Embark on a comprehensive journey through calculus with this 6-hour video series. Gain a solid conceptual foundation in differentiation and integration while honing problem-solving skills for various test scenarios. Begin with an introduction to calculus history, then delve into understanding differentiation, limits, and derivatives. Explore applications like related rates, optimization problems, and graphing functions. Progress to integration techniques, including the Fundamental Theorem of Calculus, substitution rules, and integration by parts. Tackle advanced topics such as improper integrals, volumes of solids of revolution, and series convergence. Conclude with an exploration of power series and Taylor and Maclaurin series, providing a comprehensive overview of calculus concepts and techniques.
Overview
Syllabus
Introduction to Calculus: The Greeks, Newton, and Leibniz.
Understanding Differentiation Part 1: The Slope of a Tangent Line.
Understanding Differentiation Part 2: Rates of Change.
Limits and Limit Laws in Calculus.
What is a Derivative? Deriving the Power Rule.
Derivatives of Polynomial Functions: Power Rule, Product Rule, and Quotient Rule.
Derivatives of Trigonometric Functions.
Derivatives of Composite Functions: The Chain Rule.
Derivatives of Logarithmic and Exponential Functions.
Implicit Differentiation.
Higher Derivatives and Their Applications.
Related Rates in Calculus.
Finding Local Maxima and Minima by Differentiation.
Graphing Functions and Their Derivatives.
Optimization Problems in Calculus.
Understanding Limits and L'Hospital's Rule.
What is Integration? Finding the Area Under a Curve.
The Fundamental Theorem of Calculus: Redefining Integration.
Properties of Integrals and Evaluating Definite Integrals.
Evaluating Indefinite Integrals.
Evaluating Integrals With Trigonometric Functions.
Integration Using The Substitution Rule.
Integration By Parts.
Integration by Trigonometric Substitution.
Advanced Strategy for Integration in Calculus.
Evaluating Improper Integrals.
Finding the Area Between Two Curves by Integration.
Calculating the Volume of a Solid of Revolution by Integration.
Calculating Volume by Cylindrical Shells.
The Mean Value Theorem For Integrals: Average Value of a Function.
Convergence and Divergence: The Return of Sequences and Series.
Estimating Sums Using the Integral Test and Comparison Test.
Alternating Series, Types of Convergence, and The Ratio Test.
Power Series.
Taylor and Maclaurin Series.
Taught by
Professor Dave Explains
