Faculty of Science

Model (No 12)

Course Specification : تفاضل وتكامل (أ)

2010 - 2011

Farabi Quality Management of Education and Learning - 22/12/2024

University :Mansoura University

Faculty :Faculty of Science

Department :Mathematics Department

1- Course data :-

2- Course aims :-

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- Course Learning Outcomes :-

4- Course contents :-

No	Topics	Week
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- Teaching and learning methods :-

S	Method
	3 Hours lectures per week
	3 Hours tutorials per week

6- Teaching and learning methods of disables :-

7- Student assessment :-

A. Timing

No	Method	Week
1	Oral Exam	15
2	Final_Term Examination	16

B. Degree

8- List of books and references

S	Item	Type
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- Matrix of knowledge and skills of the course

S	Content	Study week
	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

Course Coordinator(s): -

Head of department: -

Ahmed Habeb Mohamed Nageb Elbassiony