# Math 116 Section 028 Calculus II

## Basic Information

 Course Title Calculus II Meeting Times TWF 11:30 -- 13:00 at Zoom (Link will be sent through email) Instructor Yiwang Chen Email yiwchen@umich.edu Office East Hall 5080 Office Hours Tuesday 13:00-14:00 Wednesday 15:00-16:00 Syllabus Click Here
Date Section(s) covered Notes Summary
Tuesday, Sep 1st Review of definite integral 5.1, 5.2
• Riemann sums (Left and Right)
• Definition of definite integral
Wednesday, Sep 2st Review of definite integral 5.3, 5.4
• Fundamental Theorem of Calculus!
• Average of function: Application of Definite Integral
• Friday, Sep 4th Review of Indefinite integral(Antiderivatives) 6.1-6.4
• Summary of Chapter 6.
• If you are looking for exercises, they are essentially in your gateway exam and I did put the section 6.4 in Chapter 5.
• Definite integral using area.
• Some properties of definite integral.
• Antiderivatives of some common function.
• Second fundamental Theorem
• Tuesday, Sep 8th Review of Section 7.1-7.2
• Quick review of even/odd function.
• Substitution.
• Integral by parts.
• Wednesday, Sep 9th Review of Section 7.1-7.2 plus partial fractions
• Substitution.
• Integral by parts.
• Partial Fractions.
• Friday, Sep 11th Review of Section 7.1-7.2 plus partial fractions
• Substitution.
• Integral by parts.
• Partial Fractions.
• Tuesday, Sep 15th Partial fractions, and review of Fundamental theorems
• More Integral by parts, with repeated roots and irreducible quadratic terms.
• Some reviews of Fundamental Theorem of Calculus.
• Ready for more Riemann sums.
• Wednesday, Sep 16th Riemann Sums(Mid and Trapezoid)
• Riemann Sums(Mid and Trapezoid).
• Introduction to Area/Volume using definite integral.
• Friday, Sep 18th Area, Volume(Disk Method)
• Application of integral: Area.
• Application of integral: Volume(Disk Method).
• Tuesday, Sep 22nd Volume(Shell Method)
• Application of integral:Volume(Shell Method) .
• Wednesday, Sep 23th Mass(density) and arc length
• Arc length of curve $$y=f(x)$$ from $$a$$ to $$b$$$$=\int_a^b \sqrt{1+(f'( x ))^2} dx.$$
• Arc length of curve $$x=h(y)$$ from $$c$$ to $$d$$$$=\int_c^d \sqrt{1+(h'( y ))^2} dy.$$
• Mass(integral of object with density).
• Friday, Sep 25th Work
• Work.
• Tuesday, Sep 29th Exam 1 Review 1
• Work (In non-math and non-physics sense).
• Wednesday, Sep 30th Exam 1 Review 2
• Topic class for reviewing! We went over questions about work/mass/volume/FTC/multiple choice
• Friday, Oct 2nd Exam 1 Review 2
• Topic class for reviewing! We went over questions about work/mass/volume/FTC/multiple choice
• Tuesday, Oct 6th Chapter 4.7
• L'Hospital Rult
• Wednesday, Oct 7th Chapter 7.6: Improper Integral
• Introduction to improper integral, with calculation.
• Friday, Oct 9th Chapter 7.7: Comparison Test
• Improper integral comparison test/p-test/... and more!
• Tuesday, Oct 13th Chapter 7.7: Comparison Test
• Improper integral comparison test/p-test/Exponential Decay Test/Limit Convergence Test(optional) and more!
• Wednesday, Oct 14th Chapter 8.7
• Probability Density Function, Cumulative Distribution function.
• Friday, Oct 16th Chapter 8.8
• Probability, mean and median
• Tuesday, Oct 20th Chapter 9.1
• Sequences.
• Bounded monotone sequences converge.
• Wednesday, Oct 21st Chapter 9.2
• Series.
• Geomtetric Series.
• Friday, Oct 23th Chapter 9.3
• Determining convergence of series: Integral Test/n-th term test.
• Tuesday, Oct 27th Chapter 9.4
• Convergence of Series：Comparison Test/Limit Comparison Test.
• Wednesday, Oct 28th Chapter 9.4
• Convergence of Series:Absolute Convergence, Alternating Series Test, Ratio Test.
• Friday, Oct 30th Chapter 9.5
• Power Series, radius of convergence, interval of convergence.
• Tuesday, Nov 3rd Chapter 9.5
• Power Series, radius of convergence, interval of convergence.
• VOTE!
• Wednesday, Nov 4th Exam 2 Review
• Exam review, some partial information question.
• Friday, Nov 6th Exam 2 Review summary
• Jam Exam review.
• Tuesday, Nov 10th 10.1 Taylor Polynomial
• Taylor Polynomial.
• Wednesday, Nov 11st 10.2 Taylor Series
• Taylor Series.
• Friday, Nov 13rd 10.3 More on Taylor Series
• Taylor Series, manipulating the Taylor series.
• Tuesday, Nov 17th 4.8 Parametrization
• Section on Parametrization.
• Wednesday, Nov 18th 8.2 Parametrization
• Section on Parametrization, start Polar Coordinate.
• Friday, Nov 20th 8.3 Polar Coordinate
• Polar Coordinate.
• Monday, Dec 1st Review of Parametrization and Polar Coordinates
• Polar Coordinate.
• Wednesday, Dec 2nd Review of Parametrization and Polar Coordinates
• Taylor Polynomials and Taylor Series.
• Friday, Dec 4th Review of Taylor Polynomials and Taylor Series.
• Polar Coordinate.
• Tuesday, Dec 8th (Last Day of Class) La Dernière Classe.
• Math, a lifelong class.