Faculty of Science

Model (No 12)

Course Specification : تفاضل وتكامل - جبر وهندسة

2010 - 2011

Farabi Quality Management of Education and Learning - 4/12/2024

University :Mansoura University

Faculty :Faculty of Science

Department :Physics Department

1- Course data :-

2- Course aims :-

The programme unit aims to provide a firm foundation in the concepts and techniques of the calculus, including real numbers, standard functions, curve sketching, limits, continuity, differentiation, integration of functions of one variable. The core concepts of limits, differentiation and integration are revised. Techniques for applying the calculus are developed and strongly reinforced. Also, the aims of this course are to provide a basic introduction to various methods of proof used in mathematics and to the fundamental ideas in the study of sets, numbers, functions and conic sections. This course is basic course for biologically students and other students.

3- Course Learning Outcomes :-

4- Course contents :-

No	Topics	Week
1	Differention: Functions. Limits and continuity.
2	Differentiation: (Basic ideas; tangent to a curve; the product and quotient rule; the chain rule for differentiating f(g(x)); higher derivatives, implicit differentiation)
3	Derivatives of trigonometric functions and their inverse. Derivatives of the log function ln; the exponential function exp and ax.
4	Derivatives of hyperbolic functions and their inverse. Applications of derivatives
5	Integration: Integration
6	Techniques of Integration: (Integration by substitution-Integration of trigonometric and hyperbolic functions - Integration of parts - Integration of rational functions by partial fractions- Integration of parameter dependent functions)
7	Applications of Integration
8	Algebra: sets.
9	Determinants – matrices
10	mathematical induction. Partial fractions . Geometry: Translation and Rotation of Axes,
11	complex numbers. Pairs of Straight Lines
12	Conic Sections

5- Teaching and learning methods :-

S	Method
	Lectures (4H/W).
	Tutorial (4H/w).

6- Teaching and learning methods of disables :-

The same as normal students, only skeletal disabilities are allowed in the Faculty of Science.

7- Student assessment :-

A. Timing

No	Method	Week
1	final exam	14
2	oral exam	14

B. Degree

8- List of books and references

S	Item	Type
1	Course Notes: Available in the Dept.
2	H Edwards, Elementary differential equations with boundary value problems, Pearson Prentice Hall, 2004.
3	H. Anton, Elementary Linear Algebra, Wiley 1994. Linear Algebra, by Seymour Lip schuts.
4	1- W.E. Boyce & R.C. Di Prima, "Elementary Differential Equations and Boundary Value Problems", Wiley. 2- M. Braun, "Differential Equations and their Applications", Springer-Verlag
5	C.H. Edwards & D.E. Penney, "Elementary Differential Equations with Boundary Value Problems", Prentice Hall.
6	5- R.K. Nagle & E.B. Saff, & A.D. Snider, "Fundamentals of Differential Equations and Boundary Value Problems", Addison-Wesley.
7	1- http://en.wikipedia.org/wiki/Calculus 2- http://www.math.niu.edu/~beachy/aaol / 3- http://www.sosmath.com/calculus/calculus.html

9- Matrix of knowledge and skills of the course

S	Content	Study week
	Differention: Functions. Limits and continuity.
	Differentiation: (Basic ideas; tangent to a curve; the product and quotient rule; the chain rule for differentiating f(g(x)); higher derivatives, implicit differentiation)
	Derivatives of trigonometric functions and their inverse. Derivatives of the log function ln; the exponential function exp and ax.
	Derivatives of hyperbolic functions and their inverse. Applications of derivatives
	Integration: Integration
	Techniques of Integration: (Integration by substitution-Integration of trigonometric and hyperbolic functions - Integration of parts - Integration of rational functions by partial fractions- Integration of parameter dependent functions)
	Applications of Integration
	Algebra: sets.
	Determinants – matrices
	mathematical induction. Partial fractions . Geometry: Translation and Rotation of Axes,
	complex numbers. Pairs of Straight Lines
	Conic Sections

Course Coordinator(s): -

Head of department: -

Ahmed Habeb Mohamed Nageb Elbassiony