Dive into advanced calculus techniques with this comprehensive video series. Master integration methods including trig substitution, u-substitution, integration by parts, and partial fractions. Explore completing the square, L'Hopital's Rule for limit evaluation, and delve into sequences and series. Learn about sequence convergence, geometric series, and series convergence tests like the ratio test. Understand power series, including radius and interval of convergence. Discover Taylor series, their creation through substitution, integration, and differentiation. Analyze specific examples of Taylor series expansions, such as e^x and natural logarithm, to solidify your understanding of these crucial calculus concepts.
Overview
Syllabus
Calculus Technique of Integration: Trig Substitution.
Calculus Techniques of Integration: U-Substitution.
Calculus Techniques of Integration: Trig Substitutions (Another Example).
Calculus Techniques of Integration: Integration by Parts.
Calculus Techniques of Integration: Integration by Parts (Another Example).
Calculus Techniques of Integration: Partial Fractions.
Completing the Square.
Calculus Techniques of Integration: Trig Substitution (Completing the Square + Tangent Substitution).
Using L'Hopital's Rule to Evaluate Limits.
Calculus: Introduction to Sequences.
Calculus: Sequence Convergence.
Calculus: Geometric Series.
Calculus: Series Convergence.
Calculus: Ratio Test for Series Convergence.
Calculus: Convergence of Power Series (Radius of Convergence, Interval of Convergence).
Calculus: Radius of Convergence for a Power Series (Example).
Calculus: Radius of Convergence.
Calculus: Taylor Series Introduction.
Calculus: Creating a new Taylor Series by Substitution.
Calculus: Integrating Taylor Series.
Calculus: Radius of Convergence for a Taylor Series Example 1 (e^x).
Calculus: Differentiating Taylor Series.
Calculus: Radius of Convergence for the Taylor Series Expansion of the Natural Log.
Taught by
Professor Knudson
