- عن بعد/اونلاين
- رياضيات | Mathematics
- جامعة ام القرى
## أولاً: كالكولاس 1 (Calculus 1)
**1. الدوال والتمثيلات البيانية (Functions and Graphs)**
Types of functions (linear, polynomial, rational, trigonometric, exponential, logarithmic), domain, range, and transformations.
*(تمت دراستها عبر Zoom)*
**2. النهايات والاستمرارية (Limits and Continuity)**
Definition of limit, limit laws, one-sided limits, infinite limits, limits at infinity, and continuity of functions.
*(تمت دراستها عبر Google Meet)*
**3. المشتقات (Derivatives)**
Definition of derivative, tangent lines, rates of change, differentiation rules, and derivatives of basic functions.
*(تمت دراستها عبر Microsoft Teams)*
**4. قواعد الاشتقاق (Differentiation Rules)**
Product rule, quotient rule, chain rule, and implicit differentiation.
*(تمت دراستها عبر Zoom)*
**5. تطبيقات المشتقات (Applications of Derivatives)**
Related rates, linear approximations, and differentials.
*(تمت دراستها عبر Google Meet)*
**6. القيم القصوى والدنيا (Maximum and Minimum Values)**
Absolute and local extrema, critical points, and the Extreme Value Theorem.
*(تمت دراستها عبر Microsoft Teams)*
**7. نظرية القيمة المتوسطة (Mean Value Theorem)**
Rolle's Theorem, Mean Value Theorem, and their applications.
*(تمت دراستها عبر Zoom)*
**8. رسم المنحنيات (Curve Sketching)**
Increasing/decreasing functions, concavity, inflection points, asymptotes, and graphing functions.
*(تمت دراستها عبر Google Meet)*
**9. المسائل الأمثلى (Optimization Problems)**
Solving real-world optimization problems using derivatives.
*(تمت دراستها عبر Microsoft Teams)*
**10. قواعد لوبيتال (L'Hôpital's Rule)**
Evaluating indeterminate forms using derivatives.
*(تمت دراستها عبر Zoom)*
**11. التكاملات غير المحددة (Antiderivatives and Indefinite Integrals)**
Definition of antiderivative, indefinite integrals, and basic integration formulas.
*(تمت دراستها عبر Google Meet)*
**12. التكامل المحدد (Definite Integrals)**
Riemann sums, definition of definite integral, properties, and the Fundamental Theorem of Calculus Part 1.
*(تمت دراستها عبر Microsoft Teams)*
**13. النظرية الأساسية للتكامل (Fundamental Theorem of Calculus)**
FTC Part 2, relationship between differentiation and integration, and applications.
*(تمت دراستها عبر Zoom)*
## ثانياً: كالكولاس 2 (Calculus 2)
**1. تقنيات التكامل - التعويض (Integration Techniques - Substitution)**
Integration by substitution, including trigonometric substitution and u-substitution.
*(تمت دراستها عبر Zoom)*
**2. التكامل بالتجزئة (Integration by Parts)**
Formula, repeated integration by parts, and applications.
*(تمت دراستها عبر Google Meet)*
**3. التكامل بالكسور الجزئية (Integration by Partial Fractions)**
Decomposing rational functions into partial fractions for integration.
*(تمت دراستها عبر Microsoft Teams)*
**4. التكاملات المثلثية (Trigonometric Integrals)**
Integrals involving powers of trigonometric functions and trigonometric identities.
*(تمت دراستها عبر Zoom)*
**5. التعويض المثلثي (Trigonometric Substitution)**
Using trigonometric substitutions for integrals involving √(a⊃2;-x⊃2;), √(a⊃2;+x⊃2;), and √(x⊃2;-a⊃2;).
*(تمت دراستها عبر Google Meet)*
**6. التكاملات غير الصحيحة (Improper Integrals)**
Integrals with infinite limits and discontinuous integrands, convergence and divergence tests.
*(تمت دراستها عبر Microsoft Teams)*
**7. تطبيقات التكامل - المساحات (Applications of Integration - Areas)**
Finding areas between curves and regions bounded by curves.
*(تمت دراستها عبر Zoom)*
**8. الحجوم (Volumes)**
Volumes by slicing, disk method, washer method, and cylindrical shells.
*(تمت دراستها عبر Google Meet)*
**9. أطوال المنحنيات ومساحات السطوح (Arc Length and Surface Area)**
Length of curves and area of surfaces of revolution.
*(تمت دراستها عبر Microsoft Teams)*
**10. المتتابعات (Sequences)**
Definition, limits of sequences, monotonic sequences, and bounded sequences.
*(تمت دراستها عبر Zoom)*
**11. المتسلسلات (Series)**
Definition of series, partial sums, geometric series, and the divergence test.
*(تمت دراستها عبر Google Meet)*
**12. اختبارات التقارب (Convergence Tests)**
Integral test, comparison test, limit comparison test, alternating series test, ratio test, and root test.
*(تمت دراستها عبر Microsoft Teams)*
**13. متسلسلات القوى (Power Series)**
Definition, radius and interval of convergence, and representations of functions as power series.
*(تمت دراستها عبر Zoom)*
**14. متسلسلات تايلور وماكلورين (Taylor and Maclaurin Series)**
Taylor and Maclaurin series expansions, remainder term, and approximations.
*(تمت دراستها عبر Google Meet)*
**15. الإحداثيات القطبية (Polar Coordinates)**
Polar coordinate system, converting between polar and Cartesian coordinates, and graphing polar equations.
*(تمت دراستها عبر Microsoft Teams)*
**16. المساحات والأطوال في الإحداثيات القطبية (Areas and Lengths in Polar Coordinates)**
Finding areas bounded by polar curves and lengths of polar curves.
*(تمت دراستها عبر Zoom)*
**17. المعادلات الوسيطية (Parametric Equations)**
Parametric curves, derivatives, and tangents to parametric curves.
*(تمت دراستها عبر Google Meet)*
**18. الأطوال والمساحات في المعادلات الوسيطية (Areas and Arc Lengths in Parametric Equations)**
Finding arc lengths of parametric curves and areas of surfaces of revolution.
*(تمت دراستها عبر Microsoft Teams)*
روابط ذات صلة