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Calculus AB
$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 AB
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. Pre-requisite: precalculus
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 higher-order derivatives of functions
- Contextual applications of differentiation
- Identifying relevant mathematical information in verbal representations of real-world 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
- Differential equations
- Interpreting verbal descriptions of change as separable differential equations
- Sketching slope fields and families of solution curves
- Solving separable differential equations to find general and particular solutions
- Deriving and applying a model for exponential growth and decay
- 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 cross-sections, the disc method, and the washer method
Our Calculus Tutors
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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, Part-Time Engineering Professor, Part-time 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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