Calculus Lectures Online - Table of Contents. Derivatives, Sketching Graphs, Chapter, Derivatives

Calculus - Table of Contents
Chapter: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Chapter / Section:
Ordinal Name Duration Assets
1.0 Chapter 1: Pre-Calculus  
          1.1 Pre-Calculus Part 1 - Functions the Basics 10:56
          1.2 Pre-Calculus Part 2 - Polynomials and Rational Functions 13:39
          1.3 Pre-Calculus Part 3 - Algebra of Functions 15:45
          1.4 Pre-Calculus Part 4 - Inverse Functions, the Basics 13:32
          1.5 Pre-Calculus Part 5 - Polynomial and Rational Equations and Inequalities 17:34
          1.6 Pre-Calculus Part 6 - Absolute Value 13:05
          1.7 Pre-Calculus Part 7 - Trigonometric Functions 23:29
          1.8 Pre-Calculus Part 8 - Inverse Trigonometric Functions 26:06
          1.9 Pre-Calculus Part 9 - Exponential and Logarithmic Functions 23:38
          1.10 Pre-Calculus Part 10 - Exponential and Logarithmic Equations 21:49
          1.11 Pre-Calculus Part 11 - Domains of Functions 25:11
          1.12 Pre-Calculus Part 12 - More Important Facts 26:45
2.0 Chapter 2: Limits and Continuity  
Limits, the Basics    
             2.1 Limits, the Basics - Part 1 17:19
             2.2 Limits, the Basics - Part 2 20:29
Evaluating Limits    
             2.3 Evaluating Limits Part 1- Cancellation and Rationalization 20:09
             2.4 Evaluating Limits Part 2- The Theorem Evaluating Limits Part 2 - The Theorem 17:16
             2.5 Evaluating Limits Part 3 - The Squeeze Theorem 14:32
Limits and Infinity    
             2.6 Limits and Infinity Part 1 - Introduction to Infinity 18:47
             2.7 Limits and Infinity Part 2 - Infinite Limits of Rational Functions 11:06
             2.8 Limits and Infinity Part 3 - Infinite Limits of more Functions 14:13
             2.9 Limits and Infinity Part 4 - Limits that are Infinite 9:57
The Precise Definition of a Limit    
             2.10 The Precise Definition of a Limit - Part 1 19:21
             2.11 The Precise Definition of a Limit - Part 2 16:09
Continuity    
             2.12 Continuity Part 1 - Continuity, the Basics 26:02
             2.13 Continuity Part 2 - Properties of Continuous Functions 10:23
             2.14 Continuity Part 3 - The Intermediate Value Theorem 17:05
3.0 Chapter 3: Derivatives  
Derivatives, the Basics    
             3.1 Derivatives, the Basics Part 1 - Slope of a Tangent Line 11:18
             3.2 Derivatives, the Basics Part 2 - The Definition of the Derivative as a Limit 15:46
             3.3 Derivatives, the Basics Part 3 - More Derivatives as Limits 9:01
             3.4 Derivatives, the Basics Part 4 - Differentiability 13:19
             3.5 Derivatives, the Basics Part 5 - Differentiability of Piecewise Functions 10:11
Computing Derivatives    
             3.6 Computing Derivatives Part 1 - Basic Rules of Derivatives 21:31
             3.7 Computing Derivatives Part 2 - The Product and the Quotient Rules 17:00
             3.8 Computing Derivatives Part 3 - Derivatives of Trigonometric Functions 10:25
             3.9 Computing Derivatives Part 4 - The Chain Rule 22:46
             3.10 Computing Derivatives Part 5 - Higher Order Derivatives 13:05
             3.11 Computing Derivatives Part 6 - Complicated Derivatives 15:55
Proofs    
             3.12 Proofs Part 1 - Some Basic Proofs 13:48
             3.13 Proofs Part 2 - More Proofs 15:39
Implicit Differentiation    
             3.14 Implicit Differentiation Part 1 - Implicit Differentiation 15:31
             3.15 Implicit Differentiation Part 2 - More Implicit Differentiation 21:44
             3.16 Implicit Differentiation Part 3 - Derivatives of Inverse Functions 21:13
             3.17 Implicit Differentiation Part 4 - Logarithmic Differentiation 21:12
4.0 Chapter 4: Applications of Derivatives  
Rate of Change    
             4.1 Rate of Change Part 1 - Rate of Change in Physics 15:34
             4.2 Rate of Change Part 2 - Rate of Change in Biology 10:00
Related Rates    
             4.3 Related Rates - Part 1 20:49
             4.4 Related Rates - Part 2 25:43
Differentials    
             4.5 Differentials Part 1 - Differentials, the Basics 21:36
             4.6 Differentials Part 2 - Linear Approximation 18:23
Newton's Method    
             4.7 Newton's Method 23:14
5.0 Chapter 5: More Applications of Derivatives  
Minima and Maxima    
             5.1 Minima and Maxima Part 1 - Critical Points 21:40
             5.2 Minima and Maxima Part 2 - Relative and Absolute Extreme Values 13:34
             5.3 Minima and Maxima Part 3 - Minimum and Maximum on a Closed Interval 21:26
             5.4 Minima and Maxima Part 4 - The Mean Value Theorem 30:46
Indeterminate Forms and L'Hospital's Rule    
             5.5 Indeterminate Forms and L'Hospital's Rule Part 1 - Simple Forms of L'Hospital's Rule 25:01
             5.6 Indeterminate Forms and L'Hospital's Rule Part 2 - More Indeterminate Forms 18:35
             5.7 Indeterminate Forms and L'Hospital's Rule Part 3 - The Indeterminate Form f(x)^g(x) 14:04
Sketching Graphs    
             5.8 Sketching Graphs Part 1 - Increasing / Decreasing and The First Derivative Tests 21:33
             5.9 Sketching Graphs Part 2 - The Second Derivative Test 12:48
             5.10 Sketching Graphs Part 3 - Concavity 26:47
             5.11 Sketching Graphs Part 4 - Analyzing the First and the Second Derivatives 24:53
             5.12 Sketching Graphs Part 5 - Asymptotes 17:35
             5.13 Sketching Graphs Part 6 - Sketching the Graph of a Function - Part 1 15:54
             5.14 Sketching Graphs Part 7 - Sketching the Graph of a Function - Part 2 17:16
Optimization    
             5.15 Optimization Part 1 - Optimization, the Basics 23:21
             5.16 Optimization Part 2 - Optimization, more Examples 18:18
             5.17 Optimization Part 3 - Advanced Optimization: The Wire Problem 8:54
             5.18 Optimization Part 4 - Advanced Optimization: Inscribed Shapes 20:59
             5.19 Optimization Part 5 - Optimization in Economy 27:38
6.0 Chapter 6: Hyperbolic Functions and their Inverses  
          6.1 Hyperbolic Functions, the Basics 13:48
          6.2 Hyperbolic Functions, Identities 8:01
          6.3 Inverse Hyperbolic Functions 17:02
          6.4 Derivatives of Hyperbolic Functions and their Inverses 19:12
7.0 Chapter 7: Integrals  
Antiderivatives    
             7.1 Antiderivatives Part 1 - Antiderivatives of Basic Functions 23:27
             7.2 Antiderivatives Part 2 - Antiderivatives of More Functions 8:25
Integrals and Areas    
             7.3 Integrals and Areas Part 1 - Riemann Sums, the Basics 25:44
             7.4 Integrals and Areas Part 2 - The Sigma Notation 21:10
             7.5 Integrals and Areas Part 3 - Riemann Sums 16:07
             7.6 Integrals and Areas Part 4 - More Riemann Sums 15:19
             7.7 Integrals and Areas Part 5 - Definite Integrals and Areas 24:21
             7.8 Integrals and Areas Part 6 - The Fundamental Theorem of Calculus - Part 1 13:13
             7.9 Integrals and Areas Part 7 - The Fundamental Theorem of Calculus - Part 2 15:17
             7.10 Integrals and Areas Part 8 - Average Value of a Function 16:07
             7.11 Integrals and Areas Part 9 - Area Between Curves 20:34
Numerical Integration    
             7.12 Numerical Integration Part 1 - The Trapezoidal and The Midpoint Rules 24:36
             7.13 Numerical Integration Part 2 - The Simpson's Rule 14:32
             7.14 Numerical Integration Part 3 - A Different Approach to The Simpson's Rule 10:45
8.0 Chapter 8: Techniques of Integration  
Integration by Substitution    
             8.1 Integration by Substitution Part 1 - the Basics 24:18
             8.2 Integration by Substitution Part 2 - more Examples 12:42
             8.3 Integration by Substitution Part 3 - Tricky Examples 16:34
Integration by Parts    
             8.4 Integration by Parts Part 1 - the Basics 21:53
             8.5 Integration by Parts Part 2 - more Examples 22:47
Trigonometric Integrals    
             8.6 Trigonometric Integrals Part 1 26:38
             8.7 Trigonometric Integrals Part 2 14:59
             8.8 Trigonometric Integrals Part 3 - Reduction Formulas 17:22
Integrals and the Hyperbolic Functions and their Inverses    
             8.9 Integrals and the Hyperbolic Functions and their Inverses 18:16
Integration by Trigonometric Substitution    
             8.10 Integration by Trigonometric Substitution Part 1 - the Main Idea 19:39
             8.11 Integration by Trigonometric Substitution Part 2 - Examples 17:52
             8.12 Integration by Trigonometric Substitutions Part 3 - more Examples 12:41
Integration by Hyperbolic Substitution    
             8.13 Integration by Hyperbolic Substitution 15:11
Integration by Partial Fractions    
             8.14 Integration by Partial Fractions Part 1 - the Basics 29:22
             8.15 Integration by Partial Fractions Part 2 - Linear Terms 15:56
             8.16 Integration by Partial Fractions Part 3 - Irreducible Quadratic Terms 15:20
Integration by Rationalizing Substitutions    
             8.17 Integration by Rationalizing Substitutions 12:53
Techniques of Integration, Advanced    
             8.18 Techniques of Integration, Advanced 23:25
Summary    
             8.19 Techniques of Integration, Summary 11:26
9.0 Chapter 9: Improper Integrals  
          9.1 Improper Integrals Part 1 - Improper Integrals Type 1 25:26
          9.2 Improper Integrals Part 2 - The Comparison Test, the Basics 21:51
          9.3 Improper Integrals Part 3 - The Comparison Test, more Examples 20:39
          9.4 Improper Integrals Part 4 - Improper Integrals Type 2 22:13
          9.5 Improper Integrals Part 5 - Summary 12:44
10.0 Chapter 10: Applications of Integration  
Evaluating Volumes    
             10.1 Evaluating Volumes Part 1 - Evaluating Volumes by Cross Sections 25:20
             10.2 Evaluating Volumes Part 2 - The Disk and the Washer Methods 24:57
             10.3 Evaluating Volumes Part 3 - The Cylindrical Shells Method 17:03
             10.4 Evaluating Volumes Part 4 - Volumes, Advanced 6:05
             10.5 Evaluating Volumes Part 5 - Volumes, Summary 13:01
Arc-Length and Surface Area    
             10.6 Arc-Length and Surface Area Part 1 - Arc Length 31:32
             10.7 Arc-Length and Surface Area Part 2 - Area of a Surface of Revolution 28:57
             10.8 Arc-Length and Surface Area Part 3 - Gabriel's Horn 11:08
Applications of Integration to Economy    
             10.9 Applications of Integration to Economy Part 1 - Present and Future Values of Income Stream 33:37
             10.10 Applications of Integration to Economy Part 2 - Consumer and Producer Surpluses 19:25
Work    
             10.11 Work Part 1 - the Basics 24:52
             10.12 Work Part 2 - Stacking Up. Pumping Out 18:02
             10.13 Work Part 3 - Pumping Out, an Example 9:39
11.0 Chapter 11: Differential Equations and Models  
Separable Differential Equations    
             11.1 Separable Differential Equations 20:22
Exponential Models    
             11.2 Exponential Models Part 1 - Exponential Models in the Sciences 24:46
             11.3 Exponential Models Part 2 - Exponential Models in Finance 15:06
             11.4 Exponential Models Part 3 - The Logistic Equation 29:24
First Order Differential Equations    
             11.5 First Order Differential Equations Part 1 - First Order Linear Differential Equations - Part 1 11:00
             11.6 First Order Differential Equations Part 2 - First Order Linear Differential Equations - Part 2 17:05
             11.7 First Order Differential Equations Part 3 - Euler's Method 25:34
12.0 Chapter 12: Sequences and Series  
Infinite Sequences    
             12.1 Infinite Sequences Part 1 - the Basics 13:50
             12.2 Infinite Sequences Part 2 - Theorems and Properties 19:21
             12.3 Infinite Sequences Part 3 - The Monotonic Bounded Sequence Theorem - Part 1 12:49
             12.4 Infinite Sequences Part 4 - The Monotonic Bounded Sequence Theorem - Part 2 16:37
Introduction to Infinite Series    
             12.5 Introduction to Infinite Series Part 1 - Infinite Series, the Basics, Telescopic Series 25:06
             12.6 Introduction to Infinite Series Part 2 - The Test for Divergence, Geometric Series 27:03
All Positive Infinite Series    
             12.7 All Positive Infinite Series Part 1 - The Integral Test - Part 1 27:20
             12.8 All Positive Infinite Series Part 2 - The Integral Test - Part 2 25:30
             12.9 All Positive Infinite Series Part 3 - Comparison Tests for Infinite Series - Part 1 18:09
             12.10 All Positive Infinite Series Part 4 - Comparison Tests for Infinite Series - Part 2 18:12
Alternating Series    
             12.11 Alternating Series Part 1 - Alternating Series 19:16
             12.12 Alternating Series Part 2 - The Remainder Estimate for Alternating Series 11:18
             12.13 Alternating Series Part 3 - Absolute and Conditional Convergence - Part 1 15:56
             12.14 Alternating Series Part 4 - Absolute and Conditional Convergence - Part 2 14:57
The Ratio and the Root Tests    
             12.15 The Ratio and The Root Tests - Part 1 16:06
             12.16 The Ratio and The Root Tests - Part 2 25:34
Summary    
             12.17 Infinite Series, Summary 19:11
13.0 Chapter 13: Power and Taylor Series  
Power Series    
             13.1 Power Series Part 1 - the Basics 23:42
             13.2 Power Series Part 2 - Examples 18:37
Functions as Power Series    
             13.3 Functions as Power Series Part 1- the Basics 18:22
             13.4 Functions as Power Series Part 2 - Functions as Power Series 17:50
             13.5 Functions as Power Series Part 3 - More Functions as Power Series 14:14
             13.6 Functions as Power Series Part 4- An Advanced Example 13:54
Taylor Series and Polynomials    
             13.7 Taylor Series and Polynomials Part 1 - The Taylor Series Expansion of a Function 26:45
             13.8 Taylor Series and Polynomials Part 2 - Easy Manipulations of Existing Taylor Series 18:14
             13.9 Taylor Series and Polynomials Part 3 - The Sum and the Product of Taylor Series and Polynomials 18:18
             13.10 Taylor Series and Polynomials Part 4 - The Quotient of Taylor Series and Polynomials 18:14
             13.11 Taylor Series and Polynomials Part 5 - The Binomial Series - Part 1 14:40
             13.12 Taylor Series and Polynomials Part 8 - The Binomial Series - Part 2 15:57
Taylor's Inequality    
             13.13 Taylor's Inequality Part 1 - the Basics 23:44
             13.14 Taylor's Inequality Part 2 - Examples 19:15
             13.15 Taylor's Inequality Part 3 - More Examples 15:45
Numbers as Infinite Series    
             13.16 Numbers as Infinite Series Part 1 - lnx as Infinite Series 22:08
             13.17 Numbers as Infinite Series Part 2 - More Exact Sums of Infinite Series 15:20
14.0 Chapter 14: Parametric Equations and Polar Coordinates  
Parametric Equations    
             14.1 Parametric Equations Part 1 - the Basics 28:33
             14.2 Parametric Equations Part 2 - First Derivatives of Parametric Equations 14:24
             14.3 Parametric Equations Part 3 - Second Derivatives, Areas 10:51
             14.4 Parametric Equations Part 4 - Sketching Parametric Curves Using Derivatives - Part 1 19:00
             14.5 Parametric Equations Part 5 - Sketching Parametric Curves Using Derivatives - Part 2 18:42
             14.6 Parametric Equations Part 6 - Arc Lengths of Parametric Curves 15:40
             14.7 Parametric Equations Part 7 - Parametric Curves, Surface Area, Speed 17:29
Polar Coordinates    
             14.8 Polar Coordinates Part 1 - the Basics 21:54
             14.9 Polar Coordinates Part 2 - Polar Curves 31:31
             14.10 Polar Coordinates Part 3 - Derivatives and Tangent Lines of Polar Curves 23:51
             14.11 Polar Coordinates Part 4 - Area, Arc Length and Surface Area in Polar Coordinates 24:42