Briggs Calculus (Briggs, Cochran, Gillett, Schulz): Early Transcendentals, 3rd Edition - Videos and Guided Notes for Each Section

Quick Links: Chapter 2 video/notes guide, Chapter 3 guide, Chapter 4 guide, Chapter 5 guide

Chapter 2 - Limits

2.1 The Idea of Limits

  • Lesson: Where Do We Begin with Calculus, An Intro

    • Video

    • This is the only section where I have no notes, sit back and enjoy

  • Examples: How to Find Average Value of a Function

  • Examples: How to Calculate the Slope at a Point and Find the Tangent Line (without limits or derivatives)

2.2 Definitions of Limits

  • Lesson: An Intro to the Idea of Limits and Calculating Basic Limits

  • Lesson: Intro to One-Sided Limits

2.3 Techniques for Computing Limits 

  • Examples: Basic Limits

  • Lesson: Algebraic Tricks for Limits When You Get 0/0

  • Examples: Algebraic Tricks for Limits

  • Lesson: Limits that Do Not Exist

  • Lesson: The Sandwich Theorem (Squeeze Theorem) and Intro to Basic Trig Limits

  • Examples: Evaluating Basic Trig Limits

  • Examples: One-Sided Limits - Basic Examples

  • Examples: One-Sided Limits - Absolute Value Examples

  • Lesson: Lim_(x->0) sin x/x = 1 Proof

  • Examples: How to Solve Limit Problems that Use lim_(x->0) sin x/x = 1

  • More Examples: How to Solve Limit Problems that Use lim_(x->0) sin x/x = 1

2.4 Infinite Limits

  • Lesson: Limits that Equal Infinity

  • Examples: Limits that Equal Infinity

  • Lesson: Using Substitution with Some Tricky Limits Involving Infinity

  • Examples: Finding Horizontal / Vertical / Oblique Asymptotes

2.5 Limits at Infinity 

  • Lesson: A Quick Explanation of Limits as x->Inifinty or that Equal Infinity

  • Lesson: How to Evaluate Limits as x approaches infinity for Rational Functions

  • Review: How to do Polynomial Long Division / Finding Oblique Asymptotoes

  • Examples: Limits as x Approaches Infinity

  • Trickier Examples: Limits as x Approaches Infinity

  • Examples: Using the Conjugate Trick as x Approaches Infinity - A Comparison of Examples

  • Lesson: Horizontal Asymptotes and Limits at Infinity

  • Examples: Finding Horizontal / Vertical / Oblique Asymptotes

  • More Examples: Finding Horizontal / Vertical / Oblique Asymptotes

2.6 Continuity

  • Lesson: An Intro to Continuity

  • Examples: Determining When Functions are Continuous

  • Examples: Finding Limits of Compositions of Continuous Functions

  • Lesson: The Intermediate Value Property and Continuity

  • Examples: Determining a Value that Will Make a Piecewise Function Continuous

2.7 Precise Definitions of Limits

  • Lesson: Understanding the Precise Definition of a Limit, the general idea behind this

  • Examples: When a Precise Epsilon is Given

  • Examples: When a Precise Epsilon is Given, f(x)=1/x

  • Examples: When No Precise Epsilon is Given

Chapter 3 - Derivatives

3.1 Introducing the Derivative

3.2 The Derivative as a Function

3.3 Rules of Differentiation

3.4 The Product and Quotient Rules

3.5 Derivatives of Trigonometric Functions 

3.6 Derivatives as Rates of Change 

3.7 The Chain Rule 

3.8 Implicit Differentiation 

3.9 Related Rates

Chapter 4 - Applications of the Derivative

4.1 Maxima and Minima 

4.2 Mean Value Theorem

4.3 What Derivatives Tell Us 

4.4 Graphing Functions 

4.5 Optimization Problems 

4.6 Linear Approximation and Differentials 

4.7 L’Hôpital’s Rule 

4.8 Newton’s Method 

4.9 Antiderivatives

Chapter 5 - Integration

5.1 Approximating Areas under Curves

5.2 Definite Integrals 

5.3 Fundamental Theorem of Calculus 

5.4 Working with Integrals 

5.5 Substitution Rule