Calculus

About the Book

The books covers all the basic topics of differential and integral calculus of functions of two variables all of the differentiation an integration formulas used to differentiate and integrate functions are derived with all of the steps included. Numerous examples and solved problems are also included illustrating the differentiating and integrating of a wide range of elementary functions. The elementary functions considered are:

1. The algebraic functions – polynomials, multinomials, etc.
2. Exponential functions
3. Logarithmic functions
4. Trigonometric functions
5. Inverse trigonometric functions
6. Hyperbolic functions
7. Inverse hyperbolic functions

The geometric applications of the derivative and the integral are discussed. The following topics are considered:

1. Increasing and decreasing curves
2. Relative maxima and minima
3. concave up, concave down, and points of inflection
4. Derivatives of arc length.
5. curvature, radius of curvature, center of curvature, and circle of curvature.
6. the area under a curve and the area between two curves
7. The length of an arc of a curve
8. The volume of revolution of a curve
9. The lateral surface area of revolution of a curve
10. Centroids:
    1. The centroid of an arc of a curve
    2. The centroid of a plane area
    3. The centroid of a volume of revolution
    4. The centroid of a lateral surface area of revolution

    The differentiation and integration of curves in polar coordinates is also discussed along with the geometric applications.

    Finally, numerous topics in the study of infintie series are discussed. Differential calculus is used to derive the McLauring series for the elementary functions. These infinitive series are then used to derive the basic relationships among the elementary functions.

About the Author

Edward Walsh graduated from Moorhead State College in Moorhead, Minnesota with a B.A. degree in Mathematics. He took a year of applied mathematics including coarses in Vector and Tensor analysis; partial differential equations: fourier analysis: and complex analysis.