Math 1410 Prep

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:

1. Integration by Parts and Trig Substitution 

2. Slope Fields

3. Sequences 

4. Infinite Series

5. Taylor Series

6. Parametric Equations and Curves

7. Polar Coordinates and Graphs

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:

1. Integration by Parts and Trig Substitution 

2. Linearization

3. First and Second Derivative Tests

4. Inverse Function Theorem and Fundamental Theorem of Calculus

5. Slope Fields 

6. Taylor Series

7. Parametric Equations and Curves

8. Polar Coordinates and Graphs

9. Intro to Matrices

10. Intro to Vectors

**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