Calculus I

Embark on a comprehensive 11-hour journey through Calculus I, exploring fundamental concepts from limits and continuity to derivatives and their applications. Gain a solid foundation in calculus by studying topics such as differentiation rules, rates of change, trigonometric functions, chain rule, and implicit differentiation. Delve into advanced concepts like partial derivatives, related rates, linear approximations, and optimization problems. Master important theorems and techniques including the Mean Value Theorem, L'Hopital's Rule, and Newton's Method. Conclude with an introduction to antiderivatives, preparing you for further studies in calculus.

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.