كلية العلوم

نموذج رقم(12)

توصيف مقرر دراسي : تفاضل وتكامل - جبر وهندسة

2010 - 2011

الفارابى لإدارة جودة التعليم والتعلم - 30/10/2025

الجامعة :جامعة المنصورة

الكلية :كلية العلوم

القسم :الرياضيات

1- 1- بيانات المقرر :-

2- 2- أهداف المقرر :-

To provide an elementary itroduction to the caculus including a review of foundation in algebra and geomtry.
This course is designed to introduce and develop skill in the 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	sets - determinants
2	matrices
3	complex numbers
4	the solution of the equations of the third and fourth degree
5	partial fractions
6	mathematical inductions
7	translation and rotation of axes
8	pairs of straight lines
9	conic sections
10	Functions ~ Inequalities; domain and co-domain of a function; types of function; graph of a function; continuity; curve sketching; the function sin, cos, tan
11	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.
12	Mean value theorem and Leibniz rule
13	Further functions and its 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
14	Applications of Calculus

5- 5- أساليب التعليم والتعلم :-

م	الاسلوب
	lecturing
	tutorials
	Lectures supported by problem sheets and weekly small-group tutorials.

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

7- 7- تقويم الطلاب :-

- التوقيت

- توزيع الدرجات

8- 8- قائمة الكتب الدراسية والمراجع

م	المراجع	النوع
1	Algebra - geometry
2	Calculus with analytic geometry
3	Howard Anton, Calculus, John Wily & Sons, INC 1999
4	Jordan, D.W. & Smith, P. Mathematical Techniques: An introduction for the engineering, physical, and mathematical sciences (3rd edition), Oxford University Press, Oxford, 2002

9- 9- مصفوفة المعارف والمهارات المستهدفة من المقرر الدراسي

م	المحتوى	أسبوع الدراسة
	sets - determinants
	matrices
	complex numbers
	the solution of the equations of the third and fourth degree
	partial fractions
	mathematical inductions
	translation and rotation of axes
	pairs of straight lines
	conic sections
	Functions ~ Inequalities; domain and co-domain of a function; types of function; graph of a function; continuity; curve sketching; the function sin, cos, tan
	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.
	Mean value theorem and Leibniz rule
	Further functions and its 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