Calculus I Video Lectures

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. (My Course Notes are synchronized with the lectures, that is, Chapter 2 corresponds to Lecture 2, etc.) The sequencing and notation match 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 e^x [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)


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 e^x [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)