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Single Variable Calculus — 2. Applications of Differentiation

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About this course

Source: MIT OpenCourseWare 18.01SC Single Variable Calculus, Fall 2010, Prof. David Jerison — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: this unit's sessions in MIT's listing order. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 22, 2026. How RedLectern is built.

Instructor: Prof. David Jerison
Term: Fall 2010
Level: Undergraduate
What's inside: 71 videos · 40 other files
Materials open: Videos here · files on MIT OCW

Other versions of this course

18.01 · Fall 2020 · On MIT OCW ↗
18.01SC · Fall 2010 · Study here (this version)
18.01 · Fall 2006 · Study here
18.01 · Fall 2005 · On MIT OCW ↗

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Start course: Clip 1: Introduction to Linear Approximation Find a topic

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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Session 23: Linear Approximation

Single Variable Calculus — 2. Applications of Differentiation

Materials by section

Session 23: Linear Approximation

Session 24: Examples of Linear Approximation

Session 25: Introduction to Quadratic Approximation

Session 26: Using Quadratic Approximations

Session 28: Sketching Graphs II - General Strategies

Problem Set 3

Session 30: Optimization Problems II

Session 31: Related Rates

Session 33: Newton's Method

Problem Set 4

Session 34: Introduction to the Mean Value Theorem

Session 35: Using the Mean Value Theorem

Session 36: Differentials

Session 37: Antiderivatives

Session 38: Integration by Substitution

Session 39: Introduction to Differential Equations

Session 40: Separation of Variables

Problem Set 5

Session 42: Materials for Exam 2

Clip 1: Introduction to Linear Approximation

Clip 2: Linear Approximation to ln x at x=1

Clip 3: Linear Approximation and the Definition of the Derivative

Clip 4: Approximations at 0 for Sine, Cosine and Exponential Functions

Clip 1: Approximations at 0 for ln(1+x) and (1+x)r

Clip 1: Curves are Hard, Lines are Easy

Clip 2: Linear Approximation of a Complicated Exponential

Clip 3: Question: Can We Use the Original Formula?

Clip 1: GPS Time Dilation Example

Clip 2: Relative Error

Implicit Differentiation and Linear Approximation

Clip 1: The Formula for Quadratic Approximation

Clip 2: Explaining the Formula by Example

Clip 3: Quadratic Approximation at 0 for Several Examples

Quadratic Approximation of an Exponential Function

Clip 1: List of Approximations

Clip 2: Example: ln((1+1/k)k)

Clip 3: Example: Approximation of a Complicated Function

Quadratic Approximation of a Product

Clip 1: Approximating ln(1+x) and (1+x)r

Clip 1: Introduction to Curve Sketching

Clip 2: Example: 3x-x3

Clip 3: Graphing a Rational Function

Sketching a Curve

Clip 1: General Strategy for Graph Sketching

Clip 2: Example: x/ln x

Clip 1: Maxima and Minima Using Graphs

Clip 2: Maximum Area of Two Squares

Closest Point to the Origin

Minimum Triangle Area

Clip 1: Minimal Surface Area of a Box: Direct Solution

Clip 2: Minimal Surface Area of a Box: Implicit Differentiation

Maximum Surface Area

Clip 1: Introduction to Related Rates

Clip 2: Related Rates

Clip 3: Rates: A Conical Tank

Inflating a Balloon

Sliding Ladder

Clip 1: Ring on a String

Clip 1: Introduction to Newton's Method

Clip 2: Newton's Method, Continued

Clip 3: Newton's Method: What Could Go Wrong?

Using Newton's Method