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Calculus BC
$499.00 – $1,349.00
Calculus AB is the first calculus course typically taken after pre calculus / analysis. Historically, this class has been a high school level course that is often offered in junior or senior year
Students learn: Limits and Continuity, Differentiation, Integration, Differential equations and applications
Description
Calculus BC
Calculus BC is calculus course typically taken after precalculus/ analysis or Algebra2/Trigonometry. Historically, this class has been a high school level course that is often offered in junior or senior year. Prerequisite: Algebra2/Trig
Contents of the Algebra 1 Course:
 Limits and Continuity
 How limits help us to handle change at an instant
 Definition and properties of limits in various representations
 Definitions of continuity of a function at a point and over a domain
 Asymptotes and limits at infinity
 Reasoning using the Squeeze theorem and the Intermediate Value Theorem
 Differentiation: Definition and fundamental properties
 Defining the derivative of a function at a point and as a function
 Connecting differentiability and continuity
 Determining derivatives for elementary functions
 Applying differentiation rules
 Differentiation: Composite, implicit and inverse functions
 The chain rule for differentiating composite functions
 Implicit differentiation
 Differentiation of general and particular inverse functions
 Determining higherorder derivatives of functions
 Contextual applications of differentiation
 Identifying relevant mathematical information in verbal representations of realworld problems involving rates of change
 Applying understandings of differentiation to problems involving motion
 Generalizing understandings of motion problems to other situations involving rates of change
 Solving related rates problems
 Local linearity and approximation
 L’Hospital’s rule
 Analytical applications of differentiation
 Mean Value Theorem and Extreme Value Theorem
 Derivatives and properties of functions
 How to use the first derivative test, second derivative test, and candidates test
 Sketching graphs of functions and their derivatives
 How to solve optimization problems
 Behaviors of Implicit relations
 Integration and accumulation of change
 Using definite integrals to determine accumulated change over an interval
 Approximating integrals using Riemann Sums
 Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
 Antiderivatives and indefinite integrals
 Properties of integrals and integration techniques, extended
 Determining improper integrals
 Differential equations
 Interpreting verbal descriptions of change as separable differential equations
 Sketching slope fields and families of solution curves
 Using Euler’s method to approximate values on a particular solution curve
 Solving separable differential equations to find general and particular solutions
 Deriving and applying exponential and logistic models
 Applications of integrations
 Determining the average value of a function using definite integrals
 Modeling particle motion
 Solving accumulation problems
 Finding the area between curves
 Determining volume with crosssections, the disc method, and the washer method
 Determining the length of a planar curve using a definite integral
 Parametric Equations, Polar Coordinates and VectorValued Functions
 Finding derivatives of parametric functions and vectorvalued functions
 Calculating the accumulation of change in length over an interval using a definite integral
 Determining the position of a particle moving in a plane
 Calculating velocity, speed, and acceleration of a particle moving along a curve
 Finding derivatives of functions written in polar coordinates
 Finding the area of regions bounded by polar curves
 Infinite Sequences and Series
 Applying limits to understand convergence of infinite series
 Types of series: Geometric, harmonic, and pseries
 A test for divergence and several tests for convergence
 Approximating sums of convergent infinite series and associated error bounds
 Determining the radius and interval of convergence for a series
 Representing a function as a Taylor series or a Maclaurin series on an appropriate interval
Register for AP Calculus Exam
Our Calculus Tutors

Kaitlyn Ang
Molecular Biology Major with Mathematics Minor  Freshman at UCLARoseville, CA 
Cindy Lopez
BA in Mathematics from Amherst CollegeChicago, IL 
Emilia Lim
Biochemistry Sophomore at the University of ChicagoSan Francisco, CA 
Riya Desai
Junior at the University of Texas at Austin pursing a B.S.A. in BiochemistryAustin, Texas 
Kylie Kim
Biology and Accounting Sophomore at University of California Los AngelesSan Diego, CA 
Alex Karpf
Math Major StanfordUnited States 
Nick Vecchioni
EECS and Data Science Junior at UC BerkeleyBerkeley, California 
Edgar Collado
D.Sc in Unmanned Systems Engineering (in progress), Master of Engineering in Electrical Engineering, Bachelor of Science in Industrial Engineering, PartTime Engineering Professor, Parttime EntrepreneurPuerto Rico 
Allison Gleason
Mechanical Engineering PhD Candidate at BerkeleyNorthern California 
Kelsey Jian
Biochemistry major at UCLALos Angeles, CA 
Benjamin Catalano
BS Chemistry from Rochester Institute of Technology, Graduate Coursework at University of PennsylvaniaUnited States 
Abigail DeVane
Civil Engineering/Architecture Junior at University of Southern CaliforniaBay Area
Additional information
Number of Classes  10 Classes, 20 Classes, 30 Classes 

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