微積分 II - 完整課程

This is a live course. We will be studying the main concepts of Calculus II, an important prerequisite for STEM majors in college. This class is typically a higher-level high school course and/or many times taken within the first two years of university.
Please note: This course is built like a regular math class. This is not an Advanced Placement class nor a class that gives college credit. 

The topics that we will cover are as follows:

Week 1:  Review of Algebra and Precalculus: Polynomials, fractions, Asymptotes, Trigonometry, Transformation from parent functions.
 
Week 2: Limits, derivatives and their rules, L'Hopital's Rule.

Week 3: Areas, solving problems with integration, differential equations and infinite series.

Week 4: Approximating area with Riemann Sums, left and right rectangles and trapezoid rule.

Week 5: The indefinite integral, FTC1 and FTC2, solving area problems without Riemann sum formula.

Week 6: More integrals, using 17 basic antiderivatives for integrating, integrating polynomials, understanding the principles.

Week 7: Integrating rational and radical functions, using algebra, integrating trig functions, integrating composition of functions with linear inputs.

Week 8: U-Substitution, the simpler case and the more complex case.
 
Week 9: Integration by parts, the DI-agonal chart and method.

Week 10: Trig substitution, use of sines and cosines, use of tangent and secants, knowing when to use tri substitution.

Week 11: Rational solutions, understanding partial fractions, solving integrals by using partial fractions and integrating improper rationals.

Week 12: Solving area problems, improper integrals, the Mean Value Theorem of integrals, calculating arc length.

Week 13: Solving 3D problems, finding the volume of a solid.

Week 14: Differential Equations, solving DE, solving separable equations and initial-value problems.

Week 15: Infinite sequences, sigma notation, geometric series and p-series.

Week 16: Convergence and divergence

Week 17: Taylor series, elementary functions, power series, using trigonometric functions.

Each class will have various approaches to learning. There will be a PowerPoint presentation, guided practice and interactive assessments to test understanding. There will be an E-book provided at the first week of class for students to follow along with. Students will have the opportunity discuss and writing on the online whiteboard, as well. My style is to investigate each student's previous knowledge, demonstrate the lesson and have students try on their own. Patience and perseverance are important in this course. By keeping the class size small, students will have full interaction with the teacher and each other. Before taking this class, students should have successfully completed Calculus.