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# Calculus I

### Overview

This course on Calculus I aims to teach students the fundamental concepts and techniques of differential calculus. By the end of the course, learners will be able to understand limits, derivatives, differentiation rules, rates of change, trigonometric functions, chain rule, implicit differentiation, exponential and logarithmic functions, related rates, optimization problems, antiderivatives, and more. The course utilizes a combination of theoretical explanations, examples, and problem-solving exercises to help students grasp the material effectively. This course is intended for individuals interested in building a strong foundation in calculus, particularly suitable for students pursuing studies in mathematics, engineering, physics, or related fields.

### Syllabus

2.1 A Preview of Calculus.
2.2 The Limit of a Function.
2.3 The Limit Laws.
2.4 Continuity.
2.5 The Precise Definition of a Limit.
3.1 Defining the Derivative.
3.2 The Derivative as a Function.
3.3 Differentiation Rules.
3.4 Derivatives as Rates of Change.
3.5 Derivatives of Trigonometric Functions.
3.6 The Chain Rule.
3.7 Derivatives of Inverse Functions.
3.8 Implicit Differentiation.
3.9 Derivatives of Exponential and Logarithmic Functions.
3.10 Partial Derivatives.
4.1 Related Rates.
4.2 Linear Approximations and Differentials.
4.3 Maxima and Minima.
4.4 The Mean Value Theorem.
4.5 Derivatives and the Shape of a Graph.
4.6 Limits at Infinity and Asymptotes.
4.7 Applied Optimization Problems.
4.8 L'Hopital's Rule.
4.9 Newton's Method.
4.10 Antiderivatives.

Tyler Wallace

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