Video

Title

Topics

Length

Script

1

Introduction 

Four ways to study Calculus
Pedagogical approach of the series
Student optimal learning strategy
Technology and Calculus

13 min

pdf

2

Why Calculus is Important

The importance of calculus in building dynamic mathematical models

15 min

pdf

3

Concept of a Derivative

Derivative is rate of change
Simple epidemic model

13 min

pdf

4

Limits

Informal discussion of the key limits used in calculus
Use of limits in modeling

14 min

pdf

5

Derivative

Formal definition and notations

13 min

pdf

6

Basic differentiation rules I

Linear and Product Rules
Proof outline for product rule

18 min

pdf

7

Examples I

A series of examples that review the topics so far.

10 min

pdf

8

Basic rules of differentiation II

Chain Rule
Proof outline for Chain Rule

13 min

pdf

9a

Trigonometric functions I

Sine and cosine functions, graphs, derivatives
Use of trig functions in modeling
limit of (sin h)/h as h ->0

18 min

pdf

9b

Trigonometric functions II

Derivatives of sin and cos
Limit of (sin h) / h as h ->0
Outline of proof

15 min

pdf

10

Trigonometric functions III

Tangent and secant functions, definition, graphs, derivatives.
Quotient Rule

13 min

pdf

11

Examples II

Examples of derivatives using trig functions and the differentiation rules
Remarks on effective problem solving

14.5 min

pdf

12

Exponential Functions

Exponential functions with base r.
Derivative and the limit (r^h-1)/h as h->0 
Definition of the number e and the function e^x = exp(x)
Derivative calculation examples

20 min

pdf

13a

Logarithms (Properties)

Logarithm property
Why we need logarithms: finance model
Graph and behavior of logs

10 min

pdf

13b

Logarithms (Derivatives)

Derivative of log x = ln x
Examples of derivatives
Working with other bases:log and exp
Bacterial growth model

15.5 min

With
13a

14

Implicit differentiation

Examples of implicit differentiation
Logarithmic differentiation 
Related Rates: Ideal Gas Law

19 min

pdf

15

Inverse trig functions: what and why

Inverse sin and tan functions
Graphs and Derivatives of these functions

16 min

pdf

16a

Examples III

Examples of derivatives using logs, exponentials and inverse trig functions

15 min

pdf

16b

Examples IV

Examples of implicit differentiation and function analysis

14 min

With
16a

17

Summary of Differential Calculus

Ideas, techniques and key examples

11 min

pdf