رياضيات 2

MODULE DESCRIPTION FORM

نموذج وصف المادة الدراسية

Module Information معلومات المادة الدراسية
Module Title	Calculus II				Module Delivery
Module Type	S				☒ Theory ☒ Lecture ☒ Lab ☐ Tutorial ☐ Practical ☐ Seminar
Module Code	BOG1121
ECTS Credits	6
SWL (hr/sem)	150
Module Level		UGx11 UGI	Semester of Delivery				Two
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 class objectives for the given content are to develop students' proficiency in methods of integration including trigonometric substitutions and partial fractions, understanding of improper integrals, application of integration to calculate areas and volumes, determination of lengths of plane curves, exploration of surfaces of revolution, comprehension of polar coordinates and polar curves, and mastery of matrix operations and solving systems of linear equations using matrices.

Module Learning Outcomes

مخرجات التعلم للمادة الدراسية

Demonstrate proficiency in applying various methods of integration, including trigonometric substitutions, integration by parts, and partial fractions, to solve a variety of integrals.
Understand the concept of improper integrals and apply appropriate techniques to evaluate them.
Apply integration techniques to calculate areas under curves and between curves, and understand the relationship between integration and finding the area.
Use integration to determine volumes of solids of revolution using both the disk method and cylindrical shells method.
Calculate the lengths of plane curves using the appropriate formulas and techniques.
Apply integration to find the areas of surfaces of revolution.
Understand and utilize polar coordinates and equations to solve problems involving areas, volumes, and arc lengths of polar curves.
Develop proficiency in matrix operations, including matrix addition, multiplication, and finding determinants.
Apply matrix operations to find the inverse of a matrix and solve systems of linear equations using the inverse matrix method and Cramer's method.
Demonstrate critical thinking and problem-solving skills through the application of integration, matrices, and their respective techniques to real-world problems.

Indicative Contents

المحتويات الإرشادية

-Methods of Integrations: Trigonometric Substitutions, Integration by Parts, Integration of Rational Functions by

Partial Fractions, Powers of Trigonometric Functions, The substitution tan

z  x    

  .

- Improper Integrals.

- Areas: Area under a Curve, Area between Curves.

- Volumes of Solids of Revolutions: Volumes by Disk Method, Volumes by Cylindrical Shells.

- Lengths of Plane curves: Length of a Curve y f  x  , Length of a Curve x g  y  , Length of a Parametric Curve.

- Areas of Surfaces of Revolution.

- Polar Coordinates and Polar Curves: Areas, Volumes and Arc lengths of Polar Curves.

- Matrices: Algebra of Matrices, Determinant of a matrix, Inverse of a Matrix, Solutions of Systems of Linear

Equations (Inverse of a Matrix Method, Cramer's Method).

Learning and Teaching Strategies

استراتيجيات التعلم والتعليم

Strategies

The main strategy for delivering this module is to engage students actively in the learning process through a combination of lectures, interactive problem-solving sessions, and application-based activities, fostering their critical thinking skills and enhancing their understanding and proficiency in integration techniques, areas, volumes, lengths of curves, polar coordinates, and matrix operations.

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
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Week 13
Week 14
Week 15
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 2

Calculus II

S

BOG1121

6

150