AP Calculus BC – Book 2: Application of Differentiation and Integration
Master Derivatives and Their Applications
AP Calculus Book 2: Derivatives and Application of Differentiation is designed to guide students through the essential concepts of derivatives, preparing them for success on the AP Calculus exam. This book builds on foundational pre-calculus knowledge and focuses on understanding, calculating, and applying derivatives in various contexts.
Understanding Derivatives
The book begins by introducing the concept of the derivative, its definition, and geometric interpretation. First, students learn about the limit process, rules of differentiation, and techniques for differentiating algebraic, trigonometric, exponential, and logarithmic functions. Next, it explains higher-order derivatives and their significance in understanding function behavior.
Applications of Differentiation
In addition, the book emphasizes practical applications of derivatives. Students explore topics such as rate of change, motion problems, optimization, related rates, and curve sketching. Furthermore, the book connects derivatives to real-world scenarios, helping students see the relevance of calculus in science, engineering, and economics.
Problem-Solving and Practice
AP Calculus Book 2 provides numerous examples, step-by-step solutions, and practice problems to reinforce understanding. Moreover, it includes strategies for approaching complex problems, enhancing analytical skills, and building confidence in tackling AP exam questions.
Exam Preparation
Finally, the book features practice assessments designed to simulate the AP Calculus exam environment. Additionally, review questions and exercises allow students to evaluate their progress, identify areas of improvement, and solidify their mastery of derivatives.
Whether you are preparing for the AP exam or aiming to strengthen your calculus skills, AP Calculus Book 2: Derivatives and Application of Differentiation is an essential resource for mastering one of the most critical topics in calculus.
Course Features
- Lectures 27
- Quizzes 18
- Duration 52 weeks
- Skill level All levels
- Language English
- Students 33
- Assessments Yes
- 3 Sections
- 27 Lessons
- 52 Weeks
- Applications of Differentiation8
- 1.1Related Rates
- 1.2Position, Velovity, and Acceleration
- 1.3The Roll’s Theorem and The Mean Value Theorem
- 1.4The First Derivative Test and the Extreme Values of Functions
- 1.5The Second Derivative Test
- 1.6Curves of 𝑓, 𝑓 ′, 𝑓 ′′ and Curve Sketching
- 1.7Optimization Problems
- 1.8Tangent Line Approximation and Differentials
- Integration16
- 2.1Antiderivatives and Indefinite Integrals
- 2.2Antiderivatives and Indefinite integrals Quiz10 Minutes4 Questions
- 2.3Riemann Sum and Area Approximation
- 2.4Riemann Sum and Area Approximation Quiz15 Minutes6 Questions
- 2.5Definite Integral, Area Under a Curve, and Application
- 2.6Definite Integral, Area Under a Curve, and Application Quiz20 Minutes10 Questions
- 2.7Properties of Definite Integral
- 2.8Properties of Definite Integral Quiz10 Minutes4 Questions
- 2.9Trapezoidal Rule
- 2.10Trapezoidal Rule Quiz10 Minutes5 Questions
- 2.11Fundamental Theorem of Calculus
- 2.12Fundamental Theorem of Calculus Quiz20 Minutes10 Questions
- 2.13Integration by Substitution
- 2.14Integration by Substitution Quiz15 Minutes7 Questions
- 2.15Integration of Exponential and Logarithmic Functions
- 2.16Integration of Exponential and Logarithmic Functions Quiz15 Minutes7 Questions
- Applications of Integration21
- 3.1Area of Region Between Two Curves
- 3.2Area of Region Between Two Curves Quiz10 Minutes4 Questions
- 3.3Volumes by Disk and Washers
- 3.4Volumes by Disk and Washers Quiz15 Minutes8 Questions
- 3.5Volumes of Solids with Known Cross Sections
- 3.6Volumes of Solids with Known Cross Sections Quiz15 Minutes7 Questions
- 3.7The Total Change Theorem (Application of FTC)
- 3.8The Total Change Theorem Quiz10 Minutes5 Questions
- 3.9Motion of a Particle, Distance, and Displacement
- 3.10Motion of a Particle, Distance, and Displacement Quiz20 Minutes9 Questions
- 3.11Average Value of a Function
- 3.12Average Value of a Function Quiz12 Minutes6 Questions
- 3.13Length of a Curve (Distance Traveled Along a Curve)
- 3.14Basic Integration Rules
- 3.15Basic Integration Rules Quiz10 Minutes5 Questions
- 3.16Trigonometric Integrals
- 3.17Trigonometric Integrals Quiz10 Minutes5 Questions
- 3.18Trigonometric Substitution
- 3.19Trigonometric Substitution Quiz10 Minutes5 Questions
- 3.20L’Hospital’s Rule
- 3.21L’Hospital’s Rule Quiz15 Minutes7 Questions
