MATH 113, Calculus I
### MATH 113, Calculus I

**Overview**

Calculus is the mathematics of continuously changing phenomena. In this course we will learn to describe such phenomena mathematically, identify and apply the methods of calculus to analyze these phenomena by hand and with technology, and present conclusions in plain English. The mathematical concepts and techniques include: the limit as a description of the local behavior of a function, the derivative as a measure of rate of change, the integral as a measure of accumulated change, differentiation techniques and applications, antiderivatives and the fundamental theorem of calculus, and basic integration techniques.

**Prep Packets (reading guides, with exercises)**

- Functions (Ch 1)
- Limits (2.1, 2.2)
- Combining Functions and Evaluating Limits (1.3, 2.3)
- Continuity and the IVT (2.5)
- Derivative as a Rate of Change (2.7)
- Intro to the Derivative Function (2.8A)
- First Formulas for Derivative Functions (2.8B, 3.1)
- Limits at Infinity (2.6)
- Product Rule, Quotient Rule, Derivative of Sine (3.2, 3.3A)
- More Derivatives of Trig Functions; Chain Rule (3.3B, 3.4)
- Derivatives of Inverse Functions; Practice Differentiation (3.5A, 3.6A)
- Implicit and Logarithmic Differentiation (3.5B, 3.6B)
- Linear Approximation (3.10)
- Maxima and Minima; The MVT (4.1, 4.2)
- Derivatives and Shape of a Graph (4.3)
- L'Hospital's Rule (4.4)
- Sketching Graphs (4.5, 4.6)
- Optimization (4.7)
- Accumulated Change, Area Under Curve (5.1, 5.2)
- Antiderivatives and the FTC (4.9, 5.3)
- Net Change Theorem; Indefinite Integrals (5.4)
- Substitution (5.5)

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