This course introduces single-variable calculus through limits, continuity, derivatives, applications of derivatives, antiderivatives, definite and indefinite integrals, the Fundamental Theorem of Calculus, substitution, areas, and volumes.

Syllabus

1.5 part 1 - The Limit of a Function.
1.5 part 2 - The Limit of a Function.
1.6 part 1 - Calculating Limits Using the Limit Laws.
1.6 part 2 - Calculating Limits Using the Limit Laws.
1.7 - The Precise Definition of a Limit.
1.8 part 1 - Continuity.
1.8 part 2 - Continuity.
2.1 part 1 - Derivatives and Rate of Change.
2.1 - Derivatives and Rates of Change part 2.
2.2 part 1 - The Derivative as a Function.
2.2 part 2 - Derivatives and Rate of Change.
2.3 part 1 - Differentiation Formulas.
2.3 part 2 - Differentiation Formulas.
2.3 part 3 - Differentiation Formulas.
2.4 - Derivatives of Trigonometric Functions.
2.5 part 1 - The Chain Rule.
2.5 part 2 - The Chain Rule.
2.6 - Implicit Differentiation.
2.8 part 1 - Related Rates.
2.8 part 2 - Related Rates.
2.9 part 1 - Linear Approximation and Differentials.
2.9 part 2 - Linear Approximation and Differentials.
2.9 part 3- Linear Approximation and Differentials.
3.1 part 1 - Maximum and Minimum Values.
3.1 part 2 - Maximum and Minimum Values.
3.2 part 1 - The Mean Value Theorem.
3.2 part 2 - The Mean Value Theorem.
3.3 part 1 - How Derivatives Affect the Shape of a Graph.
3.3 part 2 - How Derivatives Affect the Shape of a Graph.
3.4 part 1 - Limits at Infinity Horizontal Asymptotes.
3.4 part 2 - Limits at Infinity Horizontal Asymptotes.
3.5 part 1 - Summary of Curve Sketching.
3.5 part 2 - Summary of Curve Sketching.
3.7 - Optimization Problems.
3.8 - Newton's Method.
3.9 part 1 - Antiderivatives.
3.9 part 2 - Antiderivatives.
4.1 part 1 - Areas and Distances.
4.1 part 2 - Areas and Distances.
4.1 part 3 - Areas and Distances.
4.2 part 1 - The Definite Integral.
4.2 part 2 - The Definite Integral.
4.2 part 3 - The Definite Integral.
4.3 part 1 - The Fundamental Theorem of Calculus.
4.3 part 2 - The Fundamental Theorem of Calculus.
4.4 - Indefinite Integrals and the Net Change Theorem.
4.5 part 1 - The Substitution Rule.
4.5 part 2 - The Substitution Rule.
4.5 part 3 - The Substitution Rule.
5.1 part 1 - Areas Between Curves.
5.1 part 2 - Areas Between Curves.
5.2 part 1 - Volumes.