Courses 3

 

Course Title:

Calculus Basics

Course Code:

Math 200

Credit Hours:

4

Prerequisite:

Calculus l Math-101

Text Books:

1.

-  H. Anton, I. Bivens and S. Davis; "Calculus ",  John Wiley and Sons. (2005).

2.

-Robert T. Smith & Roland B. Minton; Calculus: Mc-Graw Hill(2007).

3.

-  G. B. Thomas  "Calculus ", Addison Wesley Pub. Co. (2005).

Course Description:

Definiteandindefinite integralsoffunctionsof a single variable.  Applications of the definite integral to area, volume, arc length and surface of revolution Fundamental Theorem of Calculus. Techniques of integration including integration by substitutions, by parts, by partial fractions and by reduction. Mean value theorems and L'Hopital's rule. Definition of Hyperbolic and Inverse Hyperbolic functions and its differentiations and integrations. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series.

Learning Objectives:

-   To let the student know the definiteandindefinite integralsoffunctionsof a single variable.

-   To let the student identify the fundamental theorem of calculus, mean value theorems and L'Hopital's rule for undetermined limits.Provide the definiteandindefinite integralsoffunctionsof a single variable.

-   To let the student acquire different techniques of integration.

-   To let the student enumerate integration and its applications in parametric and polar coordinates.

- To let the student recognize the notion of improper integrals and their kinds.

-   To let the student understand alternating series, absolute and conditional convergence, power series. Taylor & Maclaurin series

Grading: 

No.

Assessment

Evaluation

1.

Med semester exam 1

25%

2.

Med Semester exam 2

25%

3.

Home works

5%

4.

Quizzes

5%

5.

Final Exam

40%

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Tutorials

3.

Homework

4.

Quizzes

Course Outline:

Week

Lecture Topics

1.

 Indefinite integrals,  Integration by substitution

2.

 Definite integral,  The fundamental Theorem of calculus, Definite integral by Substitution

3.

 Hyperbolic Functions

4.

 Area Between Two Curves, Volumes By Slicing ; Disks And Washers

5.

 Volumes By Cylindrical Shells, Length of a plane Curve,  Area of a Surface of Revolution

6.

Integration By parts,  Trigonometric Integrals

7.

Trigonometric Substitutions, Integrating Rational fractions

8.

Improper Integrals, Sequences

9.

Monotone Sequences, Infinite Series

10.

Convergence Tests, The Comparison ,Ratio, and Root  tests

11.

Alternating Series; Conditional convergence

12.

Maclaurian and Taylor polynomials

13.

Maclaurian And Taylor series; Power Series

14.

REVIEW FOR FINAL EXAM

15.

Course Title:

Basic Mathematics

Course Code:

Math 251

Credit Hours:

3

Prerequisite:

Calculus l Math-101

Text Books:

1.

Robert Wolf, Proof, Logic and Conjecture: The mathematician Toolbox, W. H. Freeman (1997).

2.

Seymour Lipschutz, Schaum, Outline of Theory & Problems of Set Theory and Related Topics, (1994), Int. Pub. & Dist. House, Cairo, Egypt.

3.

Course Description:

Set theory-symbols and expressions-union-intersection- difference- complement- Ven's diagram - sets. Numbers - natural numbers - integers numbers - rational numbers-real numbers. Relations and functions- cartesian product- binary relations-.operations on relations- composition of relations- equivalence relations and partitions. Maps- injective, surjective and bijective. Equivalence and countable sets- finite and infinite sets- power of a set- countable and uncountable sets.

Learning Objectives:

- Let the student present Basic concepts of mathematical logic.

- Let the student study of mathematical induction.

- Let the student acquire and development of skills on theory of sets.

Grading: 

No.

Assessment

Evaluation

1.

Med semester exam 1

25%

2.

Med Semester exam 2

25%

3.

Home works

5%

4.

Quizzes

5%

5.

Final Exam

40%

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Tutorials

3.

Homework

4.

Quizzes

Course Outline:

Week

Lecture Topics

1.

Set theory- symbols and expressions- union- intersection- difference- complement- Ven's diagram- sets.

2.

Operations on Sets.

3.

Finite Sets, Power Sets. Mathematical Induction

4.

Product Sets

5.

Relations, Composition of Relations, Partition

6.

Functions, Composition of Functions, One to one, Onto.

7.

Propositions and Compound Propositions

8.

Propositions and Truth Tables

9.

Logical Equivalence, Algebra of Propositions, Logical Implication

10.

Propositional functions

11.

Boolean Algebra as Lattices, sum of products form for Sets

12.

Representation theorem

13.

Sum of products form for Boolean Algebra

14.

Binary operations

15.

Review

Course Title:

Analytic Geometry

Course Code:

Math 261

Credit Hours:

3

Prerequisite:

Calculus l Math-101

Text Books:

1.

Calculus and Analytical Geometry", 9th Ed, Addison-Wesley 1998, George B. Thomas, Ross L. Finney, Publishing Company,     

2.

3.

Course Description:

Cartesian and polar coordinates-Vectors in plane-  algebra of vectors- angle between two vectors- dot product- vector product- triple product- area of triangle-Vectors in three dimensions-.Straight lines in plane-  Straight lines in space- parametric representation of straight line-Conic sections- circle- parabola- ellipse- hyperbola-Polar form of conic sections-Applications of conic sections in Astronomy, Cylindrical coordinates- Spherical coordinates

Learning Objectives:

Present the importance of the analytical geometry in Physics and Engineering Science, study the equations of the conic sections and its polar form with some applications in orbital Mechanics and introduce new coordinate systems, cylindrical and spherical coordinates.

Grading: 

No.

Assessment

Evaluation

1.

Med semester exam 1

25%

2.

Med Semester exam 2

25%

3.

Home works

5%

4.

Quizzes

5%

5.

Final Exam

40%

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Tutorials

3.

Homework

4.

Quizzes

Course Outline:

Week

Lecture Topics

1.

Cartesian and polar coordinates

2.

Vectors in plane-  algebra of vectors- angle between two vectors- dot product .

3.

vector product- triple product- area of triangle.Vectors in three dimensions.

4.

Straight lines in plane-  Straight lines in space - parametric representation of straight line.

5.

Equation for planes in space .

6.

Conic sections:  circle- parabola.

7.

Conic sections : ellipse- hyperbola.

8.

Translation of Axes .

9.

Rotation of Axes.

10.

Polar form of conic sections : circle- parabola.

11.

Polar form of conic sections: ellipse- hyperbola

12.

Cylindrical coordinates

13.

Spherical coordinates

14.

Revision