# Calculus with Dr. Bob I: Limits and Derivatives

### Course Description

In this first in a collection of seven series of calculus lessons, Math Doctor Bob (Robert Donley) walks you through the very first steps of differential calculus: Limits; continuity; intermediate value theorem; bisection method; tangent lines; derivatives; optimization; Newton's Method; and differentials.

Dr. Bob in Lesson 48, demonstrating the Extreme Value Theorem using critical points
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### Video Lectures & Study Materials

# Lecture Play Lecture
1 Limits 1a - Definition and Basic Concepts Play Video
2 Limits 1b - Delta-Epsilon Formulation Play Video
3 Limits 1c - Limit Failure Play Video
4 Limits 1d - Polynomial and Rational Functions Play Video
5 Limits 1e - Compositions and Squeeze Theorem Play Video
6 Limits 1f - Trigonometric Functions Play Video
7 Examples of Limits Play Video
8 Continuity 1a - Definition and Basic Concepts Play Video
9 Continuity 1b - Polynomial/Rational Functions and The Extreme Value Theorem Play Video
10 Examples of Continuity Play Video
11 Fast Solution of Inequality Using Continuity Play Video
12 Bisection Method 1 Play Video
13 Bisection Method 2 Play Video
14 Vertical Asymptotes 1a Play Video
15 Vertical Asymptotes 1b Play Video
16 Definition of Tangent Line Play Video
17 Example of Tangent Line Play Video
18 Definition of Derivative Play Video
19 Power Rule for Derivatives Play Video
20 Tangent Line to x^2-4x Play Video
21 Horizontal Tangent Lines to a Polynomial Play Video
22 Derivative of sin(x) and cos(x) Play Video
23 Tangent Lines to sin(x) Play Video
24 Motion in a Line Play Video
25 The Product Rule Play Video
26 General Product Rule Play Video
27 Power Rule for Rational Exponents Play Video
28 The Quotient Rule Play Video
29 Trig Derivatives Play Video
30 Examples of Trig Derivatives Play Video
31 Tangent Lines for sec(x) Play Video
32 Tangent Lines for cot(x) Play Video
33 The Chain Rule Play Video
34 Example of Chain Rule 1 - Basic Examples Play Video
35 Example of Chain Rule 2 - Approximation with Tangent Line Play Video
36 Example of Chain Rule 3 - Trig Functions Play Video
37 Example of Chain Rule 4 - Triple Chain Rule Play Video
38 Higher Order Derivatives Play Video
39 Graphs and Higher Order Derivatives Play Video
40 Implicit Differentiation 1 - Definition and Basic Concepts Play Video
41 Implicit Differentiation 2 - Basic Example Play Video
42 Implicit Differentiation 3 - Approximation with Tangent Line Play Video
43 Implicit Differentiation 4 - Example with Trig Functions Play Video
44 Implicit Differentiation 5 - Higher Derivatives Play Video
45 Related Rates Play Video
46 Example of Related Rates 1 Play Video
47 Example of Related Rates 2 Play Video
48 Extreme Value Theorem Using Critical Points Play Video
49 Example of Extreme Value Theorem 1 Play Video
50 Example of Extreme Value Theorem 2 Play Video
51 Example of Extreme Value Theorem 3 Play Video
52 Rolle's Theorem Play Video
53 Mean Value Theorem Play Video
54 Increasing/Decreasing and Derivatives 1 Play Video
55 Increasing/Decreasing and Derivatives 2 Play Video
56 Example of Increasing/Decreasing 1 Play Video
57 Example of Increasing/Decreasing 2 Play Video
58 Example of Increasing/Decreasing 3 Play Video
59 First/Second Derivative Test for f(x) = x^4 - 12x^3 Play Video
60 First/Second Derivative Test for f(x) = sin(x) Play Video
61 First/Second Derivative Test for f(x) = x^2 - 6x^{4/3} Play Video
62 Concavity and the Second Derivative Play Video
63 Concavity for f(x) = sin(x) Play Video
64 Concavity for f(x) = (x^2 - 36)/(x-2) Play Video
65 Concavity for f(x) = |x^2 - 4x - 12| Play Video
66 Example of Limit at Infinity 1 Play Video
67 Example of Limit at Infinity 2 Play Video
68 Example of Limit at Infinity 3 Play Video
69 Checklist for Sketching Functions Play Video
70 Graph of f(x) = x^4 - 8x^3 Play Video
71 Graph of f(x) = (x-2)/(x-1) Play Video
72 Graph of f(x) = sin(x) + cos(x) Play Video
73 Graph of f(x) = sin(x)/(1+cos(x)) Play Video
74 Graph of f(x) = x^{4/3} - 8x^{2/3} Play Video
75 Optimization 1 Play Video
76 Optimization 2 Play Video
77 Optimization 3 Play Video
78 Optimization - Maximizing Profit Play Video
79 Newton's Method 1 Play Video
80 Newton's Method 2 Play Video
81 Differentials 1 Play Video
82 Differentials 2 Play Video