Title:

Author:

Introduction to Calculus

Copyright:

T. Tsujioka

Advanced Seminar

Introduction to Calculus

Part 1: Differential Calculus

Chapter 1. Limits

Finding Limits of Functions

ContinuityChapter 2. Derivatives

Definition of the Derivatives

Finding the Derivatives of Elementary (Polynomial, Rational, Irrational) Functions

Differential Coefficient and Tangent and Normal Lines to the CurvesChapter 3. Graphs of Functions

Extrema and Drawing the Graphs

Maxima and Minima

Part 2: Integral CalculusChapter 4. Integrals

Definition of the Definite Integrals

Properties of the Definite IntegralsChapter 5. Finding Anti-derivatives or Indefinite Integrals

Chapter 6. Applications

Area in 2-D Plane

Volume of Revolving Objects

Length of a Curve in 2-D Plane

Moved Distance, Velocity, and Acceleration of a Mathematical PointChapter 7. Ordinary Differential Equations

Forming Differential Equations

Solving Differential Equations - Separation of Variables