Calculus 2 - AUK ( منهج د. الهام )

Course contentAreas and DistancesThe Fundamental Theorem of CalculusIndefinite Integrals and the Net Change TheoremThe Substitution RuleAreas Between CurvesIntegration by PartsTrigonometric IntegralsTrigonometric SubstitutionIntegration of Rational Functions by Partial Fractionsimproper integralArc LengthSequencesSeriesThe Integral TestAlternating SeriesAbsolute Convergence and the Ratio and Root TestsPower SeriesTaylor and Maclaurin SeriesThis course provides a comprehensive exploration of integral calculus and its applications, building on foundational concepts to develop a deep understanding of key mathematical techniques and theorems. The content begins with areas and distances, introducing integral concepts to calculate areas under curves and between functions. The Fundamental Theorem of Calculus is presented as a cornerstone, linking differentiation and integration to solve real-world problems efficiently.

Learners will master indefinite integrals and explore the Net Change Theorem, which highlights the accumulation of quantities. The course delves into the Substitution Rule, a vital tool for simplifying complex integrals. Applications such as finding areas between curves, using integration by parts, and handling trigonometric integrals further enhance practical skills.

Techniques like trigonometric substitution and partial fractions are introduced to solve challenging rational function integrals. The concept of improper integrals extends the applicability of integration to functions with infinite limits or discontinuities. The course also explores geometric applications, including arc length calculations.

A transition to infinite processes is made through sequences and series, where students learn the Integral Test, Alternating Series Test, and convergence techniques such as the Ratio and Root Tests. Finally, the exploration of power series and Taylor and Maclaurin Series equips students with tools for approximating functions, laying the foundation for advanced mathematical and scientific studies. 4o.