Mathematics – Misr International University

Course ID

BAS111

Department

Undergraduate

Level

First Level

Credit

Faculty

Computer Science

Prerequisite

None

Overall aims of course

– Know and understand definitions, properties and graphs of transcendental functions.
– Evaluate derivatives and integrals related to transcendental functions with applications.
– Provide knowledge and ability of using different techniques of integration. As will as use integration for different engineering applications.
– Provide knowledge for conic section and know properties and operations upon complex numbers.

Intended learning outcomes of course (ILOs)

Knowledge and understanding

By the end of this course, the student should demonstrate comprehensive knowledge and clear understanding of the following:
a1- Know the different types of functions such as exponential, logarithmic, trigonometric and hyperbolic with their graphs, derivatives and integration.
a2- Define the inverse functions and their properties. Identify the L’Hospital’s rule.

a3- Identify and use almost all techniques of integration: integration by parts, integration by reduction, trigonometric integrals, and trigonometric substitutions, integrals of rational functions, quadratic expressions and substitutions.

a4- Enumerate integrals in different coordinate systems to find arc length and surface area.

a5- Identify the conic sections and knowing the basic algebraic operations on Complex Numbers.

Intellectual skills

By the end of this course, the student should be able to:
b1- Formulate mathematical problems.
b2- Apply different techniques of integration to solve engineering applications.
b3- Calculate area in polar coordinates; compute length of a curve and area of the surface generated by revolving a curve; compute limits involving indeterminate forms; evaluate improper integrals, analyze the conic sections.

Professional and practical skills

By the end of this course, the student should be able to:
c1- Develop skills to identifying and using all kinds of functions, and evaluating integrals by almost all known methods.
c2- Develop skills to constructing mathematical models corresponding to engineering problems

General and Transferable Skills

By the end of this course, the student should be able to:
d1- Work and deal with the advanced engineering mathematics.
d2- Develop skills related to creative thinking, problem solving, oral and written communication, and teamwork.

Course Contents

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Week	Topic	Intended Learning Outcomes
Week	Topic	K&U	IS	P&P	G&TS
One	Review of basic concepts of Derivative: Techniques of differentiation. Derivatives of algebraic , trigonometric functions	a1	b1	C1	d1
Two	The Derivative: The chain rule, implicit differentiation.	a1	b1	C1	d1
Three	The Derivative: Derivatives of exponential , logarithmic functions.	a1	b1	C1	d1
Four	Integrals: General integration formula for power, exponential , logarithmic and trigonometric functions	a1	b1, b2	C1	d1,d2
Five	Inverse Functions: Inverse functions and their derivatives. Inverse Trigonometric Functions.	a1, a2	b1,b2	C1, C2	d1
Six	Inverse Functions: Hyperbolic/Inverse Hyperbolic Functions. L’Hôspital’s rule.	a1, a2	b1, b2	C1, C2	d1
Seven	*Techniques of Integration*: Integration by Parts -By substitution. Trigonometric Integrals	a1, a2, a3	b1, b2	C1, C2	d1, d2
Eight	*Techniques of Integration*: Integration of Rational Functions by Partial Fractions.- Trigonometric substitutions	a1, a2, a3	b1, b2, b3	C1,C2	d1, d2
Nine	*Applications of Integration:* Areas – Volumes. Arc length – Area of a Surface of Revolution .	a1, a2, a3, a4	b1, b2, b3	C1, C2	d1,d2
Ten	*Parametric Equations and Polar Coordinates* Curves Defined by Parametric Equations – Calculus with Parametric Curves – Polar Coordinates.	a4, a5	b1, b2, b3	C1, C2	d1, d2
Eleven	Analytical Geometry: Conic Sections: Circle, Parabola. Ellipse, Hyperbolas.	a5	b1, b2, b3	C1, C2	d1, d2
Twelve	*Complex Numbers:* Basic concepts – Complex Plane – Complex Numbers in Cartesian, exponential and Polar forms. De Moivre’s Theorem. Roots of Equations. Euler’s formula with application.	a5	b1, b2, b3	C1,C2	d1,d2

Course coordinator: Dr. Emad Yacoub
Head of Department: Dr. Emad Yacoub

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