### رياضيات تطبيقية

:2 نظري2 +عملي

التعريف بأساسيات الهندسة التحليلية والتعرف على المنحنيات الشهيرة في المستوي الإحداثي إضافة إلى التركيز على كثيرات الحدود والتوابع والنهايات عليها ودراسة مفهومي الإشتقاق والتكامل وتطبيقاتهما الهندسية الشهيرة والتعرف على المجاميع والمتسلسلات اللانهائية وتقاربها وحل جمل المعادلات الخطية ودراسة المجموعات ومبادئ العد الأساسية والقواعد الأساسية لعلم الاحتمال

Preliminaries: Cartesian coordinates and distance, Lines (equation and graph), functions and their graphs, combining functions.

Limits and continuity: rates of change and limit, calculating limits using limits laws, formal definition of a limit, one-side limits, limits at infinity and asymptotes, continuity and operation on continuous functions, intermediate-value theorem for continuous functions.

Differentiation: tangents and derivatives, definition of derivatives, calculating derivatives (power rule, product rule, quotient rule, chain rule and implicit differentiation), derivatives of trigonometric functions, related rates and its applications, differential and its application.

Applications of derivatives: extreme values of functions, intermediate value theorem, monotonic function and first derivative test, second derivative test, functions variability and their graphs.

Integration: antiderivatives, sigma notation and limit of finite sums, estimating with finite sums, definite integrals, the fundamental theorem of calculus, indefinite integrals (substitution rule, integration by parts, integration of rational functions), area between curves, improper integrals.

Transcendental functions: inverse function and its derivative, inverse trigonometric functions, logarithmic and exponential functions.

Sequences and series:

Definition of a sequence.

Limit of a sequence.

Series.

Sequence of partial sums.

Tests of convergence: Dalembert and Cauchy and comparison tests.

Mac-Laurent series and its applications.