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Calculus I and II
                 CONTENTS

   (첨부 및 아래 내용은 모두 original 한 우리의 내용입니다. 그리고 앞으로 모든 사람이 무료로 사용하게 될 것이랍니다. )

Preface

Part I  Single Variable Calculus

Chapter 1. Functions

1.1 History of Calculus

1.2 Symmetry

1.3 Common Functions

1.4 Translation, Stretching and Rotation of Functions

1.5 A Few Basic Concepts

Chapter 2. Limits and Continuity

2.1 Limits of functions

2.2 Continuity

Chapter 3. Theory of Differentiation

3.1 Definition of Derivatives, Differentiation

3.2 Derivatives of Polynomials, Exponential Functions, Trigonometric Functions, The product rule

3.3 The Chain Rule and Inverse Functions

3.4 Approximation and Related Rates

Chapter 4. Applications of Differentiation

4.1 Extreme values of a function

4.2 The Shape of a Graph

4.3 The Limit of Indeterminate Forms and L’Hospital’s Rule

4.4 Optimization Problems

4.5 Newton’s Method

Chapter 5. Integrals

5.1 Areas and Distances

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 Indefinite Integrals and the Net Change Theorem

5.5 The Substitution Rule

5.6 The Logarithm Defined as an Integral

Chapter 6. Applications of Integration

6.1 Areas between Curves

6.2 Volumes

6.3 Volumes by Cylindrical Shells

6.4 Work

6.5 Average Value of a Function

Chapter 7. Techniques of Integration

7.1 Integration by Parts

7.2 Trigonometric Integrals

7.3 Trigonometric Substitution

7.4 Integration of Rational Functions by the Method of Partial Fractions

7.5 Guidelines for Integration

7.6 Integration Using Tables

7.7 Approximate Integration

7.8 Improper Integrals

Chapter 8. Further Applications of Integration

8.1 Arc Length

8.2 Area of a Surface of Revolution

8.3 Applications of Integral Calculus

8.4 Differential equations

Chapter 9. Parametric Equations and Polar Coordinates

9.1 Parametric Equations

9.2 Calculus with Parametric Curves

9.3 Polar Coordinates

9.4 Areas and Lengths in Polar Coordinates

9.5 Conic Section

Chapter 10. Infinite Sequences and Infinite Series

10.1 Sequences and Series

10.2 Tests for convergence of series with positive terms

10.3 Alternating Series and Absolute Convergence

10.4 Power Series

10.5 Taylor, Maclaurin, and Binomial Series

Part II  Multivariate Calculus

Chapter 11. Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems

11.2 Vectors

11.3 The Scalar or Dot Product

11.4 The Vector or Cross Product

11.5 Equations of straight Lines and Planes

11.6 Cylinders and Quadric Surfaces

Chapter 12. Partial Derivatives and Local Maxima and Minima

12.1 Limits and Continuity of multi-variable functions

12.2 Partial Derivatives and Directional Derivatives

12.3 Tangent Plane and Differentiability

12.4 Local and global maximum and minimum

Chapter 13. Vector Functions

13.1 Vector-Valued Functions and Space Curves

13.2 Calculus of Vector Functions

13.3 Arc Length and Curvature

13.4 Motion Along A Space Curve: Velocity and Acceleration

Chapter 14. Multiple Integrals

14.1 Double Integrals

14.2 Cylindrical Coordinates and Spherical Coordinates

14.3 Volume Integrals

Chapter 15. Vector Calculus

15.1 Vector Differentiation

15.2 Line Integrals

15.3 Surface Integrals: Surface Area and Flux

15.4 Green’s Theorem in Plane: Transformation between line integral and double integral

15.5 Stokes’ Theorem: Transformation between line integral and surface integral

15.6 Gauss Divergence Theorem: Transformation between surface integral and volume integral

References

Index

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