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1
Introduction to Calculus: The Greeks, Newton, and Leibniz
2
Understanding Differentiation Part 1: The Slope of a Tangent Line
3
Understanding Differentiation Part 2: Rates of Change
4
Limits and Limit Laws in Calculus
5
What is a Derivative? Deriving the Power Rule
6
Derivatives of Polynomial Functions: Power Rule, Product Rule, and Quotient Rule
7
Derivatives of Trigonometric Functions
8
Derivatives of Composite Functions: The Chain Rule
9
Derivatives of Logarithmic and Exponential Functions
10
Implicit Differentiation
11
Higher Derivatives and Their Applications
12
Related Rates in Calculus
13
Finding Local Maxima and Minima by Differentiation
14
Graphing Functions and Their Derivatives
15
Optimization Problems in Calculus
16
Understanding Limits and L'Hospital's Rule
17
What is Integration? Finding the Area Under a Curve
18
The Fundamental Theorem of Calculus: Redefining Integration
19
Properties of Integrals and Evaluating Definite Integrals
20
Evaluating Indefinite Integrals
21
Evaluating Integrals With Trigonometric Functions
22
Integration Using The Substitution Rule
23
Integration By Parts
24
Integration by Trigonometric Substitution
25
Advanced Strategy for Integration in Calculus
26
Evaluating Improper Integrals
27
Finding the Area Between Two Curves by Integration
28
Calculating the Volume of a Solid of Revolution by Integration
29
Calculating Volume by Cylindrical Shells
30
The Mean Value Theorem For Integrals: Average Value of a Function
31
Convergence and Divergence: The Return of Sequences and Series
32
Estimating Sums Using the Integral Test and Comparison Test
33
Alternating Series, Types of Convergence, and The Ratio Test
34
Power Series
35
Taylor and Maclaurin Series
Description:
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.

Calculus

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