Math 19 is a second-semester course in calculus, geared towards students interested in physics and engineering.

- 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.
- 10/01 Complex nth roots Notes on finding complex solutions to an equation z^n=c.
- 10/15 Differential Equations Some topics in differential equations. This document is still being updated as we cover more material (last update, 10/16).
- 11/05 Convergence tests summary
- 11/07 Taylor Approximation.
- Fourier Series by James Stewart.
- Complex Fourier Series (focuses on the case of finite Fourier series, sometimes called trigonometric polynomials)
- Fourier series and differential equations

- 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).

- 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)

- 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)