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Introduction to Calculus


T. Tsujioka
Advanced Seminar
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Introduction to Calculus

Part 1: Differential Calculus

Chapter 1. Limits

Finding Limits of Functions

Chapter 2. Derivatives

Definition of the Derivatives
Finding the Derivatives of Elementary (Polynomial, Rational, Irrational) Functions
Differential Coefficient and Tangent and Normal Lines to the Curves

Chapter 3. Graphs of Functions

Extrema and Drawing the Graphs
Maxima and Minima

Part 2: Integral Calculus

Chapter 4. Integrals

Definition of the Definite Integrals
Properties of the Definite Integrals

Chapter 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 Point

Chapter 7. Ordinary Differential Equations

Forming Differential Equations
Solving Differential Equations - Separation of Variables






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