Dive into advanced calculus concepts in this comprehensive 10-hour course. Begin with a review of derivatives before exploring area approximation, definite integrals, and the Fundamental Theorem of Calculus. Master integration techniques including substitution, exponential and logarithmic functions, and inverse trigonometric functions. Apply these skills to solve problems involving areas between curves, volumes of revolution, arc length, and surface area. Explore physical applications, moments, and centers of mass. Delve into exponential growth and decay models. Advance to more complex integration methods such as integration by parts, trigonometric integrals, partial fractions, and improper integrals. Conclude with an introduction to double integrals, providing a solid foundation for further mathematical study.
Overview
Syllabus
5.0 Derivative Review.
5.1 Approximating Areas.
5.2 The Definite Integral.
5.3 The Fundamental Theorem of Calculus.
4.10 Antiderivatives.
5.4 Integration Formulas and the Net Change Theorem.
5.5 Substitution.
5.6 Integrals Involving Exponential and Logarithmic Functions.
5.7 Integrals Resulting in Inverse Trigonometric Functions.
6.1 Area between Curves.
6.2 Determining Volumes by Slicing.
6.3 Volumes of Revolution Cylindrical Shells.
6.4 Arc Length of a Curve and Surface Area.
6.5 Physical Applications.
6.6 Moments and Centers of Mass.
6.7 Integrals, Exponential Functions, and Logarithms.
6.8 Exponential Growth and Decay.
3.1 Integration by Parts.
3.2 Trigonometric Integrals.
3.3 Trigonometric Substitution.
3.4 Partial Fractions.
3.5 Other Strategies for Integration.
3.7 Improper Integrals.
3.8 Double Integrals.
Taught by
Tyler Wallace
