Calculus Review/Preview, Session 2

Schedule: We will meet for two weeks, five days a week, 1.5 hours per day. (15 hours total.)

Format: An intro course to prep for a semester of calculus, with lecture to cover concepts, and lots of class interaction and individual practice. We will learn concepts and practice them to attain the mastery we can in a short time, in preparation for a longer, graded course during a school year. No grading; homework is optional.

Cost: $275 per person for a group class of 4 or more students; $935 for one-on-one tutoring.

Payment options: Payments can be made via PayPal, Venmo, Zelle, cash, or check.

Materials: A graphing calculator like a TI-84, TI-89, HP Prime, or Casio is recommended. No text. We’ll use free worksheets on the Internet for homework and supplements.

For more details or to schedule a class, contact Michael by phone at 281-770-2276 or by email at michaelgold@goldams.com.

“This class was excellent! My daughter said “He is the best teacher ever! He actually explains why things work so you understand what’s going on instead of just memorizing it.” She took Calc 1 a year ago and wanted to review. She feels she understands it so much better now. She said they covered an entire semester in two weeks more in depth than her original college level class. She can’t wait to take the next level.”
–Danielle L., parent, about the Outschool class “Summer Calculus Review/Preview, Session 1,” 7 Aug 2021

Class Description

In this course, we will learn all about integration and how to use it to find area and volume and more. We will meet for two weeks, five days per week, 1.5 hours per day.

We will have a mix of lecture, Q&A, and in-class work. We will have some interactive lecture in which students practice concepts and techniques as we go. Everyone will get a chance to ask and answer questions, get feedback, and check their understanding.

You will get some class notes posted everyday on Outschool (you will need to take some of your own notes!), some optional extra reading for understanding, and lots of optional practice work. All classes on Outschool are recorded, so you can watch ones you might have to miss and watch class over again to take notes or review.

Prerequisites: geometry, algebra 1, algebra 2, and precalculus (including trig).

Topics covered

1. The concept of integration
2. Using integration to find area and volume
3. Techniques of integration

Tentative schedule

Week 1
Day 1: antiderivatives and integrals
Day 2: area under curves/graphs; the concept of Riemann sum; definite integrals
Day 3: the fundamental theorem of calculus
Day 4: integration by substitution
Day 5: finding the area between two curves

Week 2
Day 6: the disc method: volume of a figure
Day 7: the shell method: volume of a figure
Day 8: integration rules
Day 9: integration by parts
Day 10: trig integrals

Time permitting, we might also cover:
-derivatives and integrals of natural logarithms
-inverse functions
-derivatives and integrals of exponential functions
-derivatives and integrals of logs and exponentials with bases other than e
-growth and decay
-trig substitution

Learning Goals

To understand the concept of integration.
To understand numerical integration.
To understand how to find areas using integration.
To understand how to find volume using integration.,
To know rules of integration.
To be prepared for a year-long calculus course.
To understand how integration is useful to fields like physics, chemistry, and biology.
To learn some logic and thinking skills that will help all through life in all areas of life.

“My son has enjoyed this class and made friends as well as broadened his understanding of Calculus. I recommend this class.”
–Xaidie C., parent, about the Outschool class “Calculus, Semester 1,” 14 Jan 2022

“This was a great class. My son especially liked the focus on understanding the logic behind the math.”
-Xaidie C., parent, about the Outschool class “Calculus, Semester 2,” 28 Apr 2022

“Mr. Gold has been an outstanding calculus teacher for our son. He was genuinely invested in the students’ ability to both master the math and become more independent and philosophical thinkers. He always provided detailed, helpful feedback and consistently went the extra mile, giving plenty of his own time in overtime to ensure the material was understood. He definitely has our recommendation. Thank you!!”
–Michele, parent, about the Outschool class “Calculus, Semester 2,” 26 Apr 2022