This course is a comprehensive study of single-variable calculus. It builds on the topics covered in Pre-Calculus and is the basis for theorem and problem solving that are covered in high school calculus class. It is essential for students looking to further their education with AP Calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, derivative integral series, and differential equations.‍

Chapter 1: Prerequisites for Calculus
Parametric Equations, Review of Pre-Cal 12, including exponential and logarithms, trigonometric functions
Chapter 2: Limits and Continuity
Limits, Continuity, instantaneous Rate of change
Chapter 3: Derivatives
Definition, differentiability, rules for differentiation, chain rule, implicit differentiation, derivative of trigonometric, inverse trigonometric, exponential, and logarithms. Applications in kinematics
Chapter 4: Applications of derivatives
Extreme values of functions, mean value theorem, drawing graph of derivatives, optimization, linearization and newton’s method
Chapter 5: Definite Integral
Estimation of integral, definition, antiderivatives, fundamental theorem of calculus
Chapter 6: Differential Equations and Mathematical Modeling
Slope Fields, integration by substitution and by parts, exponential growth and decay, logistic growth
Chapter 7: Applications of definite integrals
Areas in the plane, volumes, lengths of curves
Chapter 8: Sequences, L’Hopital’s rule, improper integrals
Sequences, l”hopital’s rule, relative rates of growth, improper integrals
Chapter 9: Infinite Series
Power Series, Taylor Series, Tayler’s theorem, radius of convergence, convergence tests
Chapter 10: Parametric, Vector, and Polar Functions
Parametric Functions, Vectors, Polar Functions

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This course is for students who have completed our Pre-Calculus course.

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AGES 15+
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This course typically takes 3-6 months to complete. This depends on the student's experience and how fast they can master the concepts and the knowledge. Our instructors move at the pace of the student, it may take extra time for some students to reinforce what they have learned.

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