This course covers advanced topics in calculus, focusing on derivatives, integrals, and their applications. By the end of the course, students will be able to calculate areas between curves, volumes of revolution, arc lengths, and surface areas. They will also learn about integration techniques such as substitution, integration by parts, and trigonometric integrals. The teaching method includes theoretical explanations, problem-solving sessions, and real-world applications. This course is intended for students who have a basic understanding of calculus and want to deepen their knowledge in the subject.
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
