Course Description form
COURSE
TITLE
DIFFERENTIAL
ENGLISH
CODE
/NO
CREDITS
ARABIC
CODE/NO.
MATH203
203‫ر‬
Th.
Pr.
Tr.
TCH
3
-
-
-
EQUATIONS (2)
Pre-requisites
Brief contents, to be posted in university site and documents(4-5 lines):
The main ingredients of the course are:
Conic Sections and Polar Coordinates, Quadratic Equations and Rotations, Areas and
Lengths in Polar Coordinates, Vectors and the Geometry of Space, Lines and Planes in
Space, Cylinders and Quadric Surfaces, Vector-Valued Functions, Modeling Projectile
Motion, Planetary Motion and Satellites, Limits and Continuity in Higher Dimensions,
Partial Derivatives, Directional Derivatives and Gradient Vectors, Optimization,
Lagrange Multipliers, Taylor’s Formula for Two Variables.
Faculties and departments requiring this course (if any)
Objectives: Prefer In points

On completion of the course, the students should be able to
know about the basics of parameterization of plane curves, polar coordinates, and conic section;

use vectors in two and three dimensions to describe lines and planes in space;

understand sketching of quadric surfaces;

comprehend vector-valued functions and their use to describe the motion of objects through space;

grasp the idea of the epsilon-delta definition of the limit, and understand the methods for proving
existence and non-existence of limit of functions of two/three variables;

learn the idea of partial derivative and application of the chain rule;
solve optimization problems without and with constraints.
Contents: Prefer In points
Contents: Prefer In points
1. Conic Sections and Polar Coordinates, Quadratic Equations and Rotations, Areas
and Lengths in Polar Coordinates.
2. Vectors and the Geometry of Space, Lines and Planes in Space, Cylinders and
Quadric Surfaces.
3. Vector-Valued Functions, Modeling Projectile Motion, Planetary Motion and
Satellites.
4. Limits and Continuity in Higher Dimensions, Partial Derivatives, Directional
Derivatives and Gradient Vectors, Optimization, Lagrange Multipliers, Taylor’s
Formula for Two Variables.
Details
Unit I. Conic Sections and Polar Coordinates: Conic Sections and Quadratic Equations,
Classifying Conic Sections by Eccentricity, Quadratic Equations and Rotations, Conics
and Parametric Equations; The Cycloid, Polar Coordinates, Graphing in Polar
Coordinates, Areas and Lengths in Polar Coordinates, Conic Sections in Polar
Coordinates.
Unit II. Vectors and the Geometry of Space: Three-Dimensional Coordinate Systems,
Vectors, the Dot Product, the Cross Product, Lines and Planes in Space, Cylinders and
Quadric Surfaces.
Unit III. Vector-Valued Functions and Motion in Space: Vector Functions, Modeling
Projectile Motion, Arc Length and the Unit Tangent Vector T, Curvature and the Unit
Normal Vector N, Torsion and the Unit Binomial Vector B, Planetary Motion and
Satellites.
Unit IV. Partial Derivatives: Functions of Several Variables, Limits and Continuity in
Higher Dimensions, Partial Derivatives, The Chain Rule, Directional Derivatives and
Gradient Vectors, Tangent Planes and Differentials, Extreme Values and Saddle Points,
Lagrange Multipliers, Partial Derivatives with Constrained Variables, Taylor’s Formula
for Two Variables.
Course Outcomes:
A-
Knowledge:
(Specific facts and knowledge of concepts, theories, formula etc.)
The student will learn the basics of parameterization of plane curves, conic section, three
dimensional geometry, vector-valued functions with applications, and calculus of several
variables with applications.
B-Cognitive Skills
(Thinking, problem solving)
The student will improve his/her logical thinking and imagination to conceive and solve the practical
problems using the knowledge learnt in this course.
C- Interpersonal skills and responsibilities
(Group participation, leadership, personal responsibility, ethic and
moral behavior, capacity for self directed learning)
The student is expected to carry out an independent investigation of the topic by studying the available
material, interacting with fellow students and the instructor to obtain sufficient information, and then
analyse and manipulate this information to arrive at logical conclusions.
D- Analysis and communication:
)communication, mathematical and IT skills)
Activities such as group discussion and report-writing play a key role in enhancing communication skills.
Working independently and jointly is another important factor for developing such skills. Regular
feedback on the completed oral/written assignments with constructive and moral boosting comments must
be conveyed to the students in order to enhance such skills
Assessment methods for the above elements
Discussions, Homework, Periodic tests and final test
Text book: Only one
Thomas' Calculus, 11th Edition Media Upgrade, Addison Wesley, Pearson, 2008
Supplementary references
Details of Weekly Distributed Material
Remarks
Contents
Conic Sections and Quadratic Equations - Classifying Conic
Sections by Eccentricity
Quadratic Equations and Rotations - Conics and Parametric
10.3,10.4,10.5
Equations; The Cycloid - Polar Coordinates
Graphing in Polar Coordinates - Areas and Lengths in Polar
10.6,10.7,10.8
Coordinates - Conic Sections in Polar Coordinates
Three-Dimensional Coordinate Systems, Vectors, The Dot
12.1,12.2,12.3
Product
12.4,12.5
The Cross Product - Lines in Space
12.5,12.6
Planes in Space - Cylinders and Quadric Surfaces
13.1,13.2
Vector Functions, Modeling Projectile Motion
Arc Length and the Unit Tangent Vector T, Curvature and the
13.3,13.4
Unit Normal Vector N
Torsion and the Unit Binomial Vector B, Planetary Motion and
13.5,13.6
Satellites
Functions of Several Variables, Limits and Continuity in Higher
14.1,14.2
Dimensions
14.3,14.4
Partial Derivatives -The Chain Rule
Directional Derivatives and Gradient Vectors - Tangent Planes
14.5,14.6,14.7
and Differentials - Extreme Values and Saddle Points
Lagrange Multipliers - Partial Derivatives with Constrained
14.8,14.9,14.10
Variables Taylor’s Formula for Two Variables
Review
Review
10.1,10.2
Final exam.
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