Sinopsis
Calculus is fundamentally different from the mathematics that you have studied previously: calculus is less static and more dynamic. It is concerned with change and motion; it deals with quantities that approach other quantities. For that reason it may be useful to have an overview of the subject before beginning its intensive study. Here we give a glimpse of some of the main ideas of calculus by showing how the concept of a limit arises when we attempt to solve a variety of problems.
Content
- Functions and Limits
- Derivatives
- Applications of Differentiation
- Integrals
- Applications of Integration
- Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
- Techniques of Integration
- Further Applications of Integration
- Differential Equations
- Parametric Equations and Polar Coordinates
- Infinite Sequences and Series
- Vectors and the Geometry of Space
- Vector Functions
- Partial Derivatives
- Multiple Integrals
- Vector Calculus
- Second-Order Differential Equations
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