Calculus: Chapter 5 Part 10: Taylor / Maclaurin Series
For the final video in the Calculus Class, the Math Record introduces the concept of the Taylor and Maclaurin Series and how to estimate its error using the Lagrange Error Bound.
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---------- Table of Contents ---------
Chapter Pre
1: Introduction to Calculus
2: Limits
Chapter 1: Derivatives
1: Introduction to the Derivative
2: Power Rule
3: Product Rule, Quotient Rule, & Chain Rule
4: Derivatives of Exponential Functions
5: Derivatives of Trigonometric Functions
6: Derivatives of Inverse Functions
7: Derivatives of Inverse Trigonometric Functions
8: Derivatives of Logarithmic Functions
9: Implicit Differentiations
10: Higher-Order Derivatives
Chapter 2: Applications of Derivatives
1: Understanding Graphs: Maximum & Minimums
2: Understanding Graphs: Increasing & Decreasing Intervals
3: Understanding Graphs: Concavity & Inflection Points
4: Understanding Graphs: 2nd Derivative Test
5: Understanding Graphs: Intermediate & Mean Value Theorem
6: Newton's Method to Approximating Zeroes
7: Euler's Method to Approximating Points
8: Related Rates
9: Optimization
10: Indeterminants & L'Hôpital Rule
Chapter 3: Integrals
1: Introduction to the Integral
2: Basic Integration
3: Integration by Substitution
4: Integration by Parts
5: Integration using Partial Fractions
6: Integration of Trigonometric Functions
Chapter 4: Applications of Integrals
1: Displacement, Total Distance, and Position
2: Area
3: Volume from Revolutions
4: Volume from Cross Sections
5: Riemann Sums
6: Newton's Law of Cooling & Logistic Functions
7: Arc Length
Chapter 5: Sequences and Series
1: Introduction to Sequences and Series
2: P-series & Infinite Geometric Series
3: Convergence Test #1: Integral Test
4: Convergence Test #2: Comparison Test
5: Convergence Test #3: Limit Comparison Test
6: Convergence Test #4: Ratio Test
7: Convergence Test #5: Root Test
8: Alternating Series
9: Power Series
10: Taylor & Maclaurin Series