AP Calculus for US Curriculum
Calculus is one of the toughest branches of Mathematics. Students in Grades 11 or 12 take AP Calculus as part of the Course. Everyone cannot guide the students in Calculus, you need an expert tutor for the same. Noble Learners has the best online tutor for Calculus.
AP Calculus
AP Calculus is a college-level course offered to high school students. It delves deep into the concepts of calculus, which is the study of change and motion. In simple terms, calculus helps us understand how things change over time. From finding the slope of a curve to determining the area under a curve, AP Calculus covers a wide range of topics crucial for understanding advanced mathematics and its real-world applications.
Difference Between AP Calculus AB & BC:
- AP Calculus AB: This course covers a broad range of topics in differential and integral calculus. It’s designed to provide students with a solid foundation in calculus and prepare them for further studies in mathematics, engineering, and related fields.
- AP Calculus BC: Building upon the concepts covered in AB, AP Calculus BC goes into greater depth and introduces additional topics such as parametric, polar, and vector functions. It’s typically taken by students who have a strong interest in mathematics and plan to pursue majors like mathematics, physics, or engineering in college.
AP Calculus AB Syllabus:
- Limits and Continuity
- Differentiation: Definition and Fundamental Properties
- Applications of Differentiation
- Integration and Accumulation of Change
- Differential Equations
- Applications of Integration
- Infinite Sequences and Series
AP Calculus BC Syllabus:
- All topics covered in AB, plus:
- Parametric Equations and Polar Coordinates
- Vectors and the Geometry of Space
- Vector-Valued Functions
- Integration Techniques and Applications
- Taylor and Maclaurin Series
Detailed Calculus Syllabus
The chapters given below is the part of syllabus which we will discuss in course. In case of any variation in the syllabus our expert tutors from India will teach as per the need of the course from one student to another.
CHAPTER 1 – Introduction to Calculus
CHAPTER 2 – Velocity and Distance
CHAPTER 3 – Calculus Without Limits
CHAPTER 4 – The Velocity at an Instant
CHAPTER 5 – Circular Motion
CHAPTER 6 – A Review of Trigonometry
CHAPTER 7 – A Thousand Points of Light
CHAPTER 8 – Computing in Calculus
CHAPTER 9 – Derivatives
CHAPTER 10 – The Derivative of a Function
CHAPTER 11 – Powers and Polynomials
CHAPTER 12 – The Slope and the Tangent Line
CHAPTER 13 – Derivative of the Sine and Cosine
CHAPTER 14 – The Product and Quotient and Power Rules
CHAPTER 15 – Limits
CHAPTER 16 – Continuous Functions
CHAPTER 17 – Applications of the Derivative
CHAPTER 18 – Linear Approximation
CHAPTER 19 – Maximum and Minimum Problems
CHAPTER 20 – Second Derivatives: Minimum vs. Maximum
CHAPTER 21 – Graphs
CHAPTER 22 – Ellipses, Parabolas, and Hyperbolas
CHAPTER 23 – Iterations x,+ ,= F(x,)
CHAPTER 24 – Newton’s Method and Chaos
CHAPTER 25 – The Mean Value Theorem and l’Hôpital’s Rule
