Our Best-Selling Calculus Manuals
We divide our calculus material into two categories: The first is the everyday classroom activities. This includes teaching and testing. The second is preparing for the AP exam. While teachers are encouraged to incorporate AP exam prep in their everyday teaching, sometimes you have to have students do many mundane problems to nail down differentiation and integration techniques. These problems are covered in the everyday materials.
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Evolution of the A.P. Calculus Manuals
I started teaching A.P. calculus AB in 1993 after years of teaching a college preparatory calculus course. The textbook was Larson and Hostetler, 3rd edition. It has been my experience that we buy expensive and heavy textbooks for the students but find that students simply have trouble learning from them. Students see the textbook as a source of problems, but not a teaching tool.
As is my practice, I developed worksheets that would lead students through certain types of problems. If a student was absent and wanted the work that we missed, I found it easier just to hand the student the worksheet rather than refer him to the text.
Since our periods were short, I also found that rather than assign many problems from the textbook, I would assign what I felt to be essential problems I needed to get through and simply added them to the worksheet. Over a period of six years, I developed worksheets for just about every topic in A.P. calculus.
However, I found myself spending most of free periods in front of the copy machine. One year, I got the brainstorm to put all of these worksheets together in one comprehensive manual so the reproducing could be done all at once and the students would receive the manual at the start of school. I did so, adding a table of contents, and explaining where the concepts taught in the manual were to be found in the textbook we were using.
Over a summer, I copied these 225 page manuals and put them together. I used them first in the 1999-2000 school year and had unbelievable testimonials from students. I have been using them ever since. A textbook is distributed at the beginning of the school year and students are encouraged to take it home and use it as a reference if they need more insight to a proof of a theorem or simply want more practice problems.
Taking over the BC calculus class in 2000, I spent the summer writing a BC manual and my students have used it for seven years as well. The reactions were even stronger.
My school moved to a copying service. At the start of the summer, I requested that these manuals be published. They came back to me in August, double sided, and with holes punched in them. They were given to the students on day one and we complete the entire manual. In using a text, we rarely complete half of it. The students are allowed to keep the manual at the end of the course. Many have told me that they have taken it to college with them and it remains a valuable source of review for them. If students are diligent and do all the classwork and homework in the appropriate places in the manual, they have a complete record of the entire AP calculus course.
Several years later, I decided to write an accompanying solution manual. I do not like answer keys as there is too much fumbling trying to find the correct page. My thought was to have a solution manual that was exactly like the manual I give the students, except that the solutions to the problems are written in the spaces. So the teacher can teach directly out of the solution manual and not have to handle two separate documents.
The manuals changed little over the years with the exception of correcting some errors. But I felt that the look of the manual, using much older technology, had become dated. Graphics were blocky and hard to understand. Because the manual used a much older version of Microsoft Word that was no longer supported, I ended up typing the manual again and it took more than 6 months to re-create it. But it is a huge improvement in terms of looks and content. Both manuals now cover all topics in the revised AB and BC curriculum for 2016-2017. Each manual has an Essentials section and a Non-Essential section that covers topics if you have more time to spend. The AB manual has a brief review of important precalculus topics and the BC manual has a review of essential AB topics. There is a Combination manual available as well for schools that teach AB/BC as one course.
Use of the A.P. Calculus Manuals
The manual is not a textbook. It is not intended to be one. It simply presents topics and walks students through a series of classwork problems. The teacher does the teaching of the problem. The students take notes in the space provided. There is little or no attempt to prove theorems. You can still do that on your own. The manual provides you and your students sample problems, which will touch upon every concept that is covered in the A.P. curriculum. (and some that has been eliminated from the curriculum as well). To reiterate, this manual still needs a good teacher - you. You cannot just hand the student the manual and expect him or her to read it and understand it.
There are also homework problems for every concept. Again, space is provided for students to complete them. There are enough challenging problems but the idea is to give students enough problems to test whether they understand a concept without overburdening them. I am not smart enough to write a math book. In coming up with sample problems and homework problems, I used a number of calculus textbooks for ideas. While one cannot copyright "take the derivative of 2x," there are word problems that I adapted from these sources. In most cases, I attempted to change the problem slightly by altering a given value or the context of the problem.
By downloading the free manuals (or purchasing paper copies), you have the right to make as many copies as you wish as long as you use them for face-to-face classroom use. They may not be placed on a school's website except by special permission. Solutions should never be placed on the Internet.
Calculus Manual Topics
Topics for AB Calculus
2. Tangent Lines
3. Slopes of Secant and Tangent Lines
4. Graphical Approach to Limits
5. Finding Limits Algebraically
6. Definition of Derivative
7. Derivatives Using Technology
8. Techniques of Differentiation
9. Differentiation by the Chain Rule
10. Differentiation of Trig Functions
11. Implicit Differentiation
12. Derivatives/Transcendental Funct.
13. Derivatives of Inverse Functions
14. Linear Approximations
15. Continuity and Differentiation
16. Related Rates
17. Straight-Line Motion
18. Three Important Theorems
19. Function Analysis
20. Curve Sketching
21. Finding Absolute Extrema
22. Optimization Problems
23. Economic Optimization Problems
24. Indeterminates/L'Hospital's Rule
25. Indefinite Integration
27. Riemann Sums
28. Definite Integrals
29. The Accumulation Function
30. Fundamental Theorem of Calculus
32. Transcendentals & Integration
33. Straight-Line Motion Revisited
34. Average Value/2nd FTC
35. Inverse Trig Functions
36. Area of Region Between 2 Curves
37. Volums of Revolution
38. Slope Fields
39. Deparable Differential Equations
40. Exponential Growth
41. Other Growth & Decay Models
12. Logarithmic Differentiation
24a. Newton's Method
26a. L'Hopital's Rule Advanced
29a. Exact Area Using Limits
37a. Volume Using Cylindrical Shells
III. Precalculus Review
Eliminating Complex Fractions
Exponentials & Logarithms
Topics for BC Calculus
1. Indeterminates/L'Hospital's Rule
2. Integration by Parts
3. Integration by Partial Fractions
4. Improper Integrals
5. Arc Length/Surface Area
6. Eule'rs Method
7. Logistic Growth
8. Curves Defined by Parametric Equations
9. Calculus and Parametric Equations
10. Polar Coordinates & Graphs
11. Polar Coordinates Area/Arc Length
12. Vectors in the Plane
13. Vector-Valued Functions
14. Velocity/Acceleration of Vectors
15. Taylor Polynomial approximations
17. Infinite Series
18. Geometric and p-series
19. The Integral Test
20. Comparison of series
21. Alternating series
22. Ratio and root tests
23. Series Convergence Review
24. Power Series
25. Taylor & Maclaurin Series
26. Manipulation of Series
0a. Marginal Analysis/Demand Elasticity
1a. Epsilon Delta Definition of Limits
2a. Power of Sines & Cosines
3a. Partial Fractions Advances
5a. Simpson's Method
7b. Fluid Force
7c. Center of Mass
27. First Order Differential Equations
III. AB Review
R1. Basic Differentiation
R2. Linear Approximation
R4. Related Rates
R5. Function Analysis
R6. Integration Techniques
R7. Definite Integral/Accumulation
R8. Riemann Sums
R9. Fundamental Theorem of Calculus
R10. Straight-Line Motion
R11. Area and Volume
R12. Differential Equations/Growth & Decay
We are happy to offer these manuals for no charge. Go to the Calc AB Manual or Calc BC Manual page to download any or all sections of either the AB or BC manual. Each section has approximately 5 topics. They are in PDF format.
The manual is also available in paper format as well as the solution manual for both AB and BC calculus. Go to the page on paper manual and solution manuals. These do have a cost associated with them. You can order them from the same pages. Go to Purchase Options to order them in combination for less money.
Every teacher needs an answer key. You can either solve the problems in your own copy of the student manual, or purchase the answer key in paper format. The answer key has the same page numbering as the student manual to make it easy to keep your students 'on the same page'.
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