Calculus I (10-Week)

Completed by 1 learner

Ages 12-17

Live Group Class

In this 10 week course, students will learn the topics included in a college-level Calculus I course.

Frank Curotto

Average rating:

5.0

Number of reviews:

(11 reviews)

Live video meetings

3x per week, 10 weeks

1-18 learners per class

120 min

About Learning Overview Teacher Reviews

What's included

30 live meetings

60 in-class hours

Class Experience

Topics include limits; continuity; and differentiation techniques for algebraic, trigonometric, natural logarithms/exponentials.  The define integral and the anti-derivative are linked by the Fundamental theorem of Calculus.  Numerical methods such as Newton’s method as well as Trapezoidal and Simpson’s rule will be explored. Theory is augmented by application from a variety of disciplines.

Prerequisites
The class is taught with the assumption that the student has taken Intermediate Algebra and Trigonometry. 

Calculator
Students should have a graphing calculator. Most schools/colleges/universities only permit the TI-83 or TI-84, so if you need to purchase a calculator, I would recommend investing in one of those models.

Purpose
Calculus I is designed for prospective math/science majors as well as for students whose primary interest is engineering, business or the physical and social sciences.

Calculus I
Course Schedule
Class meets three times weekly

Week 1	
Lesson 1: Rates & Tangents/Limits & Laws
Lesson 2: One sided limits
Lesson 3: Continuity

Week 2	
Lesson 1: Infinite limits
Lesson 2: Derivatives & Tangents
Lesson 3: Review

Week 3	
Lesson 1: Exam 1
Lesson 2: Derivative Function
Lesson 3: Rates of Change/Derivatives & Trig

Week 4	
Lesson 1: Chain Rule/Implicit Derivative
Lesson 2: Derivative of Inverses
Lesson 3: Inverse Trig Derivatives

Week 5	
Lesson 1: Related Rates
Lesson 2: Review
Lesson 3: Exam 2

Week 6	
Lesson 1: Linearization/ Extreme Value Theorem
Lesson 2: Mean Value Theorem/First Derivative Test
Lesson 3: Concavity, Curve Sketching

Week 7
Lesson 1: L’Hopitals Rule
Lesson 2: Optimization
Lesson 3: Review

Week 8
Lesson 1: Exam 3
Lesson 2: Anti-derivatives
Lesson 3: Areas & Finite Sums/Sigma Notation & Limits

Week 9
Lesson 1: Definite Integral/Fundamental Theorem
Lesson 2: Indefinite Integral & Substitution
Lesson 3: Area Between Curves

Week 10
Lesson 1: Logarithm Definition
Lesson 2: Review
Lesson 3: Final Exam

Learning Goals

Student Learning Outcomes
The student will at least be able to demonstrate competency in:
1)	Functions
a.	Express/Evaluate a function explicitly and implicitly
b.	Add/Subtract/Multiply/Divide and use compositions
c.	Describe domain & range
d.	Classify as algebraic/transcendental
e.	Use in Mathematical models
f.	Find absolute/relative extrema, influx points
g.	Find intervals where increasing/decreasing
h.	Find intervals where concave up/down

2)	Graphing
a.	Draw a representative graph to model phenomena
b.	Use graphs to infer function behavior & evaluation
c.	Locate points on a graph satisfying certain requirements about continuity/limits/derivatives
d.	Describe a graph (function rule not needed) satisfying certain requirements about continuity/limits/derivatives
e.	Visually describe the meaning of all critical theorems/ideas in Calculus through a graphical picture

3)	Limits
a.	Explore limits numerically, graphically, and analytically
b.	State informal definitions of one and two sided limits
c.	Use Limit laws to evaluate simple limits
d.	Use various techniques to evaluate limits
e.	State definition of Continuity and express continuity on an interval in terms of a graph
f.	Describe/provide examples of the forms of discontinuity

4)	Derivatives
a.	Describe, evaluate, and relate rates of change
b.	State definition of the derivative of a function
c.	Evaluate derivative of algebraic functions by definition
d.	Evaluate derivatives of algebraic, trigonometric, logarithmic, and exponential functions through rules
e.	Find equation of tangent/secant lines
f.	Use 1st/2nd Derivative Tests
g.	Use Newton’s method/differentials to approximate values

5)	Summation & Integration
a.	Evaluate Basic Anti-derivatives through rules
b.	Evaluate Anti-derivatives through variable substitution and pattern recognition
c.	Use & simplify summation notation
d.	State the definition of a definite integral
e.	Evaluate definite integrals by definition/graphical means
f.	Evaluate definite integral through the fundamental theorem of calculus and properties of definite integrals

Other Details

Supply List

Course Materials
Textbook (**OPTIONAL**) 
Thomas’ CALCULUS Early Transcendentals
14th Edition
Author: Weir, Hass
(The textbook is NOT required for this course, but it is useful to have. The required material from the textbook will be provided as part of the cost of the class)

Calculator
Students should have a graphing calculator. Most schools/colleges/universities only permit the TI-83 or TI-84, so if you need to purchase a calculator, I would recommend investing in one of those models.

External Resources

Learners will not need to use any apps or websites beyond the standard Outschool tools.

Meet the teacher

Frank Curotto

Joined March, 2021

5.0

11reviews

Profile

Teacher expertise and credentials

Classes: I'm still working on the full range of classes I will teach. I will have a variety of Mathematics courses, Computer Science courses, clubs (including chess and Dungeons & Dragons 5th Edition Adventure leagues), and possibly some more in other fields.

Background: I am an instructor and supplemental instructor at the Rowan College of South Jersey, specializing in the areas of Mathematics and Computer Science. Prior to that, I was a Network Engineer for 10 years. I've also worked with the Writing Center at RCSJ on English papers. I've played chess since high school, and have competed in chess tournaments around the world. When it comes to my Dungeons & Dragons background, I've played since the early 2000's. In 2004, I was a certified DM (Wizards of the Coast used to have DM exams) and was invited to host a 30th Anniversary Eberron Campaign.

Philosophy: When it comes to teaching, I like to tackle topics from multiple angles. A student who struggles with a concept is rarely unable to grasp the knowledge; they simply need it explained in a way that makes sense to them.