رياضيات 3

MODULE DESCRIPTION FORM

نموذج وصف المادة الدراسية

Module Information معلومات المادة الدراسية
Module Title	Calculus III				Module Delivery
Module Type	B				☒ Theory ☒ Lecture ☒ Lab ☐ Tutorial ☐ Practical ☐ Seminar
Module Code	BOG1131
ECTS Credits	6
SWL (hr/sem)	150
Module Level		UGx11 UGII	Semester of Delivery				Three
Administering Department		Oil and Gas Engineering	College	Oil and Gas Engineering
Module Leader			e-mail
Module Leader’s Acad. Title			Module Leader’s Qualification
Module Tutor			e-mail
Peer Reviewer Name			e-mail
Scientific Committee Approval Date			Version Number			1.0

Relation with other Modules

العلاقة مع المواد الدراسية الأخرى

Prerequisite module

Semester

Co-requisites module

Semester

Module Aims, Learning Outcomes and Indicative Contents

أهداف المادة الدراسية ونتائج التعلم والمحتويات الإرشادية

Module Objectives

أهداف المادة الدراسية

The objectives of this class are to develop a solid understanding and proficiency in several key mathematical concepts. Firstly, students will learn about polar coordinates and their applications, including the representation of polar curves and the calculation of area in polar coordinates. Secondly, they will explore the principles of vectors, lines, planes, and surfaces, gaining the ability to manipulate and analyze these geometric entities. Additionally, the class will cover cylindrical and spherical coordinates, providing students with the tools to describe and work with objects in three-dimensional space.

Furthermore, students will delve into the realm of functions of two and three variables, studying topics such as limits, continuity, and partial derivatives. This knowledge will enable them to evaluate directional derivatives and solve optimization problems by identifying extrema of functions with multiple variables. The class will also introduce the concept of double integrals, teaching students how to calculate them in both rectangular and polar coordinates and apply them in the context of area and volume calculations.

Lastly, the course will cover triple integrals and their applications, with a focus on cylindrical and spherical coordinates. Students will develop proficiency in evaluating triple integrals and utilizing them for problems involving volumes and mass calculations. By the end of the class, students will have acquired a solid foundation in these mathematical concepts and be equipped with the necessary skills to apply them in various fields of study.

Module Learning Outcomes

مخرجات التعلم للمادة الدراسية

Understand and apply the concepts of polar coordinates, including the representation of polar curves and the calculation of area in polar coordinates.
Demonstrate proficiency in working with vectors, lines, planes, and surfaces, and apply them to solve geometric problems.
Gain proficiency in cylindrical and spherical coordinates, and effectively describe and manipulate objects in three-dimensional space using these coordinate systems.
Develop a strong understanding of functions of two and three variables, including limits, continuity, and partial derivatives, and apply these concepts to solve problems involving multivariable functions.
Apply the principles of extrema to optimize functions of two variables, identifying maximum and minimum values.
Master the techniques of evaluating double integrals, both in rectangular and polar coordinates, and apply them to calculate areas and solve related problems.
Understand the concept of triple integrals and apply them in cylindrical and spherical coordinates to calculate volumes and solve relevant problems.
Develop critical thinking and problem-solving skills through the application of mathematical concepts to real-world scenarios.
Enhance computational skills through the use of mathematical software and tools for numerical calculations and visualizations.
Prepare for further studies in mathematics, engineering, physics, and other disciplines that require a solid foundation in multivariable calculus.

Indicative Contents

المحتويات الإرشادية

Polar coordinates, polar curves, area in polar coordinates. Vectors, lines, planes and surfaces. Cylindrical and spherical coordinates. Functions of two and three variables, limits and continuity. Partial derivatives, directional derivatives. Extrema of functions of two variables. Double integrals, double integrals in polar coordinates. Triple integrals, triple integrals in cylindrical and spherical coordinates.

Learning and Teaching Strategies

استراتيجيات التعلم والتعليم

Strategies

The main strategy for delivering this module is to actively engage students in the learning process, fostering their participation in exercises and activities. The aim is to enhance their critical thinking skills and deepen their understanding of the subject matter. This will be accomplished through interactive classes, tutorials, and practical experiments that involve hands-on experiences and relevant sampling activities. By creating an engaging and interactive learning environment, students will be encouraged to actively explore and apply the concepts of polar coordinates, vectors, functions, derivatives, and integrals in various contexts.

Student Workload (SWL)

الحمل الدراسي للطالب محسوب لـ ١٥ اسبوعا

Structured SWL (h/sem)

الحمل الدراسي المنتظم للطالب خلال الفصل

Structured SWL (h/w)

الحمل الدراسي المنتظم للطالب أسبوعيا

Unstructured SWL (h/sem)

الحمل الدراسي غير المنتظم للطالب خلال الفصل

Unstructured SWL (h/w)

الحمل الدراسي غير المنتظم للطالب أسبوعيا

Total SWL (h/sem)

الحمل الدراسي الكلي للطالب خلال الفصل

150

Module Evaluation تقييم المادة الدراسية
As		Time/Number	Weight (Marks)	Week Due	Relevant Learning Outcome
Formative assessment	Quizzes		10% (10)	5 and 10	LO #1, #2 and #10, #11
	Assignments		10% (10)	2 and 12	LO #3, #4 and #6, #7
	Projects / Lab.		10% (10)	Continuous	All
	Report		10% (10)	13	LO #5, #8 and #10
Summative assessment	Midterm Exam	1hr	10% (10)	7	LO #1 - #7
Summative assessment	Final Exam	2hr	50% (50)	16	All
Total assessment			100% (100 Marks)

Delivery Plan (Weekly Syllabus) المنهاج الاسبوعي النظري
Week	Material Covered
Week 1	Introduction to Polar Coordinates and Polar Curves
Week 2	Area in Polar Coordinates
Week 3	Vectors, Lines, Planes, and Surfaces
Week 4	Introduction to Cylindrical and Spherical Coordinates
Week 5	Functions of Two and Three Variables, Limits, and Continuity
Week 6	Partial Derivatives and Directional Derivatives
Week 7	Extrema of Functions of Two Variables
Week 8	Double Integrals and Double Integrals in Polar Coordinates
Week 9	Triple Integrals and Triple Integrals in Cylindrical and Spherical Coordinates
Week 10	Review and Practice
Week 11	Mid-semester Examination (Week 7)
Week 12	Applications of Multivariable Calculus
Week 13	Review of Concepts and Problem-solving Techniques
Week 14	Final Exam Preparation and Practice
Week 15	Revision and Recap
Week 16	Preparatory week before the final Exam

Delivery Plan (Weekly Lab. Syllabus) المنهاج الاسبوعي للمختبر
Week	Material Covered
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7

Learning and Teaching Resources مصادر التعلم والتدريس
	Text	Available in the Library?
Required Texts
Recommended Texts
Websites

Grading Scheme مخطط الدرجات
Group	Grade	التقدير	Marks %	Definition
Success Group (50 - 100)	A - Excellent	امتياز	90 - 100	Outstanding Performance
	B - Very Good	جيد جدا	80 - 89	Above average with some errors
	C - Good	جيد	70 - 79	Sound work with notable errors
	D - Satisfactory	متوسط	60 - 69	Fair but with major shortcomings
	E - Sufficient	مقبول	50 - 59	Work meets minimum criteria
Fail Group (0 – 49)	FX – Fail	راسب (قيد المعالجة)	(45-49)	More work required but credit awarded
Fail Group (0 – 49)	F – Fail	راسب	(0-44)	Considerable amount of work required

Note: Marks Decimal places above or below 0.5 will be rounded to the higher or lower full mark (for example a mark of 54.5 will be rounded to 55, whereas a mark of 54.4 will be rounded to 54. The University has a policy NOT to condone "near-pass fails" so the only adjustment to marks awarded by the original marker(s) will be the automatic rounding outlined above.

رياضيات 3

Calculus III

B

BOG1131

6

150