Introduction to Calculus 3: Infinite Sequences and Series

🎉 Explore the World of Calculus with "Introduction to Calculus 3: Infinite Sequences and Series" 📚

Course Overview:

HOW THIS COURSE WORK: Dive into the fascinating realm of Infinite Sequences and Series with Gina Chou's "Introduction to Calculus 3." This comprehensive course is a segment of our complete Calculus 3 series, meticulously crafted for learners who wish to understand the intricacies of sequences and series. Through engaging videos, detailed notes, and hands-on practice problems (complete with solutions), Gina guides you every step of the way.

Course Structure:

Section 2: Infinite Sequences

• Sequences: Understand the concept and notation.
• Convergence of a Sequence: Learn what it means for a sequence to converge or diverge.
• Monotonic and/or Bounded Sequence: Explore sequences that have specific monotonic properties or are bounded by certain values.

Section 3: Infinite Series

• Series: Discover the definition of an infinite series and its significance.
• Geometric Series: Dive into a specific type of series where each term is a constant ratio times the previous term.
• Telescoping Series: Unpack series that simplify in a particular way to yield a simple sum or difference.
• Harmonic Series: Analyze one of the most famous divergent series and its variations.
• Tests for Divergence: Learn various tests to determine if a series converges or diverges.
• Integral Test, Estimating the Sum, Comparison Test, Limit Comparison Test, Alternating Series Test: Master these key tools for evaluating series.
• Estimating the Sum of an Alternating Series: Understand how to approximate the sum of alternating sequences.
• Absolute Convergence: Explore series that converge absolutely and the implications this has.
• Ratio Test, Root Test: Get to grips with two pivotal tests for determining convergence or divergence.

Section 4: Power Series

• Power Series: Introduce power series and their general form.
• Radius of Convergence and Interval of Convergence: Learn how to determine the range over which a power series converges.
• Representations of Functions as Power Series: Discover how functions can be represented by power series.
• Taylor Series and Maclaurin Series: Master the difference between Taylor and Maclaurin series and their applications.
• Taylor's Inequality: Understand how to use this inequality to approximate functions.
• Method 1: Direct Computation: Learn to compute Taylor polynomials directly.
• Method 2: Use Term-by-term Differentiation and Integration: Understand how to differentiate and integrate power series term-by-term.
• Method 3: Use Summation, Multiplication, and Division of Power Series: Explore techniques involving operations on power series.
• Applications of Taylor Polynomials: Apply Taylor polynomials in various practical scenarios.

Inside the Course:

Videos:

Gina starts each topic with a comprehensive video, explaining concepts and demonstrating problem-solving techniques with real examples. These videos are designed to cover a wide range of math issues you might face in class.

Notes:

Accompanying each section, you'll find downloadable notes taken during Gina's lectures. This allows for review even without internet access, and it's encouraged to take your own notes alongside the course!

Assignments:

After learning through videos and notes, you'll have the opportunity to test your understanding with practice problems. These exercises are a crucial part of mastering the material.

Highlights of This Course:

• Downloadable lectures for on-the-go learning.
• Comprehensive lecture notes and extra resources for review and offline study.
• Practice problems sets with solutions to reinforce your learning and application of concepts.
• A step-by-step guide for tackling problems effectively.

Ready to embark on this mathematical adventure? Let's get started!

• Gina Chou 😄

Sign up now and transform your understanding of Infinite Sequences and Series with "Introduction to Calculus 3!"