Video Supplement for Math 1C

Chapters 10 and 11

Section Alexander Paulin Meredith Burr Khan Academy (KA) PatrickJMT (PJMT) MIT Asher Roberts ProfRobBob Professor Leonard blackpenredpen Organic Chemistry Tutor Other
10.3 Introduction to Polar Curves, Example on converting a polar equation to a Cartesian equation, Basic Polar Curves, Sketching polar curves Polar Coordinates 1 Polar Coordinates - The Basics Polar coordinates; area in polar coordinates Section 10.3 Understanding Polar Coordinates Using Polar Coordinates and Polar Equations Polar Review 1, , Polar Slope 1, Polar Slope 2, Polar Slope 3 Polar Coordinates Introduction, Graphing Polar Curves, Tangent Line Equations, Slope, & Derivatives In Polar Form
10.4 Area and Lengths in Polar Coordinates I, Area and Lengths in Polar Coordinates II, Area and Lengths in Polar Coordinates III, Area and Lengths in Polar Coordinates IV, Area and Lengths in Polar Coordinates V Justification for polar arc length formula Finding Areas in Polar Coordinates Polar coordinates; area in polar coordinates Section 10.4 Calculus of Polar Equations Area Example 1, Area Example 2 Finding Area In Polar Coordinates, Finding Area Bounded By Two Polar Curves, Arc Length of Polar Curves
10.5 Review of Conic Sections Introduction to Conic Sections Section 10.5 Finding Equations of Conics from Given Conditions Circle and Parabola, Ellipse and Hyperbola Parabola, Ellipse, Hyperbola Conic Sections, Parabolas, Hyperbolas, Ellipses Introduction to Conic Sections
10.6 Polar Form of a Conic: Finding the Type, the Directrix and Eccentricity Section 10.6 Polar Equations of Conic Sections In Polar Coordinates Conic Sections -- Polar Coordinate System
11.1 Sequences Introduction to sequences and series, Introduction to Taylor Polynomials, Definition and Examples of Geometric Sequences Sequences and Series (part 1), Convergent and divergent sequences Infinite series and convergence tests Section 11.1 Convergence and Divergence of Sequences Example 1, Example 2, Example 3, Example 4, Example 5, Example 6, Example 7, Example 8, Example 9, Example 10 Converging and Diverging Sequences Using Limits, Monotonic Sequences and Bounded Sequences Sequences, Math 2B. Calculus. Lecture 19. Sequences
11.2 Infinite Series Introduction to Infinite Series, Definition of series convergence and two examples, Example on determining convergence or divergence of a telescoping series, Geometric Series Test and Several Examples Divergence Test (nth Term test), Geometric Series Geometric Series and the Test for Divergence - Part 1, Geometric Series and the Test for Divergence - Part 2, Test for Divergence for Series, Two Examples p-Series Test Section 11.2 p-Series Test, Geometric and Telescoping Series Series, Geometric Series, Harmonic Series, and Divergence Test Divergence Test Example Convergence and Divergence - Introduction to Series, Harmonic Series, Telescoping Series, Geometric Series and Geometric Sequences - Basic Introduction, Divergence Test Infinite series of numbers, Math 2B. Calculus. Lecture 20. Series
11.3 The Integral Test Introduction to the Integral Test, Example on applying the Integral Test, Another example applying the Integral Test, p-Series Test and Examples, Introduction to Estimating the Sum of a Series Integral test intuition , Integral test to show series divergence Integral Test - Basic Idea, Integral Test for Series Example 1, Integral Test for Series - Example 2, Integral Test to Evaluate Series, Ex 3, Using the Integral Test for Series Integral Test, Integral Test as Estimation Section 11.3 Integral Test Integral Test for Convergence/Divergence for Series Integral Test Rationale and Examples, Integral Test Example Integral Test For Convergence and Divergence of Series, Remainder Estimate For The Integral Test The Integral Test, Math 2B. Calculus. Lecture 21. Integral Test and Estimates of Sums
11.4 Comparison Tests Introduction to Comparison Test and Examples, Discussion of Limit Comparison Test and an Example, Three examples applying the Limit Comparison Test Comparison Test, Limit Comparison Test Limit Comparison Test and Direct Comparison Test, Limit Comparison Test and Direct Comparison Test, Direct Comparison Test / Limit Comparison Test for Series - Basic Info, Limit Comparison Test for Series - Another Example 1, Limit Comparison Test for Series - Another Example 2 Comparison Tests Section 11.4 Limit Comparison Test, Direct Comparison Test Comparison Tests Limit Comparison Test, Example Direct Comparison Test, Limit Comparison Test Comparison Test, Math 2B. Calculus. Lecture 22. The Comparison Test, Math 2B. Calculus. Lecture 23. The Comparison Test/ Alternating Series Test, Part II
11.5 Alternating Series Introduction to Alternating Series, Introduction to Alternating Series Test, Four examples on applying the Alternating Series Test, Alternating Series Estimation Theorem Alternating series test, Alternating series error estimation Alternating Series, More Alternating Series Examples, Alternating Series - Another Example 2, Alternating Series Estimation Theorem Section 11.5 Alternating Series Test Alternating Series Test Alternating Series Test, Alternate Series Estimation Theorem Math 2B. Calculus. Lecture 23. The Comparison Test/ Alternating Series Test, Part II
11.6 Absolute Convergence and the Ratio/Root Tests Introduction to Absolute and Conditional Convergence and 3 Examples, Example on using absolute convergence to determine convergence of a series, Introduction to the Ratio Test Two examples applying the Ratio Test, Example on determining absolute or conditional convergence or divergence, Introduction to the Root Test and an Example Absolute Convergence, Conditional Convergence and Divergence Ratio Test Example Section 11.6 Example 1, Example 2 Root and Ratio Test Ratio Test Example 1, Ratio Test Example 2, Ratio Test Example 3, Ratio Test Example 4, Root Test Example 1, Root Test Example 2 Absolute Convergence, Conditional Convergence, and Divergence, Ratio Test, Root Test
11.8 Power Series Introduction to Power Series, Three basic examples on finding where a power series converges, Theorem on the 3 possibilities for the set of x for which a power series converges, Example on determining radius and interval of convergence of a power series Power series function representation using algebra Power Series Representation of Functions Power Series Practice Section 11.8 Interval of Convergence of Power Series Power Series Radius and Interval of Convergence, Example 1, Example 2 Power Series - Finding The Radius & Interval of Convergence Math 2B. Calculus. Lecture 25. Power Series
11.9 Representing Functions as Power Series Introduction to Representations of Functions as Power Series, Three examples on manipulating series and differentiating series, Three examples on integrating series, Approximating a definite integral using series and an estimation theorem Power series representation using integration Power Series Representation of Functions Section 11.9 Power Series Representation of Functions, Differentiation and Integration of a Power Series Power Series Example 1, Example 2, Example 3, Example 4, Example 5, Example 6 Power Series - Representation of Functions, Power Series - Differentiation and Integration Math 2B. Calculus. Lecture 26. Representing Functions as Power Series Representing Functions as Power Series
11.10 Taylor and Maclaurin Series Introduction to Taylor and Maclaurin Series, Two examples on finding Taylor and Maclaurin series, Discussion of Taylor's Inequality and when a function equals its Taylor Series, Two examples on proving a function equals its Taylor series, Additional examples on working with Taylor Series Maclaurin and Taylor Series Intuition, Taylor Polynomials Taylor and Maclaurin Series - Example 1, Finding a Taylor Polynomial to Approximate a Function Taylor Series, Taylor's Series of a Polynomial, Finding Taylor Series Section 11.10 Taylor Series and Maclaurin Series Taylor Series and Maclaurin Series Taylor Series, Example 1, Example 2, Example 3 Taylor Series and Maclaurin Series Math 2B. Calculus. Lecture 27. Taylor Series and Maclaurin Series
11.11 Approximating functions using Taylor polynomials, Example on approximating a function at a particular value using Taylor polynomials Taylor Error 1, Taylor Error 2 Taylor's Inequality, Example 1, Example 2, Example 3, Example 4 Section 11.11 Taylor Polynomials and Estimation Error Approximation of Functions by Taylor Polynomials Taylor Polynomials & Maclaurin Polynomials With Approximations, Taylor's Remainder Theorem


Chapters 12 and 13

Section Michael Hutchings Alexandra Niedden Travis Kowalski Adrian Banner Denis Auroux
12.1 1.3.1 Three-Dimensional Coordinate Systems Topic 2
12.2 1.3.2 Vectors Part 1, Vectors Part 2 Topic 2 (34:00) Lec 2 (1:26) Lec 1 (1:08)
12.3 1.3.3, 1.3.4 Dot Product Part 1, Dot Product Part 2 Topic 3 Lec 2 (9:45) Lec 1 (15:30)
12.4 1.3.5, 1.3.6 Cross Product Topic 4 Lec 3 (1:45) Lec 2 (33:38)
12.5 1.4.1, 1.4.2 Equations of Lines and Planes Part 1, Equations of Lines and Planes Part 2 Topic 5 Lec 2 (31:10) Lec 4
13.1 1.5.1 Vector Functions and Space Curves Topic 6 Lec 3 (1:03:45-1:23:08) Lec 5, Lec 6 (stop at 5:30)
13.2 1.5.2 Derivatives and Integrals of Vector Functions Part 1, Derivatives and Integrals of Vector Functions Part 2 Topic 7 Lec 3(1:23:08-1:34:00)
13.3 Arc Length and Curvature 1, Arc Length and Curvature 2 Lec 8 (12:30)
13.4 Motion Part 1, Motion Part 2 Topic 8 Lec 3 (1:34:00) Lec 6 (5:30)