Math 1410 Prep
There are three ways to use this material:
If you took AP Calc AB and want to learn some of the additional material taught in AP Calc BC, there is a suggested order for looking through the material
If you took AP Calc AB/BC and want to review only the AP Calc BC concepts that will be helpful for Math 1410, there is a suggested order
**Suggested Approach**: If you want to review concepts in chronological order based on potential prerequisite material for each week in Math 1410, there is a suggested order
Notes:
Click on each hyperlink, which will direct you to the pdf note on that topic. Throughout the pdf's, there are little purple textboxes with websites that you may look at for more detailed descriptions and examples.
At the end of some of the pdfs, there is a "Foreshadow" part of the notes. It is not expected that you already know the content in the "foreshadowing" sections -- the content in these sections are provided to give you a hint about how certain topics from single variable calculus connect to ideas you will learn in multivariable calculus (Math1410).
Approach 1: If you took AP Calc AB and want to learn some of the additional material taught in AP Calc BC material, this is the suggested order for looking through the material:
Approach 2: If you took AP Calc AB/BC and want to review only the concepts from AP Calc BC that will be helpful for Math 114, this is the suggested order:
**Approach 3: If you want to review concepts in chronological order based on potential prerequisite material for each week in Math 114, this is the suggested order with some descriptions: (each week's material is based on Ghrist's Calculus BLUE schedule on his website -- his website is listed under the "Other Resources" tab on this website)
In general, you should know integration techniques: Integration by Parts and Trig Substitution
Week 1 -- Intro to Vectors and Parametric Equations and Curves
When learning about the velocity for a curve, we need to know about the derivatives of ordinary functions. When learning about the arclength for a curve, we need to know about integrals of ordinary functions.
Week 2 and 3 -- Intro to Matrices
When learning about linear algebra, some previous exposure to the basic level of linear algebra is helpful.
Week 4
When learning about partial derivatives, we need to know about ordinary derivatives.
Week 5 -- Inverse Function Theorem and Fundamental Theorem of Calculus
When learning about basic differentiation rules / chain rule / Inverse Function Theorem for general functions, it is helpful to know about the basic differential rules / chain rule / Inverse Function Theorem for ordinary functions.
Week 6 -- Taylor Series and Linearization
When learning about the Taylor Series for functions of several variables, we need to know about the Taylor Series for functions of single variable.
Week 7 -- First and Second Derivative Test
When learning about the First and Second Derivative Test for functions of several variables, it is helpful to know about the First and Second Derivative Test for functions of single variable.
Week 8
When learning about multiple integrals (for functions of several variables), we need to know about the ordinary integral (for functions of single variable).
Week 10 -- Polar Coordinates and Graphs
When learning about cylindrical coordinates (for R^3), it is helpful to know about the polar coordinates (for R^2). When learning about the "change of variables theorem" for multiple integrals, it is helpful to know the "u-substitution theorem" for ordinary integrals.
Week 11 - Slope Fields
When identifying vector fields, it is helpful to know about slope fields.
Weeks 11, 12, and 13
We will use basic vector calculus learned in Weeks 1-10 to study more advanced topics
These are all the material on this website in alphabetical order for your reference:
References:
All of this material could not have been made without the following resources. Many of the definitions and examples in the notes on this website come from these resources:
Thomas, George Brinton. Thomas Calculus: Early Transcendentals. Edited by Maurice D. Weir et al., 13th ed., Pearson, 2014.
Robert Ghrist, Calculus BLUE Video Lectures
Paul's Online Calculus Notes
Anton, Howard, et al. Calculus Early: Early Transcendentals - Single Variable. John Wiley & Sons Inc, 2005.