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MIT videos are lecture-style; CalcVids videos are shorter topic videos.
| Section |
Title of Section |
MIT Videos |
CalcVids.org |
| Sec 2.1 |
The Tangent and Velocity Problems |
Lecture 1: Rate of Change |
Finding the speed of a baseball at a moment in time graphically
|
| Graphing the rate of change of metabolizing ibuprofen |
| SPS: The Imprecision of Tangents |
| Sec 2.1, 2.7 |
Constant Rate of Change |
Solving the Problem of Pouring Water |
| Formal Definition of Constant Rate of Change |
| SPS: Pouring Water into a Cylinder |
| Sec 2.1, 2.7 |
Graphing Constant Rate of Change |
Graphing CannonCow |
| Graphing Pouring Water |
| SPS: Cannon Cow! |
| Sec 2.1, 2.7 |
Varying Rates of Change |
Solving the Problem of Pouring Water |
| Frozen Yogurt in a Cone |
| SPS: Pouring Water into an Erlenmeyer Flask |
| Sec 2.1, 2.7 |
Graphing Varying Rates of Change |
Making a Graph for Filling a Spherical Flask |
| SPS: Filling a Spherical Flask |
| Sec 2.1, 2.7 |
Average Rates of Change |
Average Rates of Change as Constant Rates of Change |
| A Precise Description of Average Rates of Change |
| SPS: Two Race Cars, Constant Rates, and Average Rates |
| Sec 2.1, 2.7 |
Approximating Instantaneous Rates of Change |
Approximating the Speed of a Baseball |
| Using Average Rates of Change to Approximate an Instantaneous Rate of Change |
| SPS: The Stationary Baseball |
| Sec 2.2 |
The Limit of a Function |
Lecture 2: Limits |
Limit at a Point |
| One-Sided Limits |
| Sec 2.3 |
Calculating Limits Using the Limit Laws |
| Sec 2.4 |
The Precise Definition of a Limit |
Using Limits to Compute Instantaneous Rates of Change |
| SPS: Using Limits to Compute Derivatives |
| Sec 2.5 |
Continuity |
Continuity |
| SPS: Continuity |
| Sec 2.6 |
Limits at Infinity; Horizontal Asymptotes |
| Sec 2.7 |
Derivatives and Rates of Change |
Lecture 1: Rate of Change |
| Sec 2.8 |
The Derivative as a Function |
Lecture 3: Derivatives |
Defining the derivative |
| SPS: Rate of Absorbing Ibuprofen |
| Sec 3.1 |
Derivatives of Polynomials and Exponential Functions |
The Power Rule |
| Exponential and Logarithmic Functions |
| SPS: Trying to Use the Limit Definition |
| Sec 3.2 |
The Product and Quotient Rules |
Procedural Description of the Product Rule |
| Conceptual Explanation of the Product Rule |
| SPS: Products of Polynomials |
| The Quotient Rule |
| Why the Quotient Rule Works |
| SPS: Derivatives of Quotients |
| Sec 3.3 |
Derivatives of Trigonometric Functions |
Trigonometric Functions |
| Sec 3.4 |
The Chain Rule |
Lecture 4: Chain Rule |
| Computing the Average Rate of Change of a Composition of Functions |
| How to Use the Chain Rule |
| Why the Chain Rule Works |
| SPS: A Ripple in a Pond |
| Sec 3.5 |
Implicit Differentiation |
Lecture 5: Implicit Differentiation |
| Introduction to Implicit Differentiation |
| Tangent Lines for a Cardioid |
| SPS: A Complicated Tangent Line |
| Sec 3.6 |
Derivatives of Logarithmic Functions |
Lecture 6: Exponential and Log |
| Sec 3.7 |
Rates of Change in the Natural and Social Sciences |
| Sec 3.8 |
Exponential Growth and Decay |
| Sec 3.9 |
Related Rates |
Lecture 12: Related Rates |
| Defining a Related Rate Formula |
| Solving A Related Rates Problem |
| SPS |
| Sec 3.10 |
Linear Approximation and Differentials |
Lecture 9: Linear and Quadratic Approx. |
Local Linearity |
| SPS: Growth of a Rabbit Population |
| Sec 3.11 |
Hyperbolic Functions |
| Sec 4.1 |
Maximum and Minimum Values |
Lecture 11: Max-Min |
| Sec 4.2 |
The Mean Value Theorem |
Lecture 14: Mean Value Theorem |
What the Mean Value Theorem Says |
| Why the Mean Value Theorem Works |
| Extended version of Why the Mean Value Theorem Works |
| SPS |
| Sec 4.3 |
How Derivatives Affect the Shape of a Graph |
Lecture 10: Curve Sketching |
Graphing the Derivative Function |
| SPS: Graphing the Speed of a Baseball |
| Interpreting the Derivative |
| SPS: Interpreting Derivatives |
| Sec 4.4 |
Indeterminate Forms and l'Hospital's Rule |
Lecture 35: Indeterminant Forms |
Limits of Quotients |
| SPS: Evaluating Indeterminate Limits |
| Sec 4.5 |
Summary of Curve Sketching |
Lecture 10: Curve Sketching |
| Sec 4.6 |
Graphing with Calculus and Calculators |
| Sec 4.7 |
Optimization Problems |
Lecture 11: Max-Min |
Using Derivatives to Maximize Fuel Economy |
| SPS: Maximizing Fuel Economy |
| An Example of Optimization |
| How to Maximize the Area of a Rectangular Pen |
| SPS: Maximizing an Animal Pen |
| Sec 4.8 |
Newton's Method |
Lecture 13: Newton's Method |
| Sec 4.9 |
Antiderivatives |
Lecture 15: Antiderivatives |
SPS: Antiderivatives |
| Antiderivatves, Part 1: Polynomials and the Power Rule |
| Antiderivatvies, Part 2: 1/x, Exponential, and Trig Functions |
| Using Antiderivative Rules |
| Sec 5.1 |
Areas and Distances |
|
Using a Riemann Sum to Approximate the Amount of Accumulated Dust |
| A Riemann Sum for an Oil Spill |
| SPS: Dust Accumulation on the Mars Rover |
| Writing Riemann Sums using Sigma Notation |
| SPS: Writing a Riemann Sum Two Ways |
| Sec 5.2 |
The Definite Integral |
Lecture 18: Definite Integrals |
Definite Integrals as Limits of Riemann Sums |
| A Definite Integral for an Oil Spill |
| SPS: Mars Rover Using a Formula |
| Sec 5.3 |
The Fundamental Theorem of Calculus |
Lecture 19: First Fundamental Theorem |
Computing Total Accumulation |
| SPS: Computing Total Accumulation |
| Lecture 20: Second Fundamental Theorem |
Accumulation Functions |
| Antiderivatives and Accumulation Functions |
| SPS: Cumulative Probability from a Normal Distribution |
| Sec 5.4 |
Indefinite Integrals and the Net Change Theorem |
Lecture 18: Definite Integrals |
| Sec 5.5 |
The Substitution Rule |
Lecture 28: Inverse Substitution |
SPS: Evaluating Indefinite Integrals |
| Sec 6.1 |
Areas between Curves |
Lecture 21: Applications to Logarithms |
| Sec 6.2 |
Volume |
Lecture 22: Volumes |
| Sec 6.3 |
Volumes by Cylindrical Shells |
| Sec 6.4 |
Work |
Lecture 23: Work, Probability |
| Sec 6.5 |
Average Value of a Function |
Lecture 21: Applications to Logarithms |