Dive into the fundamentals of calculus in this comprehensive 11-hour course covering limits, derivatives, and integrals. Explore function limits, continuity, and precise limit definitions before delving into derivatives, rates of change, and various differentiation techniques including the chain rule and implicit differentiation. Master related rates, linear approximations, and differentials, then study maximum and minimum values, the Mean Value Theorem, and curve sketching. Tackle optimization problems, Newton's Method, and antiderivatives before concluding with definite and indefinite integrals, the Fundamental Theorem of Calculus, substitution rules, and applications in areas between curves and volumes.
Overview
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.
Taught by
Kamuela Yong
