differential equations: Equations of first order, Separable, Homogenous, Exact, Linear, Bernoulli. Equations reducible to first order, High order linear equations, System of linear differential equations,

## 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- • 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 2- • Think logically. 3- • Analyze and solve problems. 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- • Develop a professional attitude and approach to gain conceptual and practical knowledge and understanding Functions of several variables and Ordinary differential equations. 2- • Understand. Limits, Continuity, and partial derivatives, Chain rule. Tangent planes and normal lines, Extrema and Constrained Extrema 3- • Understand Multiple integrals: Double integral in Cartesian and Polar coordinates, Triple integrals, Surface integral of scalar functions , Jacobians, Cylindrical and spherical coordinates, 4- • Understand Scalar and vector fields, Gradient, Divergence, Curl and Directional derivative. Line integral, Green's theorem, Gauss's theorems, Stokes's theorems. 5- • 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. 6- • 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, 7- • Understand System of linear differential equations. differential Operator method 8- • Gain the principle of quality control. 9- • Develop skills related to creative thinking, and problem solving.

## d. General and Transferable Skills:

 1- (i) Gain the principle of quality control. 2- (ii) 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
Assignments and Quizzes 20.00 1
Attendance and Participation 10.00 1
Final-term Exam 40.00 15 To assess overall understandings, concepts, Knowledge, Problem solving, and mathematical skills delivered by the course,
First Mid Exam 15.00 7 To assess the levels of math skills needed for successful completion of the course, and to improve teaching and learning for all students.
Second Mid Exam 15.00 12 To assess comprehension, Knowledge, Problem solving, and mathematical skills delivered by the course after 9 weeks of studying.

## Books:

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

## Course notes :

Course notes Handouts

## Recommended books :

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