The Real Numbers. Infinite Sequences, Subsequences (Including Bolzano-Weierstrass Theorem). Real Function of One Variable: Limits and Continuity, Continuous Functions on a Closed Interval (Weierstrass Theorems, Intermediate Value Theorem), Monotone Functions and Invertible Functions. Differentiability and the Main Theorems of Differential Calculus: the Theorems of Fermat, Rolle, Lagrange and Cauchy. L'Hopital S Rule, Taylor S Theorem, Analyzing Functions. Primitive and Methods of Integration, Definite Integral and Its Properties, Integrable Functions, the Fundamental Theorem of Calculus, Improper Integral. Numerical Series. Remark: in This Course There Is a Greater Emphasis on Theory and Applications Than in 104018.