Here are lecture notes for Math10b: Winter 2017. These are my personal notes, so they are in rough draft form, and they do not necessarily reflect exactly what I went over in class. The notes will be uploaded as the course progresses.
- Week 1:
- Lecture 1 - Displacement from velocity.
- Lecture 2 - Riemann sums and the definition of the definite integral.
- Lecture 3 - The First Fundamental Theorem of Calculus.
- Week 2:
- Monday of week 2 is Marin Luther King Day.
- Lecture 4 - Properties of the definite integral and the Mean Value Theorem.
- Lecture 5 - Constructing antiderivatives graphically, indefinite integrals, and some basic antiderivatives.
- Week 3:
- Lecture 6 - More basic antiderivatives and how to use the FTC
- Lecture 7 - Intro to differential equations, equations of motion, and the statement of the 2nd FTC
- Lecture 8 - The Second Fundamental Theorem of Calculus proof, corollaries and examples
- Week 4:
- Monday of week 4 is a review day.
- Lecture 9 - The method of substitution (the anti-chain rule)
- Lecture 10 - Integration by parts (the anti-product rule)
- Week 5:
- Lecture 11 - A brief mention of integration tables and the method of partial fraction decomposition
- Lecture 12 - The method of trigonometric substitution
- Lecture - 13: Prof. Eggers subbed our class, and went off of his notes. For the sake of completeness, I will upload note on this section once the quarter is over.
- Week 6:
- Week 7:
- There is no class on the Monday of week 7.
- Lecture 17 - Volume of the sphere, and an introduction to solids of revolution
- Lecture 18 - More solids of revolution
- Week 8:
- Monday of week 8 is a review day.
- Lecture - 19
- Lecture 20 - Separable differential equations
- Week 9:
- Week 10:
- Lecture 24 - Geometric Series continued, and Taylor Polynomials
- Lecture 25 - Taylor Polynomials
- Friday of week 10 is a review day.