This online textbook provides an overview of Calculus in clear, easy to understand language designed for the non-mathematician. Calculus is the study of how things change. It provides a framework for modeling systems in which there is change, and a way to deduce the predictions of such models.
It provides a way for us to construct relatively simple quantitative models of change, and to deduce their consequences. The fundamental idea of calculus is to study change by studying “instantaneous” change, by which we mean changes over tiny intervals of time.
Table of Contents
- Why Study Calculus?
- Linear Functions
- Quadratics and Derivatives of Functions
- Rational Functions and the Calculation of Derivatives
- Exponential Functions, Substitution and the Chain Rule
- Trigonometric Functions and their Derivatives
- Inverse Functions and their Derivatives
- Numerical Differentiation, and Non-Differentiable Functions
- Review of Functions and Derivatives
- Modeling Applications to Physics
- More Modeling Applications
- Modeling Chemical Reactions and Predator Prey Situations
- Applications of Differentiation: Solving Equations
- Applications of Differentiation: Power Series
- The Antiderivative
- Areas and Volumes of Parallel Sided Figures
- Area under a Curve
- Numerical Integration
- Solving Differential Equations
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