A second-semester course in calculus, geared towards students interested in physics and engineering.
Textbook and readings
- Calculus by Gilbert Strang. This will be our primary text for the course. You can purchase it from the bookstore or use it online for free.
Problem sets and solutions
Solutions will be posted after class on the due date of each assignment.
Problem set 1 (due F 9/12). Review of Calculus 1; integration by parts; trigonometric integrals; trigonometric substitution.
Problem set 2 (due F 9/19). Force and energy; vectors.
Problem set 3 (due F 9/26). Paths in two and three dimensions; polar coordinates.
Problem set 4 (due F 10/3). Polar coordinates, complex numbers.
Problem set 5 (due F 10/17). Linear differential equations.
Problem set 6 (due F 10/24). Initial value problems; improper integrals; review of summation notation.
Problem set 7 (due M 11/3). Geometric series. Integral test.
Problem set 8 (due F 11/7). Convergence tests.
Problem set 9 (due M 11/24).
Problem set 10 (due M 12/8).
Exams and solutions
- Topic list for the midterm 1.
- Practice Midterm 1 (Solutions)
- Midterm 1 (solutions)
- Practice Midterm 2(Solutions)
- Midterm 2 (Solutions)
- Final review problems 1 / Answers
- Final review problems 2 / Answers
- Practice Final Exam (Solutions)
- Final Exam (Solutions)
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Students in the class have kindly provided their notes for the following lectures.
- 3 September (Integration by parts)
- 8 September (Resonance and trig. substitution)
- 12 September (Work and energy)
- 15 September (Vectors)
- 17 September (Paths)
- 19 September (Acceleration and g-force)
- 22 September (more) (Arc length, polar coordinates)
- 24 September (Polar curves)
- 26 September (Conic sections; area in polar coordinates)
- 29 September (Arc length in polar coordinates)
- 1 October (Complex numbers)
- 03 October (more) (Linear differential equations)
- 15 October (General solutions of differential equations)
- 17 October (Separable differential equations)
- 20 October (more) (Non-homogeneous linear differential equations)
- 22 October (more) (Improper integrals)
- 27 October (more) (Geometric series)
- 29 October (more) (Variations on geometric series; the integral test)
- 31 October (more) (Integral and comparison tests)
- 3 November (more) (Comparison and Ratio tests)
- 5 November (Alternating series test)
- 7 November (Linear and quadratic approximation)
- 10 November (Taylor approximation)
- 17 November (Taylor series)
- 19 November (Taylor series, cont.)
- 21 November (Fourier series)
- 24 November (Fourier series examples)
- 1 December (Fourier series examples)
- 3 December (Fourier series and differential equations)
- 5 December (Fourier series and differential equations) </ul> --