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المقرر 105 ريض

اسم المقرر بالعربي: حساب التفاضل.

اسم المقرر بالإنجليزي:  Differential Calculus.

الوصف بالعربي:

الأعداد الحقيقية، الدوال، النهايات،الاتصال،الاشتقاق، التفاضلي، قانون السلسلة، الاشتقاق الضمني، المشتقات العليا، القيم القصوى المحلية، التقعر،المستقيمات التقاربية الأفقية والرأسية، تطبيقات على القيم القصوى ومعدلات التغير المترابطة، نظرية رول، نظرية القيمة المتوسطة، الدوال المثلثية العكسية،القطوع المخروطية.

 

SYLLABUS

Real numbers, functions, Limits, continuity. Derivatives, differentials, chain rule, implicit differentiation. Higher order derivatives, local extrema, concavity, horizontal and vertical asymptotes, applications of extrema, related rates. Rolle's theorem, mean value theorem, inverse trigonometric functions. Conic sections.

 

الكتاب المقرر:

مراجع إضافية:

منسق المقرر:

 

Course Description

 

M - 105 Differential Calculus

 

Real numbers, functions, Limits, continuity. Derivatives, differentials, chain rule, implicit differentiation. Higher order derivatives, local extrema, concavity, horizontal and vertical asymptotes, applications of extrema, related rates. Rolle's theorem, mean value theorem, inverse trigonometric functions. Conic sections.

 

Prerequisite:    NIL

 

Textbook(s)/ Required Material

 

Calculus by Edward and Penny  6th Ed  (International Edition).

 

Course details:

1. Functions, Graphs, and Models.

Functions and Mathematical Modeling. Graphs of Equations and Functions. Polynomials and Algebraic Functions. Transcendental Functions. Preview: What Is Calculus?



2. Prelude to Calculus.

Tangent Lines and Slope Predictors. The Limit Concept. More about Limits. The Concept of Continuity.



3. The Derivative.

The Derivative and Rates of Change. Basic Differentiation Rules. The Chain Rule. Derivatives of Algebraic Functions. Maxima and Minima of Functions on Closed Intervals. Applied Optimization Problems. Derivatives of Trigonometric Functions. Successive Approximations and Newton's Method.



4. Additional Applications of the Derivative.

Implicit Functions and Related Rates. Increments, Differentials, and Linear Approximation. Increasing and Decreasing Functions and the Mean Value Theorem. The First Derivative Test and Applications. Simple Curve Sketching. Higher Derivatives and Concavity. Curve Sketching and Asymptotes.

5. Calculus of Transcendental Functions.  Inverse Trigonometric Functions.


10. Analytic Geometry and the Conic Sections.  Conic Sections and Applications.

 

Course Objectives/ Course outcome:

 

To provide students with knowledge and understanding of a range of  mathematical techniques appropriate to engineering.

At the end of this set of modules the student should be able to:
manipulate algebraic expressions and equations.
Understand and apply appropriately inverse functions, trigonometric functions, polynomial functions, rational functions, circular functions, conic section.

Understand the concept of Limit and continuity.

Understand the meaning of a derivative, be able to differentiate simple functions, products and quotients, and be able to use the chain rule and differentials.

In particular the course will concentrate on learning to use mathematics as a tool and will include many worked examples.



 

Class/ Tutorial (Laboratory) Schedule

 

Three  one -hour lecture sessions and two one - hour tutorial sessions per week.

 

Assessment Tools

  1. Final Examination
  2. Mid term examinations
  3. Homework Assignments
  4. Class Quizzes
  5. Attendance
  6. Tutorial Judgment

 

 

Prepared by

 

Dr. Khawaja Zafar Elahi   [ kzelahi@ksu.edu.sa]

تقسيم الدرجات:

§         اختبار الفصل الأول:

§         اختبار الفصل الثاني:

§         درجات التمارين: 10 درجات = 5 درجات لواجبين + 5 درجات لاختبارين موجزين

§         الامتحان النهائي:

 

مواعيد الاختبارات:

§         موعد الاختبار الفصلي الأول.

§         موعد لاختبار الفصلي الثاني.

§         موعد الاختبار النهائي.

§         موعد الاختبار البديل(إن وجد).

نماذج اختبارات سابقة:

الاختبار النهائي في الفصل الثاني 1425/1426هـ
الاختبار النهائي في الفصل الأول 1426/1427هـ
الاختبار النهائي في الفصل الثاني 1426/1427هـ

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 مواقع مساعدة للمقرر 105 ريض

 ملفات 105 ريض

Folder: Mid-term 1Mid-term 1No presence informationFawaz Alotaibi
Folder: Mid-term 2Mid-term 2No presence informationFawaz Alotaibi
Folder: Final ExamFinal ExamNo presence informationFawaz Alotaibi
Folder: BooksBooksNo presence informationFawaz Alotaibi
Folder: QuizzesQuizzesNo presence informationFawaz Alotaibi
Folder: HomeworkHomeworkNo presence informationFawaz Alotaibi
Folder: othersothersNo presence informationFawaz Alotaibi
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