AB Calculus
Text: Anton, Calculus,A New Horizon: Brief Edition (Sixth Edition), Wiley, 1999.
Advanced Placement Calculus AB is designed to be the rough equivalent of a one semester college level Calculus course. This course deals with underlying theory and applications which are considered standard knowledge in an intro course. Though we emphasize concepts over mathematical rigor, we will be looking at some proofs of ‘famous’ theorems to the extent that it reinforces previous knowledge and is within the grasp of the average prepared AB student.
Since this is supposedly equivalent to a college level course there are some things you should realize. There is sufficient material here that much more of the responsibility for learning will be placed on you than perhaps in earlier courses. I can't "teach you" everything; you'll have to learn a good bit on your own .
The pace of the course is fast. We only meet 4 times a week for a course that easily could eat up 5 meetings. The material is, in many cases, complex and rests heavily on understanding previous material. You'll get out of this class what you put into it. A variable you have considerable control over is the amount of time you invest in doing homework and reading over class notes. Reading class notes will be very important if you wish to do well. Please do not wrongly assume the textbook homework is adequate to get by.
Advice: Find a study group
or at least a study partner. Studies on college campuses have shown
that working in groups is one of the variables most predictive of success.
Two people can help each other through mild confusions much better than
anyone can working alone. Furthermore, this person will be helpful if you
miss class. If you depend solely on me for catching up, it may be several
days before our schedules allow for it. During that time, you may be falling
further behind.
Timeline (See Below for Details)
Assignment
#1 : Functions (2-3 weeks)
Assignment
#2 : Limits and Continuity (2-3 weeks)
Assignment
#3 : The Derivative (5 weeks)
Assignment
#4 : Applications of the Derivative (4 weeks)
Winter Break
Assignment
#5 : Area and the Definite Integral (2-3
weeks)
Midyear Exam (3 hour long cumulative)
Assignment
#6 : Integration and Applications (5 weeks)
Assignment
#7 : Differential Equations (3 weeks)
Course
Review : (3 weeks)
Final Exam (2 class periods
worth of Exam immediately before the AP)
AP Exam
Assignment
#1
Functions
Approximately 2-3 weeks
Definition of Function
Domain and Range
Finding Domain and Range graphically,
algebraically
Algebra of functions
Piecewise functions and absolute
value
Chapters 1.1-1.4, Appendix A
Calculator functions
Zoom
Table
Test
Y-Vars
Assignment
#2
Limits and Continuity
Approximately 2 to 3 weeks
Definition of a Limit
Notation
Determining Limits Graphically
Determining Limits by observing
Tables of Values
Determining Limits using Algebra
and Formal Limit properties
Limits at Infinity
Indeterminate Forms (infinity
over infinity, zero over zero)
Definition of a function being
continuous at a point
Continuous Functions
Theorems on Continuous Functions
and Limits
Intermediate Value Theorem
Chapter 2 (omit 2.3)
Calculator functions
Graphing
Table functions
Assignment
#3
Derivatives
Approximately 5 weeks
Average rates of change of a
function
Instantaneous rates of change
of a function
Notation
Derivative as the Limit of a
Difference quotient
Derivatives as functions
Quick Evaluation:Product/Quotient/Chain
Rules
Derivatives of trig/log/exponential
functions AND their inverses
Implicit differentiation
Differentiability vs. Nondifferentiability
Derivatives of Inverse Functions
Derivatives of Higher Order
Chapters 3, 4 (omit 4.6)
Calculator
nDeriv
Draw Tangent
Assignment
#4
Applications ofDerivatives
Approximately 4 weeks
Differentials
Local linearity and approximation
by Tangent Line
Rectilinear Motion Problems
Instantaneous Rates of Change
Problems
Mean Value Theorem (Rolle’s
Theorem)
Extrema (Local/Global,Maxima/Minina)
Extreme Value
Rates of Change of Rates of
Change
Analysis of Graphs (1st derivative
and intervals of increase and decrease; 2nd derivatives-concave
up/down, 1st and 2nd derivative tests)
Applied Maxima/Minima Problems
Related Rates Problems
Chapters 4.6, 5,6
Calculator
Area Approximation and the Definite
Integral
Approximately 3 weeks
Area under a curve
Trapezoidal Approximation
Rectangular Approximation: Finite
Riemann Sums
Definite Integral-infinite Riemann
Sums
Conditions for Integrability
Formal properties of definite
integrals
Notation
Calculator
fnInt
Chapters: 7.1.,7.4, 7.5, 9.7
Assignment
#6
Integration and Applications
Approximately 5 weeks
Antidifferentiation: basics,
u substitution
Indefinite Integrals as families
of functions/integral curves
Fundamental Theorem of Calculus
(FTC)
Mean (Average)Value Theorem
for Integrals
Area between curves
Volumes with similar cross sections
Volumes of revolution
Accumulation Functions
FTC Part 2
Rectilinear Motion revisited
Chapters: 7.2-7.3, 7.6 -7.9
Calculator
Assignment
#7
Differential Equations
Approximately 3 weeks
Integration by parts
n Parameter families of curves
Differential equations and vocabulary
(1st order, solution, o.d.e, Initial value problem)
Separation of variables
Exponential growth and decay
Slopefields
Euler's Method for approximating
solutions
Chapters 7.2, 9.1,10.1-10.3