名校公开课
爱荷华州立大学《微积分进阶》(2019)教学视频
课程目录
- 01 Session 1 -- Average rate of change
- 02 Session 2 -- Introduction to limits
- 03 Session 3 -- Squeeze theorem; one sided limits; sin(t)-t
- 04 Session 4 -- Continuity; intermediate value theorem
- 05 Session 5 -- Limits with infinity; asymptotes
- 06 Session 6 -- Practice with limits
- 07 Session 7 -- Tangent lines; derivative at a point
- 08 Session 8 -- Derivative as a function
- 09 Session 9 -- Rules for derivative (product rules)
- 10 Session 10 -- Rules for derivative (quotient rule); higher order derivatives
- 11 Session 11 -- Derivative as motion
- 12 Session 12 -- Derivatives of trigonometric functions
- 13 Session 13 -- Practice with derivatives
- 14 Session 14 -- Chain rule (introduction)
- 15 Session 15 -- More practice with the chain rule
- 16 Basics of differentiation exam review (Fall 2019)
- 17 Exam 1 Q&A (Fall 2019)
- 18 Session 16 -- Implicit differentiation
- 19 Session 17 -- Derivative of inverse; logarithmic differentiation
- 20 Session 18 -- Inverse trigonometric functions
- 21 Session 19 -- Related rates
- 22 Session 20 -- Linearization
- 23 Session 21 -- Absolute (global) max-min
- 24 Session 22 -- Mean value theorem
- 25 Session 23 -- Increasing-decreasing (monotonicity); first derivative test
- 26 Session 24 -- Concave up-down; inflection points; second derivative test
- 27 Session 25 -- LHospital
- 28 Session 26 -- Optimization
- 29 Session 27 -- More optimization practice
- 30 Session 28 -- Newtons method
- 31 Advanced differentiation exam review (Fall 2019)
- 32 Exam 2 Q&A (Fall 2019)
- 33 Session 29 -- Anti-derivatives
- 34 Session 30 -- Riemann sums
- 35 Session 31 -- Definite integrals; areas by limits of Riemann sums
- 36 Session 32 --Definite integrals; Mean value theorem; FUNdamental Theorem of C
- 37 Session 33 -- FUNdamental Theorem of Calculus (II); area between curves
- 38 Session 34 -- Substitution (indefinite integrals)
- 39 Session 35 -- Substitution with definite integrals
- 40 Basics of integration exam review (Fall 2019)
- 41 Exam 3 Q&A (Fall 2019)
- 42 Session 36 -- Separable differential equations
- 43 Session 37 -- Notes about logarithms; sinh and cosh
- 44 Session 38 -- Course overview
- 45 Cumulative final exam review (Fall 2019)
- 】：01 Session 1 -- Short review of calculus
- 02 Session 2 -- Integration by parts
- 03 Session 3 -- Integration of trigonometric functions
- 04 Session 4 -- Trigonometric substitution
- 05 Session 5 -- Partial fractions
- 06 Session 6 -- Numerical integration (part 1)
- 07 Session 7 -- Numerical integration (part 2); improper integrals (part 1)
- 08 Session 8 -- Improper integrals (part 2)
- 09 Session 9 -- Integration practice
- 10 Exam 1 Q&A
- 11 Exam 1 review (Spring 2020)
- 12 Session 10 -- Volumes by cross section; Disc-Washer method
- 13 Session 11 -- Volumes by Shell Method
- 14 Session 12 -- Arc length of function
- 15 Session 13 -- Surface area of revolution
- 16 Session 14 -- Additional practice with geometric applications
- 17 Session 15 -- Work (including pumping) and force problems
- 18 Session 16 -- Mass; Center of mass
- 19 Session 17 -- Parameterized curves (w- tangent lines)
- 20 Session 18 -- Integral applications of parameterized curves
- 21 Session 19 -- Introduction to polar coordinates
- 22 Session 20 -- Plotting polar curves; tangents to polar curves
- 23 Session 21 -- Area in polar coordinates
- 24 Session 22 -- Arc length in polar coordinates
- 25 Exam 2 Q&A
- 26 Session 23 -- Sequences
- 27 Session 24 -- Series; geometric series; telescoping series
- 28 Session 25 -- n-th term test; integral test
- 29 Session 26 -- Comparison test; limit comparison test
- 30 Session 27 -- Ratio-root tests
- 31 Session 28 -- Practice with series
- 32 Session 29 -- Alternating series test; absolute vs conditional convergence
- 33 Session 30 -- Power series; radius-intervals of convergence
- 34 Session 31 -- Calculus of power series
- 35 Session 32 -- Taylor series
- 36 Session 35 -- Applications of Taylor series-polynomials
课程介绍
本课程的主要内容为：常微分方程、空间解析几何、多元函数微分学（选学）、多元函数积分学（选学）、无穷级数。那么本课程与已学的《高等数学》与《数学分析》的区别在什么地方呢？
自然，与《高等数学》课程的明显区别在于我们将强调基本理论，通俗地讲就是重心更多地在于证明而不是计算.而区别于现行《数学分析》课程的地方主要在于知识的融会贯通、以点带面、和知识扩充方面。由于学生已经对相关知识有了一个较为全面的了解，使得我们不必受制于初始讲授微积分时遇到的时序上的限制，而可以对某一部分知识进行全面深入的研讨.别的，撇开了教学进度上的要求，使得我们可以有一个纲领性的把握.一言以蔽之，即做到粗的更粗，细的更细.
