Faculty of Science

Model (No 12)

Course Specification : تفاضل وتكامل - جبر وهندسة

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 :-

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- Course Learning Outcomes :-

4- Course contents :-

No	Topics	Week
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- Teaching and learning methods :-

S	Method
	lecturing
	tutorials
	Lectures supported by problem sheets and weekly small-group tutorials.

6- Teaching and learning methods of disables :-

7- Student assessment :-

A. Timing

B. Degree

8- List of books and references

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

S	Content	Study week
	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

Course Coordinator(s): -

Head of department: -

Ahmed Habeb Mohamed Nageb Elbassiony