Calculus AB

taught by Yves Simon

Course description

This course is designed for the learner to learn the materials by watching videos and doing the lesson assignments. There are different ways of taking this course (see below on price of the course). I am giving you a process to learn a subject that many people find difficult. Once you master it you shouldn't have any problems. My goal is for the learner to master the content of the course. In either way you decide to take this course I can help several learners to set up discussions in New Directions Education Services Google+ page in order to learn as a group. The first notions of this course are available but the rest will be released over time when you purchase it. The course is designed to learn the materials by doing four types of activities:

1) Watching the videos

2) Reading the lessons and learning the content

3) Doing the examples of problems solved in each lesson

4) Doing the exercises non-solved

The course is divided in four chapters:

1. Notions of limits

2. Continuity

3. Derivatives

4. Integration

The student will have to watch one or more videos and complete the assignments for each of the lessons. Answers will be provided for exercises to be solved. It is recommended that the students read the materials related to each lesson, learn the definitions, rules and other types of theories and apply these to solve problems. Each example should be done by the student even though it is solved on the material as a model. The student should first look at the examples, master the process of solving them and do it by himself without looking at the model or example. For each lesson the student has to complete the non-solved exercises. Once the the student finishes the solution of these exercises he/she can compare his/her own answers to the answers/provided. Students can send any questions related to the course by reaching the instructor via his website New Direction Education Services atwww.ndes.wikidot.com

Price of the course

The price of the course depends on the way you decide to take it. The course is delivered in three ways.

1) Independent learning

You buy the course for a one-time fee of $197.00. Lessons will be delivered by email over a certain period time as it will be too overwhelming to receive the entire course at one time. You learn the entire course by yourself at your own pace. It's recommended that you decide on the amount of time you want to spend on the course. You make your own schedule and you decide on what part of the course you are going to learn each day. During this journey you are not alone as I'll be available to answer by email any questions you may have.

2) Private coaching face-to-face or online

If you decide to have coaching or tutoring you should contact the instructor Yves Simon via his email y.ssimon@yahoo.com

a) Face-to-face coaching

Private coaching is 99.00 a month. Lessons are released over time. If you are located in Boston, Massachusetts we can meet each Monday afternoon at 4.00 P.M for a 2 hours session where I go over the lessons, answering your questions and checking your assignments. This is cheap coaching for $12.50 per hour.

b) Online coaching

The price is the same: $99.00 a month. We meet online over Skype or on Google+ on Tuesday afternoon at 4.00 P.M. for a 2 hours session . During this time I go over the lessons, answering questions and checking assignments.

3) One-one tutoring (face-to-face or online)

One-one-one tutoring either based on this course or another Calculus course your are taking is $35.00 per hour. This is cheap considering that many tutors charge at a higher rate. If you decide to receive tutoring based only on my course lessons will be released over time. While you are receiving tutoring you can decide to buy the entire course and be ahead of the tutoring sessions.

Detailed course content

Chapter 1 Limits and Continuity

Unit 1 Introduction to the notion of limits

1.1 Objectives

1.2 Video explanation

1.3 The idea

1.4 Methods for evaluating limits

1.4.1 Graph method

1.4.2 Table method

1.4.3 Algebra method

Unit 2 One-sided limits

2.1 Objectives

2.2 Video explanation

2.3 The Idea

2.4 Informal definition

2.5 One-sided limit theorem

Unit 3 Properties of limits

3.1 Objectives

3.2 Video explanation

3.3 Limit rules

3.4 Substitution theorem for polynomial and rational functions

3.5 Strategies for evaluating the limit of rational functions

3.6 Limits involving trigonometric functions

Unit 4 Limit at infinity

4.1 Objectives

4.2 Video explanation

4.3 Introduction

4.4 Definition

4.5 Limit at infinity of rational functions

4.6 Infinite limits

Unit 5 Continuity

5.1 Objectives

5.2 Video explanation

5.3 Introduction

5.4 Definition

5.5 Right and left continuity

5.6 Considerations on continuous functions

5.6.1 Sum, difference, multiplication, quotient

5.6.2 Composition of continuous functions

5.6.3 Types of functions that are continuous and non-continuous

5.7 Formal definition of limit

5.7.1 Video explanation

5.7.2 Definition

Chapter II Derivatives

Unit 1 Fundamentals of derivatives

1.1 Objectives

1.2 Concept of the derivatives

1.3 Slope of a line

1,3.1 Video explanation

1..3.2 Definition

1.4 Slope of a tangent line

1.4.1 Video explanation

1.4.2 Definition

1.5 Rate of change

1.5.1 Average rate of change

1,5.1.1 Video explanation

1.5.5.2 Definition

1.5.2 Instantaneous rate of change

1.5.2.1 Video explanation

1.5.2.2 Definition

1.6 The derivative

1.6.1 Video explanation

1.6.2 Definition

1.6 Existence and differentiability of a function

Unit 2 Derivative computations

2.1 Objectives

2.2 Derivative rules

2.2.1 Video explanation

2..2.2 Derivative of a constant function

2..2.3 Derivative of a linear function

2.2.4 Constant rule

2.2.5 Addition and subtraction rules

2.2.6 Power rule

2.2.7 Derivative of polynomials

2.2..8 Product rule

2.2.9 Quotient rule

2.2.10 Derivative of trigonometric functions

2.210.1 Video explanation

2.2.10.2 Formulas

2.2.11 Higher order derivatives: an introduction to second order derivatives

2.2.11.1 Video explanation

2.2.11.2 Lesson development:

2.2.12 implicit differentiation

2.2.12.1 Video explanation

2.2.12.2 Development

2.2.13 Derivatives of logarithm functions

2.2.13.1 Video explanation

2.2.13..2 Development

2.2.14 Derivative of exponential functions

2.2.14.1 Video explanation

2.2.14.2 Development

Unit 3 Applications of Derivatives

3.1 Objectives

3.2 Rates of change

3.2.1 Video explanation

3.2.2 Development

3.3 Related rates

3.3.1 Video explanation

3.3.2 Development

Chapter III Integrals

Unit 1 Basics of Integration

1.1 Objectives

1.2 Definite integral

1.2.1 Video explanation

1.2.2 Development

1.2.3 Fundamental theorem of Calculus

1.3 Improper integral

1.3.1 Video explanation

1.3.2 Development

Unit 2 Integration techniques

2.1 Objectives

2.2 Definite sums

2.2.1 Video explanation

2.2.2 Development

2.3 Derivative rules and the substitution rule

2.3.1 Video explanation

2.3.2 Development

2.4 Integration by parts

2.2.1 Video explanation

2.2.2 Development

2.5 Trigonometric substitutions

2.5.1 Video explanation

2.5.2 Development

2.6 Integration by partial decomposition

2.7.1 Video explanation

2,7.2 Development

2.8 Tangent half-angle substitution

2.8.1 Video explanation

2.8.2 Development

2.9 Numerical approximations

2.9 Video explanation

Chapter III Application of Integrals

3.1 Objectives

3.2 Area between two curves

3.2.1 Video explanation

3.2.2 Development

3.3 Volume

3.3.1 Disc, washers and shell methods around an axis

3.3.1.1 Video explanation

3.3,1.2 Development

3.4 Area of a surface of revolution

3.3.2 Washer and shell methods around a non-axis line

3.3.2.1 Video explanation

3.2.2 2 Development

3.5 Applications from Physics, Engineering and Statistics

3.5.1 Video explanation

3.5.2 Development

3.6 Numerical approximations to definite integrals

3.6.1 Rieman sums

3.6.1.1 Video explanation

3.6.1.2 Development

3.6.2 Trapezoidal sum

3.6.2.1 Video explanations

3.6.2.2 Development



Yves Simon
Yves Simon
Educator and Tutor face-to-face and online

I am a math certified educator with many years of experiences in public and private schools. My educational background is in k-12 education and administration, Math, Physics and Science Teaching and Civil Engineering. I have been teaching and tutoring Math, French, ESL,Spanish, etc for many years. I make learning easy and enjoyable for my students. Don't hesitate to contact me for face-to-face and online tutoring about these subjects. Face-to-face and online courses are also available. For more information visit my site New Direction Education Services at http://www.ndes wikidot.com.biz.. Contact me at y.ssimon@yahoo.com

Course Curriculum

Course content
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Integration
Lesson I Indefinite integral video lecture
Lesson I Indefinite integral written lesson
Lesson II Integral of basic functions video lecture
Integral of basic functions written lesson
Lesson III Integration by substitution video lecture
Integration by substitution written lesson
Lesson IV Integration by parts video lecture
Integration by parts written lesson
Lesson V Integration by partial fractions video lecture
Integration by partial fractions written lesson
Lesson VI Integration of simple trigonometric functions
Integration of simple trigonometric functions written lesson
Lesson VII Integration of the power of sine and cosine
Integration of the power of sine and cosine written lesson
Lesson VIII Integration of the product of the power sine by the cosine power
Integration of the product of the power of sine by the power of cosine written lesson
Lesson IX Integration of the power of secant and the power of tangent
Integration of the power of secant and the power of tangent written lesson
Lesson X Integration of the product of the power of secant by the power of tangent
Integration of the product of the power of secant by the power of tangent written lesson
Lesson XI Integrating an expression with radical by using trigonometric substitutions video lecture
Integrating an expression with radical by using trigonometric substitutions written lesson
Lesson XII An approach to calculate the area under curve video lecture
An approach to calculate the area under curve video lecture video lecture
Lesson XIII Properties of definite integrals video lecture
Properties of definite integrals written lesson
Lesson XIV Definite integrals and integration by substitution video lecture
Definite integrals and integration by substitution written lesson
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