This course on Calculus I aims to help students understand the fundamental concepts and techniques of differential and integral calculus. By the end of the course, learners will be able to calculate limits, work with derivatives, apply differentiation formulas, sketch curves, solve optimization problems, and compute definite integrals. The course teaches skills such as calculating limits, finding derivatives, applying the chain rule, using implicit differentiation, and solving optimization and related rates problems. The teaching method involves a combination of theoretical explanations, worked examples, and practice problems. This course is intended for students who want to build a strong foundation in calculus and are comfortable with algebra and trigonometry.
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
