Introduction to Single Variable Calculus

 This is the Syllabus of Single Variable Calculus.

Overall, this blog would improve your Calculus knowledge.

(Notably, this blog is based on MIT 18.01, all posts are written by the author - khiemtonthat) 

I. Differentiation

    0. Limits Review

        P1: Introduction to Limits

        P2: Continuity

        P3: Limit of quotients 

    1.Definition and Basic Rules

    2. Implicit Differentiation and Inverse Function Differentiation

    3. Applications of Differentiation.

            a) Approximation and Curve Sketching

            b) Optimization, Related Rates and Newton's Method

            c) Mean Value Theorem, Antiderivative and Differential Equations 

II. Integration

    1. Definition of Definite Integral and First Fundamental

    2. Second Fundamental Theorem, Area, Volume

    3. Average Value, Probability, and Numerical Integration

    4. Techniques of Integration

            a) Trigonometric powers, trigonometric Substitution, and Completing the Square

            b) Partial Fraction, Integration by Parts, Arc Length, and Surface Area

            c) Parametric Equations and Polar Coordinates

III. Coordinate and Infinite

    1. L'Hopital's Rule and Improper Integrals

    2. Taylor Series