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課堂經歷
英語程度 - 未知
美國等級 10 - 12
遵循 College Board Advanced Placement 課程
與 Advanced Placement (AP) Standards對齊
In this course, we will cover the material in Calculus AB, with an aim to prepare you for the AP exam. The course will consist of 30 live lectures, divided into 6 units (Note that the AP curriculum is divided into 8 units - we will cover those units, but units 2 & 3 are consolidated, as are units 4 & 5): 1. Limits and continuity 2. The derivative 3. Applications of the derivative 4. The integral 5. Applications of the integral 6. Differential Equations Each class will consist of 30-45...
6 units//32 lessons//32 Weeks
Unit 1Limits and ContinuityLimits and Continuity4 lessons4 WeeksWeek 1Lesson 1Instantaneous Change and LimitsWe'll begin by motivating the study of differential calculus in the context of instantaneous change. We will then introduce limits as a method of finding instantaneous rates. Finally, we will learn to analyze right, left, and overall limits graphically.Week 2Lesson 2Limit PropertiesIn this class, we'll look at the linearity of the limit, and limits of products and quotients. This class will meld into lesson 3, so we'll begin introducing some algebraic techniques for evaluating limits.Week 3Lesson 3Algebraic LimitsPicking up from week 2, we'll look at finding limits via factorization, conjugate multiplication, and squeeze theorem.Week 4Lesson 4Continuity and the IVTWe will look at the three conditions for continuity at a point, working through both graphical and algebraic applications. We will then introduce the intermediate value theorem.Unit 2DifferentiationDifferentiation4 lessons4 WeeksWeek 5Lesson 5Introduction to the DerivativeHaving covered limits, we'll begin by looking at the limit definition of the derivative. We will then cover the basic derivatives students should memorize - basic trig, exponential, polynomial, logarithmic.Week 6Lesson 6Product and Quotient RuleWe'll introduce product rule and quotient rule.Week 7Lesson 7Chain RuleWe'll begin with a brief review of composite functions, and then introduce the chain rule for derivatives.Week 8Lesson 8Implicit DifferentiationWe'll start off by motivating the need for implicit differentiation by looking at inverse functions and implicit functions. We will then work through the process of implicit differentiation.Unit 3Applications of the DerivativeApplications of the Derivative8 lessons8 WeeksWeek 9Lesson 9Position, Velocity, AccelerationWe'll look at velocity and acceleration as derivatives, and begin diving into more FRQ applications.Week 10Lesson 10Tangent Line approximationWe'll begin with finding tangent lines to functions, then move on to seeing how to use tangent lines for estimation. We will also discuss how concavity informs whether an estimate is an overestimate vs. underestimate. Finally, we will look at more complex applications, including tangent line approximation for implicit functions.Week 11Lesson 11Related RatesWeek 12Lesson 12L'hopital's RuleWeek 13Lesson 13The MVT and EXTWeek 14Lesson 14Local Maxima and MinimaWeek 15Lesson 15Global Maxima and MinimaWeek 16Lesson 16OptimizationUnit 4IntegrationIntegration5 lessons5 WeeksWeek 17Lesson 17Riemann Sums 1Week 18Lesson 18Riemann Sums 2Week 19Lesson 19The Fundamental Theorem of CalculusWeek 20Lesson 20Integration by SubstitutionWeek 21Lesson 21Further Integration TechniquesUnit 5Applications of the IntegralApplications of the Integral6 lessons6 WeeksWeek 22Lesson 22Accumulation of ChangeWeek 23Lesson 23Area between CurvesWe'll look at finding areas between curves, including orientation along the y-axis vs. x-axis. We'll also look at cases where the intersection results in multiple regions.Week 24Lesson 24Volume: Cross SectionsWe'll establish a general approach to finding volumes given cross sections, looking at triangular, semi-circular, and rectangular cross sections, among others.Week 25Lesson 25Volume: Disk MethodUsing reasoning from the previous week, we will derive the formula for finding the volume of a solid of revolution. We'll look at volumes of revolution about the x-axis and the y-axis.Week 26Lesson 26Volume: Washer MethodWeek 27Lesson 27Position, Velocity, and AccelerationUnit 6Differential EquationsDifferential Equations5 lessons5 WeeksWeek 28Lesson 28Modeling with Differential EquationsWeek 29Lesson 29Slope FieldsWeek 30Lesson 30Separation of VariablesWeek 31Lesson 31AP ReviewWeek 32Lesson 32AP Review
I graduated from MIT in 2019 with a major in Physics and minor in mathematics. I started tutoring Calculus in high school, and have been tutoring math and physics full-time since 2021.
2 - 4 每週課外時間
Homework
頻率: 7 or more throughout the class回饋: 包括細節: Students will be assigned weekly homework, with solutions released the following week. Homework will be self-graded, but I will be happy to discuss homework questions at any time.Assessment
頻率: 7 or more throughout the class細節: This course will have 6 timed unit assessments, with a particular aim of familiarizing students with AP-style questions. At the end of the course, students will complete a full AP practice exam as the final exam.Letter Grade
頻率: 包括細節:
Students are expected to have taken precalculus prior to this course. However, I am happy to make exceptions on a case-by-case basis, if a student is able to demonstrate proficiency with a diagnostic exam.
AP Calculus AB Prep Book: https://www.amazon.com/Princeton-Review-Calculus-Premium-Prep-dp-059351758X/dp/059351758X/ref=dp_ob_title_bk
教師專業知識和證書
學士學位 in 科學 from Massachusetts Institute of Technology
I started tutoring math and physics over 8 years ago, at my local community college. In the process, I was exposed to learners with a wide variety of backgrounds - from advanced high schoolers in the honors program, to returning adult learners...
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團體課
US$32
每週或US$1,000 用於 32 課程每週上課 x 1 次, 32 週
75 分鐘
即時視訊會議
年齡: 13-18
8-14 每班學員人數