كلية العلوم

نموذج رقم(12)

توصيف مقرر دراسي : تفاضل وتكامل (أ)

2010 - 2011

الفارابى لإدارة جودة التعليم والتعلم - 4/11/2025

الجامعة :جامعة المنصورة

الكلية :كلية العلوم

القسم :الرياضيات

1- 1- بيانات المقرر :-

2- 2- أهداف المقرر :-

This course is designed to introduce and develop skills in mathematics needed to guarantee a solid foundation for the applications of calculus to follow in later courses

3- 3- نواتج التعلم المستهدفة للمقرر :-

4- 4- محتويات المقرر :-

م	الموضوع	الأسبوع
1	Functions ~ Inequalities; domain and co-domain of a function; types of function; graph of a function; continuity; curve sketching; the function sin, cos, tan
2	Limits of functions (epsilon-delta definition of limit; negation)-continuity.
3	Differentiation ~ Basic ideas; tangent to a curve; the product and quotient rule; the chain rule for differentiating f(g(x)); the idea of implicit functions, implicit differentiation; use of derivatives in curve sketching; higher derivatives; maxima and minima of functions; conic sections, Leibniz rule.
4	Intermediate Theorem , Rolle Theorem and L’Hopitalle Rule for taking limits.
5	Leibnitz Theorem .
6	Further functions and their derivatives : Inverse functions; the log function ln ; the exponential function exp and ax; the inverse trigonometric functions sin-1, cos-1, tan-1; the hyperbolic functions sinh, cosh, tanh and their inverses sinh-1, cosh-1, tanh-1; complex exponentials.
7	Applications of Calculus

5- 5- أساليب التعليم والتعلم :-

م	الاسلوب
	3 Hours lectures per week
	3 Hours tutorials per week

6- 6- أساليب التعليم والتعلم للطلاب ذوى القدرات المحدودة :-

7- 7- تقويم الطلاب :-

- التوقيت

م	الطريقة	الأسبوع
1	Oral Exam	15
2	Final_Term Examination	16

- توزيع الدرجات

8- 8- قائمة الكتب الدراسية والمراجع

م	المراجع	النوع
1	Lecture notes prepared by academic staff members in the Department.
2	Howard Anton, Calculus, John Wily & Sons, INC 1999
3	Jordan, D.W. & Smith, P. Mathematical Techniques: An introduction for the engineering, physical, and mathematical sciences (3rd edition), Oxford University Press, Oxford, 2002
4	http://www.math.scar.utoronto.ca/calculus/Redbook/,
5	http://www.uwm.edu/Dept/Math/Resources/Calculus/Key/
6	http://math.ucalgary.ca/~ling/calculus/calculusnotes.htm
7	http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/
8	G.B.Thomas and Ross L. Finny "Calculus and Analytic Geometry(9th edition)" ,addison Wesley,1995 .

9- 9- مصفوفة المعارف والمهارات المستهدفة من المقرر الدراسي

م	المحتوى	أسبوع الدراسة
	Functions ~ Inequalities; domain and co-domain of a function; types of function; graph of a function; continuity; curve sketching; the function sin, cos, tan
	Limits of functions (epsilon-delta definition of limit; negation)-continuity.
	Differentiation ~ Basic ideas; tangent to a curve; the product and quotient rule; the chain rule for differentiating f(g(x)); the idea of implicit functions, implicit differentiation; use of derivatives in curve sketching; higher derivatives; maxima and minima of functions; conic sections, Leibniz rule.
	Intermediate Theorem , Rolle Theorem and L’Hopitalle Rule for taking limits.
	Leibnitz Theorem .
	Further functions and their derivatives : Inverse functions; the log function ln ; the exponential function exp and ax; the inverse trigonometric functions sin-1, cos-1, tan-1; the hyperbolic functions sinh, cosh, tanh and their inverses sinh-1, cosh-1, tanh-1; complex exponentials.
	Applications of Calculus

اساتذة المادة: -

رئيس مجلس القسم العلمى: -

أحمد حبيب محمد نجيب البسيونى