Math 400 Course Material M-400 Fall 2018 Syllabus Chapter 1 Review HW 1-1 Function Review 1-1A: Lecture Functions 1-1B: Lecture Domain 1-1C: Function Notation 1-1D: Even Odd Functions 1-E: 1-1 Functions 1-F: Inverse Functions 1-G: Equations of Lines HW 1-2 Basic Graphs 1-2A: Lecture Basic Graphs 1-2B: Function Translations HW 1-3 Polynomial Inequalities 1-3 Lecture HW 1-4 Trig Review 1-4A: Lecture Exact Values 1-4B: Basic Trig Equations 1-4C: Trig identifies HW 1-5 Trig Graphs 1-5A: 6 Standard Trig functions 1-5B The Frequency Changes 1-5C: Translating Graphs Chapter 1 Answers .. Chapter 2 Limits HW 2-1 : Power Functions Lecture 2-1A: Limits of Power Functions as x increases or decreases without bound Lecture 2-1B: Graphing Power Functions using roots and limits HW 2-2 : Graphs and Limits of Piece Wise Functions Lec 2-2: Limits of Set Builder Functions HW 2-3A : Rational Functions Limits as x--> Infinity Lec 2-3A1 : Rational Functions Introduction Lec 2-3A2 : Rational Functions Limits as x--> Infinity HW 2-3B : Graphing Rational Functions with Zeros and Vertical Asymptotes Lecture 2-3B Graphing Rational Functions with Zeros and Vertical Asymptotes HW 2-3C : Graphing Rational Functions with Zeros, Asymptotes and Holes Lecture 2-3C1 Rational Functions with "holes" Introduction Lecture 2-3C2 Limits Involving "holes" in Rational Functions Lecture 2-3C2 Graphing Rational Functions with Zeros, Asymptotes and Holes HW 2-4 Continuity Lecture 2-4 Continuity HW 2-5A: Limits involving vertical asymptotes HW 2-5B: Limits involving Theorem 1 and the Indeterminate Case 2-5:A: Limits involving Vertical Asymptotes 2-5B: Theorem 1 2-5C: The indeterminate Case and Theorem 1 2-5D: Intermediate Case Examples HW 2-6 Special Limits Involving Trig Functions Lecture 2-6A Special Limits Involving Trig Functions Lecture 2-6B The Squeeze Theorem Chapter 2 Answers Precise Definition of Limit A Precise Definition of Limit B Delta Epsilon Proofs Chapter 3 Derivatives HW 3-1 HW Introduction to Derivatives Lecture 3-1: Introduction to Derivatives HW 3-2: HW Basic Derivatives Lecture 3-2: Derivatives of Basic Function Examples Lecture 3-2: Basic Derivatives List HW 3-3: The Product and Quotient Rules Lecture 3-3A: Factoring Lecture 3-3B: The Product Rule Lecture 3-3C: The Quotient Rule Lecture 3-3D: Higher Order Derivatives HW 3-4: The Chain Rule Lecture 3-4A: The Chain Rule Intro Lecture 3-4B The Chain Rule Examples HW 3-5: Implicit Differentiation Lecture 3-5: Implicit Differentiation HW 3-6: Derivatives of Inverse Trigonometric Functions Lecture 3-6: Derivatives of Inverse Trigonometric Functions Lecture 3-6B: Proofs of the Derivatives of the Inverse Trig Functions HW 3-7: Related Rates Lecture 3-7A: Related Rates Intro Lecture 3-7B: Related Rates Examples HW 3-8: Newtons Method Lecture 3-8: Newtons Method Excel Examples of Newtons Method Chapter 3 Answers Derivative Notes and Rules Test Notes Chapter 4 Applications of Derivatives Lecture 4-1: Introduction to Extreme HW Section 4-2: Rolle's Theorem, Mean Value Theorem Lecture 4-2A: Rolle's Theorem and Mean Value Theorem \ Lecture 4-2B: Rolle's Theorem and Mean Value Theorem Examples Lecture 4-2C: Continuity and Differentiable HW 4-3A: Extrema for functions HW 4-3B: Extrema for functions with limited domains Lecture 4-3: Extrema of Functions HW 4-4: Concavity Lecture 4-4: Concavity HW 4-5 Curve Sketching Lecture 4-6: Curve Sketching HW 4-6: Optimization Problems 4-4A Video Intro 4-4B Video Product 4-4C Video Open Box 4-4D Video Fence 4-4E Video Cylinder 4-4F Video Apple Yield Lecture 4-6: Optimization Problems Lecture 4-6 Excel square and triangle example 4-4H Video Rental Income 4-4I Video Distance from f(x) to point 4-4J Video Cylinder and sphere 4-4K Video Triangle in Semicircle HW 4-7: Differentials Lecture 4-7: Differentials 4-7A Video Square 4-7B Video Cube 4-7C Video Sphere 4-7D Video Pendulum Chapter 4 Answers Chapter 4 Test Notes Chapter 5 Integration HW 5-1: Anti derivatives and Indefinite Integrals Basic Integral Rules Lecture 5-1A: Anti Derivatives Introduction Lecture 5-1B: Integrating Power Functions Lecture 5-1C: Integrating Log and Exponential Functions Lecture 5-1D: Integrating Trigonometric Functions HW 5-2: Reiham Sums and definite integrals Lecture only Lecture 5-2: Reiham Sums and definite integrals Lecture in class HW 5-3: Numerical Integration: Approximating Area under a Curve Lecture 5-3A: Numerical Integration Introduction Lecture 5-3B: Numerical Integration Trapezoid Rule and Simpson's Rule HW 5-5A: Integration by Substitution Lecture 5-5A: Integration by Substitution Lecture 5-5b: Integration by Substitution Definite Integrals Lecture 5-5C: Integration by Substitution extra examples HW 5-7: Integration of the Logarithmic Function Lecture 5-7: Integration of the Logarithmic Function Extra Information: Long Division Lecture HW 5-8: Integration of the Inverse Trigonometric Functions Lecture 5-8A: Integration of the Inverse Trigonometric Functions Lecture 5-8B: Review of Inverse Trigonometric Functions Lecture 5-8C: Review of Inverse Trigonometric Graphs HW 5-9: Area of Enclosed Regions Lecture 5-9: Area of Enclosed Regions Chapter 5 Homework Answers Chapter 5 Integration Rules

M-400 Fall 2018 Syllabus

HW 1-1 Function Review

1-1A: Lecture Functions

1-1B: Lecture Domain

1-1C: Function Notation

1-1D: Even Odd Functions

1-E: 1-1 Functions

1-F: Inverse Functions

1-G: Equations of Lines

HW 1-2 Basic Graphs

1-2A: Lecture Basic Graphs

1-2B: Function Translations

HW 1-3 Polynomial Inequalities

1-3 Lecture

HW 1-4 Trig Review

1-4A: Lecture Exact Values

1-4B: Basic Trig Equations

1-4C: Trig identifies

HW 1-5 Trig Graphs

1-5A: 6 Standard Trig functions

1-5B The Frequency Changes

1-5C: Translating Graphs

Chapter 1 Answers

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HW 2-1 : Power Functions

Lecture 2-1A: Limits of Power Functions as x increases or decreases without bound

Lecture 2-1B: Graphing Power Functions using roots and limits

HW 2-2 : Graphs and Limits of Piece Wise Functions

Lec 2-2: Limits of Set Builder Functions

HW 2-3A : Rational Functions Limits as x--> Infinity

Lec 2-3A1 : Rational Functions Introduction

Lec 2-3A2 : Rational Functions Limits as x--> Infinity

HW 2-3B : Graphing Rational Functions with Zeros and Vertical Asymptotes

Lecture 2-3B Graphing Rational Functions with Zeros and Vertical Asymptotes

HW 2-3C : Graphing Rational Functions with Zeros, Asymptotes and Holes

Lecture 2-3C1 Rational Functions with "holes" Introduction

Lecture 2-3C2 Limits Involving "holes" in Rational Functions

Lecture 2-3C2 Graphing Rational Functions with Zeros, Asymptotes and Holes

HW 2-4 Continuity

Lecture 2-4 Continuity

HW 2-5A: Limits involving vertical asymptotes

HW 2-5B: Limits involving Theorem 1 and the Indeterminate Case

2-5:A: Limits involving Vertical Asymptotes

2-5B: Theorem 1

2-5C: The indeterminate Case and Theorem 1

2-5D: Intermediate Case Examples

HW 2-6 Special Limits Involving Trig Functions

Lecture 2-6A Special Limits Involving Trig Functions

Lecture 2-6B The Squeeze Theorem

Chapter 2 Answers

Precise Definition of Limit A

Precise Definition of Limit B

Delta Epsilon Proofs

HW 3-1 HW Introduction to Derivatives

Lecture 3-1: Introduction to Derivatives

HW 3-2: HW Basic Derivatives

Lecture 3-2: Derivatives of Basic Function Examples

Lecture 3-2: Basic Derivatives List

HW 3-3: The Product and Quotient Rules

Lecture 3-3A: Factoring

Lecture 3-3B: The Product Rule

Lecture 3-3C: The Quotient Rule

Lecture 3-3D: Higher Order Derivatives

HW 3-4: The Chain Rule

Lecture 3-4A: The Chain Rule Intro

Lecture 3-4B The Chain Rule Examples

HW 3-5: Implicit Differentiation

Lecture 3-5: Implicit Differentiation

HW 3-6: Derivatives of Inverse Trigonometric Functions

Lecture 3-6: Derivatives of Inverse Trigonometric Functions

Lecture 3-6B: Proofs of the Derivatives of the Inverse Trig Functions

HW 3-7: Related Rates

Lecture 3-7A: Related Rates Intro

Lecture 3-7B: Related Rates Examples

HW 3-8: Newtons Method

Lecture 3-8: Newtons Method

Excel Examples of Newtons Method

Chapter 3 Answers

Derivative Notes and Rules

Test Notes

Lecture 4-1: Introduction to Extreme

HW Section 4-2: Rolle's Theorem, Mean Value Theorem

Lecture 4-2A: Rolle's Theorem and Mean Value Theorem \

Lecture 4-2B: Rolle's Theorem and Mean Value Theorem Examples

Lecture 4-2C: Continuity and Differentiable

HW 4-3A: Extrema for functions

HW 4-3B: Extrema for functions with limited domains

Lecture 4-3: Extrema of Functions

HW 4-4: Concavity

Lecture 4-4: Concavity

HW 4-5 Curve Sketching

Lecture 4-6: Curve Sketching

HW 4-6: Optimization Problems

4-4A Video Intro

4-4B Video Product

4-4C Video Open Box

4-4D Video Fence

4-4E Video Cylinder

4-4F Video Apple Yield

Lecture 4-6: Optimization Problems

Lecture 4-6 Excel square and triangle example

4-4H Video Rental Income

4-4I Video Distance from f(x) to point

4-4J Video Cylinder and sphere

4-4K Video Triangle in Semicircle

HW 4-7: Differentials

Lecture 4-7: Differentials

4-7A Video Square

4-7B Video Cube

4-7C Video Sphere

4-7D Video Pendulum

Chapter 4 Answers

Chapter 4 Test Notes

HW 5-1: Anti derivatives and Indefinite Integrals

Basic Integral Rules

Lecture 5-1A: Anti Derivatives Introduction

Lecture 5-1B: Integrating Power Functions

Lecture 5-1C: Integrating Log and Exponential Functions

Lecture 5-1D: Integrating Trigonometric Functions

HW 5-2: Reiham Sums and definite integrals Lecture only

Lecture 5-2: Reiham Sums and definite integrals Lecture in class

HW 5-3: Numerical Integration: Approximating Area under a Curve

Lecture 5-3A: Numerical Integration Introduction

Lecture 5-3B: Numerical Integration Trapezoid Rule and Simpson's Rule

HW 5-5A: Integration by Substitution

Lecture 5-5A: Integration by Substitution

Lecture 5-5b: Integration by Substitution Definite Integrals

Lecture 5-5C: Integration by Substitution extra examples

HW 5-7: Integration of the Logarithmic Function

Lecture 5-7: Integration of the Logarithmic Function

Extra Information: Long Division Lecture

HW 5-8: Integration of the Inverse Trigonometric Functions

Lecture 5-8A: Integration of the Inverse Trigonometric Functions

Lecture 5-8B: Review of Inverse Trigonometric Functions

Lecture 5-8C: Review of Inverse Trigonometric Graphs

HW 5-9: Area of Enclosed Regions

Lecture 5-9: Area of Enclosed Regions

Chapter 5 Homework Answers

Chapter 5 Integration Rules