**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.

**Course Documents**

- Syllabus, Semester Schedule
- Detailed Unit Plans: Unit 1 Plan, Unit 2 Plan, Unit 3 Plan
- Guidelines for Written Homework

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

- Familiar Functions (Ch 1, App D)
- Composition and Inversion of Functions (Ch 1)
- Approximating Slopes (2.1)
- Limits (2.2)
- Evaluating Limits (2.3)
- Continuity, Intro (2.5A)
- Continuity, Continued (2.5B)
- Rates and Derivatives (2.7)
- Derivative Functions (2.8)
- Limits at Infinity (2.6)
- Basic Differentiation (3.1)
- Product and Quotient Rules (3.2)
- Derivatives of trig functions (3.3)
- Chain Rule (3.4))
- Derivatives of Inverse Functions (3.5, 3.6)
- Practice Differentiation (3.1-3.6)
- Implicit and Logarithmic Differentiation (3.5, 3.6)
- Linear Approximation; Differentials (3.10)
- Antiderivatives (4.9)
- Intro to Max/Min (4.1A)
- More on Max/Min (4.1B), MVT (4.2)
- Shape of Graph (4.3)
- L'Hopital's Rule (4.4)
- Sketching Graphs (4.5-4.6)
- Accumulated Change (5.1)
- The Definite Integral (5.2)
- The Fundamental Theorem of Calculus (5.3)
- Indefinte Integrals and Net Change (5.4)
- Substitution (5.5)

**Additional Activities**

*Mathematica*Practice (right click to download)- Applications of the Derivative: Group Presentation Instructions
- Optimization Applications: Optimization Problems, Group Presentation Instructions

**Quiz and Exam Information**

- Quiz 1 (Prerequisites): Explanation, Sample Quiz, Solutions
- Quiz 3 (Derivatives Gateway): Explanation, Sample Quiz, Solutions
- Quiz 4: Sample Quiz, Solutions
- Exam 1 Review Solutions
- Exam 2: Practice Problems, Solutions
- Final Exam Study Guide

UST Math Department