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Differential calculus

Course Description: Introduction to functions and function modification - Function families and various types of functions - Introduction to limits and limit calculation - Continuity - Tangent lines, rates of change, and the derivative function - Various differentiation techniques - Chain rule and implicit differentiation - Derivatives of logarithmic, exponential, and inverse trigonometric functions - Related rates, local linear approximation, differentials, L'Hôpital's rule - Function analysis and concavity - Absolute maximum and minimum, optimization problems - Rectilinear motion, Rolle's Theorem, Mean Value Theorem.

Credit hours: 3

Objectives of the course :

a) This course aims to enhance students' knowledge in understanding different types of functions and their properties.
b) The course also aims to enhance students' knowledge of understanding limits and continuity.
c) It aims to enhance students' knowledge of understanding basic differentiation rules.
d) In addition, it aims to enhance students' knowledge of understanding the applications of calculus laws.
e) Furthermore, this course prepares students and develops their calculus skills, and provides them with the necessary knowledge in the English language to qualify them for enrollment in scientific colleges.

w) It aims to enhance students' mathematical thinking abilities.

Course outputs :

1. Knowledge:
Upon completion of this course, the student is expected to be able to:
Definition of different types of functions (linear, quadratic, trigonometric, and exponential) and identification of their properties.
– Explanation of the concepts of limits and continuity of functions at a point and over a given interval.
– Defining basic differentiation laws and derivation rules (such as the product rule, quotient rule, and chain rule).
- Comprehending basic mathematical terms in English used in scientific colleges.
2. Cognitive skills:
Upon completion of this course, the student is expected to be able to:
- Calculation of limits of algebraic and trigonometric functions using various analytical methods.
- Skillfully applying differentiation rules to find derivatives of complex functions.
– Analyzing mathematical problems and using calculus applications (such as finding extreme values and related rates) to solve real-life or engineering problems.
- Connecting different mathematical concepts to develop problem-solving strategies (mathematical thinking).
3. Soft Skills and Responsibility:
Upon completion of this course, the student is expected to be able to:
– Relying on oneself to find solutions to advanced mathematical problems.
– Adapting to studying scientific subjects in English as a preparation for university majors.
Making logical decisions based on sound deductive steps when solving problems.
4. Communication and Psychological Skills:
Upon completion of this course, the student is expected to be able to:
- Effective communication using the English language in a sports context (whether written or verbal).
- Skillfully and accurately using mathematical tools (whether manual or software-based) to represent functions and graphs.

Additional information:

Last update: 2026-09-08

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