Richard Hammack's

Calculus I Video Lectures

I believe calculus is best learned through four or five short lectures each week throughout a 14-week semester, and this course of video lectures is designed for such a format. It should go without saying that you should also read your text actively and work LOTS of problems yourself for practice. Ideally you will also meet as a class or small group at least once per week for discussions, problem sessions, quizzes and tests. Although working together offers crucial benefits, independence is much more important than group work. Learning calculus well requires countless hours of solitary study and practice.

These lectures are in the form of screencast slideshows. They are designed to be textbook-independent, but nonetheless should be accompanied by a good textbook. The sequencing and notation matches most standard calculus texts. The content, approach and pacing is informed by my experiences teaching Calculus more than 50 times.

The lectures in Part 1 (Functions) are a review of algebra and trigonometry, which are the foundations for Calculus I. Ideally you should already know this material. However, most students enter Calculus I with insufficient mastery of it; Part 1 is designed for them.

The lectures are on Kaltura and YouTube. Below, click on the platform you prefer. (You may need a VCU domain for Kaltura.) Here is a link to my Calculus I Page.



   
PART 1:  Function Review
Lecture 1
A Thumbnail Sketch of Calculus I
[Kaltura | YouTube] (22 minutes)
Lecture 2
Function Fundamentals
[Kaltura | YouTube] (36 minutes)
Lecture 3A
Trig Review, Part A
[Kaltura | YouTube] (46 minutes)
Lecture 3B
Trig Review, Part B
[Kaltura | YouTube] (47 minutes)
Lecture 4
Inverse Functions
[Kaltura | YouTube] (32 minutes)
Lecture 5A
Exponential Functions
[Kaltura | YouTube] (25 minutes)
Lecture 5B
Logarithms
[Kaltura | YouTube] (37 minutes)
Lecture 5C
Natural Exponential & Log Functions
[Kaltura | YouTube] (30 minutes)
Lecture 5D
Why e Is the Best Base (optional)
[Kaltura | YouTube] (18 minutes)
Lecture 6A
Inverse Trig Functions, Part A
[Kaltura | YouTube] (43 minutes)
Lecture 6B
Inverse Trig Functions, Part B
[Kaltura | YouTube] (44 minutes)
 
PART 2:  Limits
Lecture 7
Motivation for Limits
[Kaltura | YouTube] (18 minutes)
Lecture 8A
Introduction to Limits
[Kaltura | YouTube] (27 minutes)
Lecture 8B
Limit Laws
[Kaltura | YouTube] (31 minutes)
Lecture 9
Computing Limits Algebraically
[Kaltura | YouTube] (35 minutes)
Lecture 10A
Limits of Trig Functions
[Kaltura | YouTube]  (28 minutes)
Lecture 10B
The Squeeze Theorem
[Kaltura | YouTube] (19 minutes)
Lecture 11
Continuity & Limits of Compositions
[Kaltura | YouTube] (43 minutes)
Lecture 12
Infinite Limits
[Kaltura | YouTube] (46 minutes)
Lecture 13A
Limits at Infinity
[Kaltura | YouTube] (28 minutes)
Lecture 13B
Limits at Infinity, continued
[Kaltura | YouTube] (35 minutes)
Lecture 14
Formal Definitions of Limits (optional)
To be posted


PART 3. Differentiation
Lecture 15
Slopes of Tangents
[Kaltura | YouTube] (39 minutes)
Lecture 16
The Derivative
[Kaltura | YouTube] (38 minutes)
Lecture 17
Derivative Rules
[Kaltura | YouTube] (45 minutes)
Lecture 18A
Notation and Examples
[Kaltura | YouTube] (30 minutes)
Lecture 18B
Differentiability
[Kaltura | YouTube] (15 minutes)
Lecture 19
The Derivative of ex
[Kaltura | YouTube] (31 minutes)
Lecture 20
Product and Quotient Rules
[Kaltura | YouTube] (46 minutes)
Lecture 21
Derivatives of Trig Functions
[Kaltura | YouTube] (35 minutes)
Lecture 22
Higher Derivatives
[Kaltura | YouTube] (12 minutes)
Lecture 23A
The Chain Rule, Part A
[Kaltura | YouTube] (41 minutes)
Lecture 23B
The Chain Rule, Part B
[Kaltura | YouTube] (36 minutes)
Lecture 24
Derivatives of Inverses and Logarithms
[Kaltura | YouTube] (39 minutes)
Lecture 25
Derivatives of Inverse Trig Functions
[Kaltura | YouTube] (34 minutes)
Lecture 26
Meanings of the Derivative
[Kaltura | YouTube] (47 minutes)
Lecture 27
Implicit Differentiation
[Kaltura | YouTube] (57 minutes)
Lecture 28
Logarithmic Differentiation
[Kaltura | YouTube] (29 minutes)
Lecture 29
Related Rates
[Kaltura | YouTube] (39 minutes)



PART 4. Applications of Differentiation
Lecture 30
Increase-Decrease
[Kaltura | YouTube] (27 minutes)
Lecture 31
Local Extrema & First Derivative Test
[Kaltura | YouTube] (38 minutes)
Lecture 32A
Concavity and Curve Sketching
[Kaltura | YouTube] (25 minutes)
Lecture 32B
Second Derivative Test
[Kaltura | YouTube] (37 minutes)
Lecture 33
Global Extrema
[Kaltura | YouTube] (35 minutes)
Lecture 34A
Optimization Problems
[Kaltura | YouTube] (46 minutes)
Lecture 34B
Optimization Problems (More Examples)
[Kaltura | YouTube] (32 minutes)
Lecture 35
The Mean Value Theorem
[Kaltura | YouTube] (13 minutes)
Also see the short (13 minute) 1966 film The Theorem of the Mean Policeman 
Lecture 36A
Linear Approximation
[Kaltura | YouTube] (11 minutes)
Lecture 36B
Newton's Method
[Kaltura | YouTube] (28 minutes)
Lecture 37A
L'Hopital's Rule; forms 0/0 and ∞/∞
[Kaltura | YouTube] (30 minutes)
Lecture 37B
Indeterminate forms 0·∞ and ∞-∞
[Kaltura | YouTube] (38 minutes)
Lecture 37C
Indeterminate forms  ∞0,  1 and  00
[Kaltura | YouTube] (30 minutes)



PART 5. Integration
Lecture 38
Antiderivatives
[Kaltura | YouTube] (35 minutes)
Lecture 39A
Initial Value Problems
[Kaltura | YouTube] (21 minutes)
Lecture 39B
Differentials
[Kaltura | YouTube] (19 minutes) 
Lecture 39C
Differential Equations
[Kaltura | YouTube] (25 minutes)
Lecture 40
Area
[Kaltura | YouTube] (41 minutes)
Lecture 41A
Definite Integrals
[Kaltura | YouTube] (38 minutes)
Lecture 41B
Other Formulations of Definite Integrals
[Kaltura | YouTube] (29 minutes)
Lecture 42
The Fundamental Theorem of Calculus
[Kaltura | YouTube] (40 minutes)
Lecture 43
More on the Fundamental Theorem
[Kaltura | YouTube] (41 minutes)
Lecture 44A
The Substitution Rule
[Kaltura | YouTube] (41 minutes)
Lecture 44B
More Substitution Examples
[Kaltura | YouTube] (21 minutes)
Lecture 44C
Substitution in Definite Integrals
[Kaltura | YouTube] (26 minutes)
Lecture 45A
What to Do when Substitution Fails
[Kaltura | YouTube] (17 minutes)
Lecture 45B
Summary: Working with Calculus
[Kaltura | YouTube] (21 minutes)